In-beam and decay spectroscopy of transfermium nuclei

Progress in Particle and Nuclear Physics 61 (2008) 674–720

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Progress in Particle and Nuclear Physics journal homepage: www.elsevier.com/locate/ppnp

Review

In-beam and decay spectroscopy of transfermium nuclei R.-D. Herzberg a,∗ , P.T. Greenlees b a

Department of Physics, Oliver Lodge Laboratory, University of Liverpool, Oxford Street, Liverpool, L69 7ZE, UK

b

Department of Physics, University of Jyväskylä, FIN-40014 University of Jyväskylä, Finland

article

info

Keywords: Properties of nuclei Nuclear energy levels Isomer decay Beta decay Double beta decay Electron and muon capture Alpha decay A > 220

a b s t r a c t In recent years the body of experimental data on nuclei with masses A ' 250 has increased dramatically. Nuclei that had been out of reach for experimental studies have now become available for study through a variety of approaches, both with in-beam spectroscopic methods and through spectroscopy following the decay of isomeric states or alpha decays at the focal plane of powerful separators. This article aims to collect the currently available experimental data on nuclei between Cm (Z = 96) and Db (Z = 105). The review of this data builds on the evaluations in the literature and focusses on those datasets obtained most recently. © 2008 Elsevier B.V. All rights reserved.

Contents 1.

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3.

∗

Introduction............................................................................................................................................................................................. 675 1.1. Historical perspective ................................................................................................................................................................. 676 1.2. Techniques for the study of SHE ................................................................................................................................................ 677 1.3. Modern approaches .................................................................................................................................................................... 679 1.3.1. In-beam spectroscopy ................................................................................................................................................. 679 1.3.2. Isomer spectroscopy.................................................................................................................................................... 680 1.3.3. Decay spectroscopy ..................................................................................................................................................... 680 Instrumentation ...................................................................................................................................................................................... 681 2.1. Comparison of separator operating principles ......................................................................................................................... 681 2.1.1. Gas-filled separators.................................................................................................................................................... 681 2.1.2. Velocity filters .............................................................................................................................................................. 682 2.1.3. Recoil mass spectrometers.......................................................................................................................................... 682 2.2. Facilities at JYFL .......................................................................................................................................................................... 682 2.2.1. Germanium arrays ....................................................................................................................................................... 683 2.2.2. The SACRED spectrometer .......................................................................................................................................... 683 2.3. Facilities at gsi............................................................................................................................................................................. 684 2.4. Facilities at FLNR ......................................................................................................................................................................... 685 2.5. Facilities at ANL........................................................................................................................................................................... 685 2.6. Facilities at GANIL ....................................................................................................................................................................... 686 2.7. Facilities at JAEA.......................................................................................................................................................................... 686 Structure of even–even nuclei................................................................................................................................................................ 687 3.1. Systematics of ground-state rotational bands .......................................................................................................................... 687 3.1.1. Curium isotopes ........................................................................................................................................................... 687 3.1.2. Californium isotopes ................................................................................................................................................... 688

Corresponding author. Tel.: +44 0 151 / 794 3382; fax: +44 0 151 / 794 3348. E-mail address: [email protected] (R.-D. Herzberg).

0146-6410/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ppnp.2008.05.003

R.-D. Herzberg, P.T. Greenlees / Progress in Particle and Nuclear Physics 61 (2008) 674–720

4.

5.

6.

7.

8.

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3.1.3. Fermium isotopes ........................................................................................................................................................ 688 3.1.4. Nobelium isotopes ....................................................................................................................................................... 690 3.1.5. Systematics of the moments of inertia....................................................................................................................... 691 3.2. K-Isomerism and non-yrast states............................................................................................................................................. 694 Structure of odd-N, even-Z nuclei ......................................................................................................................................................... 697 4.1. In-beam studies of 253 No............................................................................................................................................................ 697 4.2. Systematics of single-particle states ......................................................................................................................................... 699 4.2.1. N = 145 ....................................................................................................................................................................... 700 4.2.2. N = 147 ....................................................................................................................................................................... 701 4.2.3. N = 149 ....................................................................................................................................................................... 702 4.2.4. N = 151 ....................................................................................................................................................................... 703 4.2.5. N = 153 ....................................................................................................................................................................... 705 4.2.6. N = 155 and 157 ......................................................................................................................................................... 706 4.2.7. Summary ...................................................................................................................................................................... 706 Structure of odd-Z , even-N nuclei ......................................................................................................................................................... 707 5.1. Systematics of single-particle states ......................................................................................................................................... 707 5.1.1. Berkelium Isotopes ...................................................................................................................................................... 707 5.1.2. Einsteinium isotopes ................................................................................................................................................... 708 5.1.3. Mendelevium, lawrencium and dubnium isotopes................................................................................................... 710 5.2. Discussion.................................................................................................................................................................................... 710 5.3. In-beam spectroscopy of 251 Md and 255 Lr................................................................................................................................. 710 Structure of odd-N, odd-Z nuclei ........................................................................................................................................................... 711 6.1. Bk isotopes .................................................................................................................................................................................. 713 6.2. Es isotopes ................................................................................................................................................................................... 713 6.3. Md isotopes ................................................................................................................................................................................. 714 6.4. Lr and Db isotopes ...................................................................................................................................................................... 714 6.5. Summary ..................................................................................................................................................................................... 714 Current and future developments.......................................................................................................................................................... 715 7.1. Instrumentation .......................................................................................................................................................................... 715 7.2. Facilities....................................................................................................................................................................................... 715 Summary and conclusions...................................................................................................................................................................... 716 Acknowledgments .................................................................................................................................................................................. 717 References................................................................................................................................................................................................ 717

1. Introduction One of the first and most important questions of any field of research is one of scope. How many chemical elements are there? How many isotopes of a given element can form bound states? These questions are at the heart of modern nuclear structure physics, and have yet to be answered in a general way. While the proton dripline (i.e. those nuclei with vanishing proton separation energy (Sp = 0) is being mapped along large parts of the entire nuclear chart [1], the neutron dripline (Sn = 0) is only experimentally known for very light nuclei, the heaviest being the recently discovered 44 Al [2]. The situation is even less clear for the high mass end of the nuclear chart. Steady experimental efforts have pushed the limits of high mass up to element 118 [3–25], (and references therein) with elements up to Rg (Z = 111) officially named [26,27]. This quest for the heaviest elements is crucially intertwined with theoretical predictions of an ‘‘island’’ of shell-stabilized nuclei, the so-called ‘‘island of stability’’. Predictions of the location of this ‘‘island of stability’’ have varied over the years with different theoretical approaches yielding different regions where the underlying single-particle structure gives rise to several MeV of extra binding energy leading to greatly enhanced half-lives. These predictions depend crucially on the details of the underlying nuclear structure. However, when one tries to confront the various approaches with experimental data, one quickly realises that the available experimental data do not necessarily provide the most sensitive tests, as a substantial part of the data are integral (masses, half-lives, decay modes, α -decay Q-values, deformation), and therefore less sensitive to the detailed sequence of single-particle orbitals near the Fermi surface. Detailed structural information, however, is available for the lighter systems up to Es (Z < 100). In Fig. 1 we illustrate this situation by showing the level of detailed information available for nuclei with 105 ≥ Z ≥ 96. The data for this table have been selected from the evaluated nuclear structure data file (ENSDF) [28] with the majority of cutoff dates for inclusion of published data between 1997 and 2004. It thus serves as an indicator of the level of information available at the beginning of the research programme and provides a baseline for the rapid experimental progress made in this region. Indeed, it does not yet contain some of the data covered in this review. In recent years a programme has started aimed at extending the region where detailed spectroscopic data are known towards heavier systems with Z ≥ 100. This programme is based on two main methods: (1) In-beam spectroscopic methods using traditional γ ray and conversion electron spectroscopic techniques together with an event-by-event tag provided by a recoil separator (Recoil Decay Tagging, RDT), (2) Spectroscopy following alpha decays. These topics have been recently reviewed in [29,30].

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Fig. 1. Schematic summary of evaluated nuclear data available in the ENSDF data base in November 2007 for nuclei from Cm to Db. We give for each isotope the mass number, the number of known excited levels, the number of assigned rotational bands and the ground state spin. The thickness of the outline gives a visual aid as to how much information is available for a given isotope. Note that some of the data reviewed in this article has not yet been entered into ENSDF.

In this paper we will review the progress of both in-beam spectroscopy and spectroscopy following α decay for the heavy actinide and light transactinide region, i.e. nuclei between Cm and Db. Where appropriate, we will extend systematical pictures to nuclei outside this range, but a review of all available experimental data in all the actinides would provide material for several review articles of this kind and is beyond the scope of the present work. In Section 1 we set out the historical context and establish a background for the discussion of spectroscopic data. We then briefly describe the main experimental methods before Section 2 gives a detailed review of the experimental apparatus currently used for this work. In Section 3 we discuss the rotational structure of even–even nuclei and pay special attention to the study of high-K isomeric states. Sections 4 and 5 discuss odd neutron- and proton-nuclei respectively, both from in-beam data and decay work, and give a systematic overview of the deduced single-particle states in the region. Section 6 reviews the available data on odd–odd isotopes. Section 7 provides an outlook on current and future developments in the field before we conclude in Section 8. 1.1. Historical perspective The crucial success of the nuclear shell model of Goeppert-Mayer and Jensen et al. [31–34] was the correct explanation of the magic numbers for both protons (2, 8, 20, 28, 50, 82) and neutrons (2, 8, 20, 28, 50, 82, 126). Experimentally we have easy access to many stable semi-magic nuclei and five stable doubly magic nuclei (4 He, 16 O, 40,48 Ca, and 208 Pb), the latter being the heaviest stable nucleus in nature. Only four more primordial elements with half-lives comparable to or longer than the age of the earth (4.5 billion years) are found in nature: 209 Bi, whose half-life has recently been measured as T1/2 = (1.9 ± 0.2) × 1019 yr [35], 232 Th (T1/2 = 1.40 × 1010 yr), 235 U (T1/2 = 7.04 × 108 yr), and 238 U (T1/2 = 4.468 × 109 yr). Up to N = Z = 82 the major shell gaps occur at the same numbers for protons as for neutrons. The suggestion that the nuclear shell model predicts a spherical, shell-stabilised nucleus at a magic proton number different from the well established next magic neutron number 126 was first made by Meldner in 1966 [36], who predicted Z = 114. This prompted a wealth of predictions using different models, all aimed at determining the next spherical doubly-magic nucleus. Historically, the most widely used approaches are the macroscopic–microscopic approaches which tend to predict Z = 114, N = 184 [37–48]. Calculations using self-consistent mean-field approaches have been performed by a number of authors and broadly fall into two categories, namely relativistic versus non-relativistic approaches. Within each approach a large number of parameterizations of the effective Skyrme and Gogny forces are commonly used. However, systematic comparisons [49, 50] show that most non-relativistic mean-field calculations [45,51,52] favour Z = 124, 126 and N = 184. In contrast, the relativistic mean-field models [51–56] show that the magicity of a single nucleonic configuration valid in lower mass magic nuclei (Sn, Pb, etc) is dissolved in favour of more extended regions of additional shell stabilization [49,51], centred mainly around Z = 120, N = 172. For recent reviews of theoretical progress in this area, see e.g. [57,55,56,58–61].

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Fig. 2. Calculated Nilsson diagram for single-particle proton levels in the actinides as a function of deformation ν2 , taken from [62].1

One way of obtaining information on the single-particle orbitals in the vicinity of the island of stability is to study welldeformed, somewhat lighter nuclei around nobelium. The deformation causes the spherical single-particle states to split and states originating from high-lying spherical orbitals come close to the Fermi surface in much lighter systems. This is illustrated in the calculated single-particle Nilsson diagrams shown in Figs. 2 and 3, which we have chosen as representative examples from [62]. 1.2. Techniques for the study of SHE The study of superheavy nuclei presents a number of experimental challenges. The first and most obvious obstacle is the production mechanism. While it is possible to breed macroscopic quantities of elements up to Fm in nuclear reactors, nuclei beyond Z = 100 require the fusion of two heavy ions. Unfortunately, in these heavy compound systems the compound nucleus is no longer formed ‘‘inside’’ the fission barrier. Thus, even though a compound nucleus may be formed, it tends to fission rather than de-excite by particle- and γ -emission and finally form a ‘‘superheavy’’ evaporation residue. Two main approaches have been used over the past decades: cold fusion reactions with Pb and Bi targets and various medium-mass heavy ion projectiles, and ‘‘hot’’ fusion reactions with actinide targets and 48 Ca beams. Reviews of the cross section systematics for the different reaction mechanisms can be found in e.g. [4,25,63–65], all of which show a trend to decrease down to the most challenging cross sections in the 1 pb range with increasing mass. The cold fusion reactions tend to suffer from increased fusion hindrance at the barrier, but the doubly-magic character of the heavy Pb target leads to very low excitation energies in the compound systems and the final evaporation residues are usually formed after evaporation of a single neutron. These reactions have been used successfully in the synthesis of elements up to 113 (e.g. [15,18,19] and references therein).

1 R.R. Chasman, Rev. Mod. Phys. 49, 833 (1977) Fig. 4. Reprinted with permission. Copyright (1977) by the American Physical Society.

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Fig. 3. Calculated Nilsson diagram for single-particle neutron levels in the actinides as a function of deformation ν2 , taken from [62].2

In hot fusion reactions one encounters less hindrance at the barrier, but the lighter doubly-magic 48 Ca can not produce as cold a compound system, which typically has enough energy to evaporate between 3 and 5 neutrons leading to more neutron-rich systems. It has been successfully used in the production of elements up to 118 (e.g. [3,5] and references therein). These reaction mechanisms present a problem for the in-beam study of excited states: On the one hand it is necessary to have sufficient excitation energy in the nucleus to populate a range of excited states for spectroscopic studies, but on the other hand the survival probability decreases as more energy is available in the compound system. This clearly gives greater scope to the hot fusion reactions to allow spectroscopic studies. Indeed a large body of experimental data in this region has historically been obtained through the study of light-ion reactions on actinide targets. This includes many experiments with single-nucleon transfer reactions (pickup/stripping) in the vicinity of nuclei with long enough half-lives to be formed into suitable targets, e.g. [66–68]. One possible way to study excited states is to use long-lived high-spin isomers and to study the decay products after online separation via a tape or gas transport system or after chemical separation. In this way, the level scheme of, e.g., 256 Fm was studied through the β decay of an 8+ isomer in 256 Es [69,70]. A more widely applicable approach is to study α decays connecting odd-mass nuclei. Here the decay mechanism favours decays between states with similar single-particle structure, and the observed hindrance factors can be used to establish the systematic behaviour of single-particle states along α decay chains. Indeed the majority of excited states observed in nuclei, where only a few states are known, have been deduced from the observed α decay fine structure. To realise the full potential of this method, one has to detect the radiation emitted in the de-excitation of the levels populated in α decay down to the ground states of the daughter nuclei. Without this information it is impossible to pin down the experimental excitation energy of the state populated in the daughter without resorting to calculated masses, but it is quite possible to determine the relative excitation energies of several levels populated in the decay of one mother nucleus.

2 R.R. Chasman, Rev. Mod. Phys. 49, 833 (1977) Fig. 3. Reprinted with permission. Copyright (1977) by the American Physical Society.

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Fig. 4. Schematic illustration of the tagging principle using the jurogam/ritu/great setup as an example. Prompt γ rays at the target position are detected in jurogam and selected based on a delayed coincidence with an implanted recoil nucleus at the focal plane of the recoil separator. A subsequent highly characteristic α decay in the same pixel then identifies and tags that recoil event and the coincident γ rays.

1.3. Modern approaches 1.3.1. In-beam spectroscopy One of the most successful experimental approaches has been the use of in-beam spectroscopic methods to study nuclei in the vicinity of the deformed nucleus 254 No. We will refer to this region of heavy actinides as the ‘‘transfermium’’ region. The general principle is as follows and shown schematically in Fig. 4: The beam is incident on the production target which is surrounded by a spectrometer to detect prompt radiation, typically a ball of germanium detectors for γ -ray spectroscopy, such as gammasphere, jurogam or a conversion-electron spectrometer such as sacred [71,72]. The recoiling heavy reaction products then enter a recoil separator (e.g. ritu or fma) where they are separated from unreacted beam and unwanted reaction products, such as transfer products, fission products etc, and implanted in a position-sensitive, highly pixellated detector at the focal plane. The known flight time through the separator then allows a coincidence measurement to extract only prompt radiation in the correct time relation to the detected recoil of interest (Recoil Tagging, RT). If the implanted nucleus undergoes α decay, the emitted α particle will be detected in the same position in the implantation detector and the highly characteristic α decay energy serves as a tag to identify the implanted nucleus on an event-by-event basis (Recoil Decay Tagging, RDT) [73,74], shown schematically in Fig. 4. This allows extremely clean selection of very weakly populated reaction channels. Note that for transfermium elements the use of recoil tagging is usually sufficient because the reaction channel of interest tends to be the only open fusion–evaporation reaction channel, and the α tag is only used to confirm that all observed transitions can indeed be attributed to the nucleus under study. This situation is very different from that encountered when studying lighter α emitting nuclei where usually many more reaction channels are open and the α tag is necessary to disentangle the complex level schemes and assign γ rays uniquely to a given nucleus. The power of the recoil-decay tagging technique is illustrated by Fig. 5. The figure shows the γ -ray spectra obtained using the jurosphere array of germanium detectors coupled to the ritu gas-filled recoil separator, from the reaction 144 Sm(36 Ar, 4n)176 Hg at a bombarding energy of 190 MeV [75]. The cross section for this reaction is estimated to be approximately 5 µb, with a transmission efficiency for fusion–evaporation residues through the ritu device of approximately 27%. The spectrum labelled ‘‘γ -singles’’ is the total spectrum of prompt γ rays collected in the jurosphere array. By demanding that an observed γ ray is in coincidence with a fusion–evaporation residue detected in the ritu silicon-strip detector, the spectrum labelled ‘‘Recoil-γ ’’ is obtained. This spectrum is dominated by transitions in the ground-state band of 176 Pt, which is the major fusion–evaporation channel produced in the reaction. Fusion-evaporation residues from other reaction channels also contribute to this spectrum. In order to isolate the γ rays that are associated with 176 Hg residues, a recoil-α correlation is performed. Here, two successive events are selected; the first corresponding to a recoil implant in the Si-strip detector at a position (x, y) and at time, t. A search is made for subsequent events with an energy corresponding to that of the 176 Hg α -decay, at the same (x, y) position in the detector, within a time ∆ T. This time, known as the search time (in this case 100 ms), normally corresponds to around three half-lives of the decay of interest. The resulting spectrum is labelled ‘‘α recoil-γ ’’. Here, only transitions in 176 Hg are observed. It can also be seen that these γ rays are buried in the background of the recoil-gamma spectrum. Thus the recoil-decay-tagging technique allows weak reaction channels to be selected from an extremely large background. In in-beam studies the total count rate in the prompt spectrometer forms a bottleneck by limiting the maximum beam current useable in the experiment. This in turn puts an upper limit on the ratio of the cross section leading to the channel of interest σCN to the total reaction cross section σtot . As σtot remains fairly constant at about 0.1–1 b, this limits σCN to values of 100 nb or greater. Any improvement in the capability to handle large data rates directly lowers the limit on the observable cross section σCN . This is the reason for current efforts to use fully-digital data processing for Ge detectors, as the count rate capability can easily be improved by a factor 3–5.

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Fig. 5. Example spectra from the reaction 144 Sm(36 Ar, 4n)176 Hg illustrating the power of the RDT technique. Top: γ -ray singles spectrum. Middle: γ -ray spectrum in coincidence with recoiling reaction products at the focal plane of ritu dominated by the main reaction channel leading to 176 Pt. Bottom: γ rays in coincidence with recoils tagged by the characteristic 176 Hg α decays. Note the different scales on the y-axes.

The in-beam experiments discussed here have all been performed using a combination of isotopically enriched Pb/Bi/Tl/Hg targets and 48 Ca beams producing nuclei with cross sections between 100 nb and 2 µb, sufficient to create several thousand nuclei of interest during a typical 10 day experimental period. 1.3.2. Isomer spectroscopy The RDT technique can be extended to allow the selective spectroscopy of isomeric states. The following technique has been suggested by Jones [76] and used successfully in a number of experiments [77–82]: If a recoiling nucleus enters an isomeric state with a lifetime comparable or greater than the flight time through the recoil separator, it will still be in the isomeric state when implanted into the focal plane detector. The decay of an isomeric state is usually accompanied by a cascade of γ rays, conversion electrons, low energy X-rays and Auger electrons. The last three leave a sizeable amount of energy in the same detector position as the implanted recoil nucleus, thus providing a signal that an isomeric state has decayed. The nucleus then undergoes normal α decay, again leaving a signal at the same detector position (see Fig. 6). Thus the isomer decay is ‘‘sandwiched’’ between the implantation signal and the α decay, allowing an unambiguous assignment of the isomer to the nucleus in question, and allowing the isomer lifetime to be determined. If one surrounds the implantation detector by an appropriate detector system sensitive to conversion electrons, X-rays and γ rays, one can even unravel the decay path of the isomer and place it in the level scheme. Furthermore, at this point it becomes possible to select only those γ rays observed at the target position which were in coincidence with a recoil nucleus implanted in an isomeric state. Thus the γ rays (or conversion electrons) observed at the target position must have populated the isomeric state. This allows the experimentalist to build up complex level schemes even if full coincidence information is lacking, see Section 3. 1.3.3. Decay spectroscopy Spectroscopy following α decay is a very powerful technique, especially for the study of odd-mass nuclei, because the sensitivity of the α decay to the structure of the parent and daughter nuclei tends to connect levels with similar structure, and the observed hindrance factors will be invaluable in assigning spins, parities, and Nilsson labels for an observed decay sequence. This usually means that the ground state of the parent nucleus will decay to an excited state in the daughter

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Fig. 6. Schematic illustration of the isomer-tagging principle [76]. The implanted recoil nucleus leaves a signal at detector position (x, y) (a), followed by the isomer decay proceeding via a cascade of conversion electrons, low energy X-rays and Auger electrons in the same pixel (b). Later still the nucleus undergoes α decay which is again detected in the same pixel (c). The isomeric decay is thus sandwiched in time between the implant and the α decay and identified on an event-by-event basis.

nucleus, and it becomes possible to perform spectroscopy studies on the decay of this state in the daughter, in much the same way as discussed above for isomer studies. Once the decay path has been established and the state has been firmly established in the level scheme, the observed α decay Q -value becomes a measurement of the mass difference between the parent and daughter nuclei. A number of studies have been performed recently and will be discussed in Section 4. For a recent review see [30]. A complication is given by the fact that in heavy systems internal conversion becomes the dominant decay mode for low energy transitions. As a rule of thumb, M1 transitions below 400 keV and E2 transitions below 200 keV have conversion coefficients greater than one in nuclei with Z ' 100, i.e. their decay proceeds predominantly through internal conversion. The conversion electrons emitted in the daughter nucleus following α decay can sum with the alpha signal, usually leading to a broadening of the observed α peak. However, if one avoids implantation, e.g. by depositing the nucleus on the surface of the detector through gas-jet techniques, one is able to detect the conversion electron in a separate detector, and one can recover a clean α spectrum not suffering from the summing problem. Recently this technique has been used to good effect to study the α decay of 257 No [83]. In even–even nuclei this technique is limited, because the decays tend to connect the ground states of even–even nuclei, with rapidly increasing hindrance as the angular momentum difference between parent and daughter state increases. Similarly, the applicability in odd–odd nuclei is limited. Although a large number of states can usually be populated, in this region the knowledge about the states in either parent or daughter is not usually well enough established to allow an unambiguous assignment of the other. 2. Instrumentation 2.1. Comparison of separator operating principles The vast majority of experiments to study the spectroscopic properties of heavy nuclei involve a recoil separator which is used to extract the fusion–evaporation residues of interest from the overwhelming background of other reaction products. These separators operate according to different principles, which have important consequences for factors such as transmission efficiency, mass resolving power and primary beam suppression. A brief comparison of the different operating principles is given in the following section, followed by a presentation of the facilities available at various laboratories which have been active in the spectroscopy of transfermium nuclei in recent years. 2.1.1. Gas-filled separators Gas-filled separators have been used in nuclear structure studies for almost fifty years, since charge distributions of fission products were measured by Cohen and Fulmer [84]. Separators of this type take advantage of the fact that when a heavy ion moves in a dilute gas, charge-exchange collisions with the gas molecules lead to fluctuation in the electronic charge state of the ion. If the number of collisions is large, then the ion follows a trajectory in the magnetic field according to the average charge state, qav e : Bρ =

mv qav e

=

mv 0.0227A = Tm, [(v/v0 )eZ 1/3 ] Z 1/3

(1)

where B is the magnetic flux density, A, Z and v are the mass number, proton number and velocity of the recoiling ion, respectively, and v0 = c /137 is the Bohr velocity. The radius of curvature of the ion trajectory in the field is ρ , and the expression qav e = (v/v0 )eZ 1/3 is obtained using the Thomas–Fermi model of the atom. Since qav e is proportional to the ion velocity, charge and velocity focusing is achieved and the device acts as a mass separator. To first order, Bρ is independent of the initial velocity and charge-state distribution of the ions, though it has been shown that the average charge is determined

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by the atomic shell structure of the ion. Discussion of higher order effects can be found in the work of Ghiorso et al. [85]. Due to the fact that essentially all of the charge state and velocity distributions are collected, gas-filled separators have high transmission efficiencies (up to 50% or more, depending on the reaction). However, this is offset by poor mass resolving power (typically of the order of 5%). Identification of the reaction products is achieved through the use of characteristic charged-particle decay observed in the focal plane detectors, along with time-of-flight and energy loss measurements which allow discrimination of fusion–evaporation products from other beam-related background. A recent overview of the use of gas-filled recoil separators in research can be found in Ref. [86]. 2.1.2. Velocity filters The goal of a velocity filter is to provide charge-independent velocity separation, leading to high transmission of the fusion products. In asymmetric fusion–evaporation reactions, the velocity of the fusion products is usually significantly different from that of the beam, but may have a broad charge-state distribution. Velocity selection is achieved by an arrangement of crossed magnetic and electric fields. The fields can be superimposed, as in the classic Wien filter, or separated. In order to pass the filter without being deflected, the ion velocity must be such that the electrostatic force is balanced by the Lorentz force. This can be understood from consideration of the following formulae for the Lorentz force and the electric force, FB = qv B,

Fel = qE

Ftot = (FB − Fel ) = q(v B − E ) → Ftot = 0

(2) for v = −E /B

(3)

where B is the magnetic field strength, E is the electric field strength, v is the ion velocity and q the charge state. The above relations show that for a given v there is a combination of E and B fields which exert no net force on the particle. In practice, the efficiency for transmission of different charge states is not equal, and velocity filters have a charge and velocity acceptance which reduces the total transmission efficiency. As in the case of gas-filled separators, the mass resolving power is limited. For reactions where the difference in velocity of fusion products and the beam is large, the background suppression of a velocity filter can be very high. For more symmetric reactions where the velocities are similar, the background suppression will not be as good. 2.1.3. Recoil mass spectrometers Recoil mass spectrometers aim to achieve energy-independent mass separation, which is often realised through the use of a symmetric combination of two electric dipoles with a magnetic dipole ‘‘sandwiched’’ in between. The electric dipoles separate according the ratio of kinetic energy to charge state (E /q) whereas the magnetic dipole separates according to the ratio of momentum to charge (P /q). The net effect is then dispersion at the focal plane according to the mass-to-charge ratio, A/q. With the addition of quadrupoles, an energy and angular focussing device is obtained. Such devices can have a high mass resolving power (typically 1/300), but suffer from the fact that only a small part of the total charge state distribution is transmitted. Such separators can often be used to good effect for symmetric reactions and even reactions in inverse kinematics, as the initial separation of beam and fusion products is normally done in the first electric dipole and the kinetic energy to charge state ratios are significantly different. 2.2. Facilities at JYFL The facilities at the Department of Physics at the University of Jyväskylä (jyfl) are centered around the ritu gas-filled recoil separator (Recoil Ion Transport Unit) [87]. ritu was originally designed for studies of heavy elements, and differs from most gas-filled separators in that it has an additional strong vertically-focusing quadrupole magnet before the dipole magnet, which provides better matching to the dipole acceptance. The angular acceptance of ritu is 8 msr with a maximum beam rigidity of 2.2 Tm. The dispersion at the focal plane is 10 mm per % of Bρ . The focal plane of ritu was originally instrumented with a sixteen-strip silicon detector identical to that used at the focal plane of ship (see Section 2.3). The sensitivity was lowered with the addition of a multi-wire proportional counter system upstream of the strip detector which allowed for time-of-flight measurements. The transmission detector could also be used in ‘‘anti-coincidence’’ with the strip detector in order to discriminate between decay and beam-related events. These developments (described in Ref. [88]) contributed to the design of the current focal plane spectrometer system great (Gamma Recoil Electron Alpha Tagging), which was for the main part funded and constructed by a collaboration of UK Universities and Daresbury Laboratory [89]. great consists of two 60 × 40 mm2 double-sided silicon strip detectors (dsssd) mounted side-by-side giving a total coverage of approximately 120 × 40 mm2 . The standard detector thickness is 300 µm, with a strip pitch of 1 mm giving a total of 4800 individual pixels. This high granularity is advantageous when studying activities with long decay half-lives and/or if the total focal plane implant rate is high. Immediately behind the dsssd’s is a segmented planar germanium detector which has an active area of 120 × 60 mm2 and thickness 15 mm. The planar germanium is a highly efficient detector for low-energy photons and is invaluable in the study of heavy elements. Higher energy photons are detected with a largevolume segmented Clover detector, placed directly above the dsssd’s. An array of twenty-eight 28 × 28 mm2 PIN diode detectors in a ‘‘box’’ configuration surrounds the dsssd’s on the upstream side. This array can be used to detect escaping α particles or internal conversion electrons emitted from the nuclei implanted in the dsssd. The detectors of great are completed by a position-sensitive multiwire proportional counter upstream of the dsssd’s which yields time-of-flight and

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Fig. 7. Schematic drawing of the jurogam germanium detector array coupled to the ritu gas-filled recoil separator and the great focal plane spectrometer. Drawing courtesy of D. Seddon, University of Liverpool.

energy information. Details of the detectors and simulations of the various detector efficiencies can be found in Refs. [89,90]. A further important part of the great spectrometer is the novel Total Data Readout (tdr) data acquisition system [91]. The data acquisition system is ‘‘triggerless’’, meaning that data from all detector channels are read out and time-stamped with a 100 MHz clock. The data are then merged into a time-ordered stream and temporal- and spatial-correlations between the various detector groups are made in software. This overcomes the dead-time limitations imposed by traditional triggered data acquisition systems, and gives much greater flexibility in the subsequent offline analysis of the data. Software specific to the analysis of data from the tdr system has been developed in-house at jyfl [92]. 2.2.1. Germanium arrays In parallel with the developments at the focal plane of ritu, the arrays of germanium detectors deployed at the target position for RDT measurements have also evolved steadily. The first array to be constructed was the rather modest doris (DOdecahedral aRray In Suomi), which consisted of nine tessa-type Compton-suppressed 23% germanium detectors [93]. The total photopeak efficiency was around 0.5% at 1.3 MeV, and the array was used to successfully study excited states in 192 Po for the first time (in 1995). The production cross section for 192 Po is approximately 10 µb [94]. Following this (in 1997 and from 1999–2001), various incarnations of an array known as jurosphere were used in campaigns of experiments at ritu. The jurosphere array had a photopeak efficiency of 1.5%–1.7% at 1.3 MeV, and consisted of 10–12 tessa-type detectors and up to 15 eurogam Phase-I type germanium detectors, which were provided by the UK–France loan pool [95]. In 1998, an array of four unsuppressed segmented Clover detectors was employed, known as sari (Segmented Array at ritu). The array had a comparable photopeak efficiency to jurosphere and was used to study 254 No in the first in-beam experiment carried out at jyfl in the transfermium region [96]. Highlights in the study of heavy nuclei from the campaigns with jurosphere included the first observation of excited states in 226 U, 250 Fm and 252 No [97–99]. The coupling of jurosphere to ritu also heralded a new regime in in-beam spectroscopy, with the studies of 182 Pb, 190 Po and 198 Rn, all of which have production cross-sections of the order of 200 nb [100–102]. The most recent array to be hosted at jyfl is the jurogam array of 43 eurogam Phase-I type Compton-suppressed germanium detectors, which are provided from the gammapool of resources from the former euroball, again combined with detectors from the UK–France loan pool. The array is essentially identical to the eurogam spectrometer, with the detectors arranged in rings of 5 at 157.6◦ , 10 at 133.6◦ , 10 at 107.9◦ , 5 at 94.2◦ , 5 at 85.8◦ and 8 at 72.1◦ with respect to the beam direction. The total photopeak efficiency of the array is 4.2% at 1.3 MeV. A schematic drawing of jurogam coupled to ritu and great is shown in Fig. 7. At the time of writing, jurogam has been used in four campaigns of RDT experiments (2003–2007) covering a total of over 10,000 hours of beamtime. The increase in efficiency over previous arrays again allowed the spectroscopic limit to be lowered, with a study of 106 Te carried out at the level of 25 nb [103]. Highlights from the experiments dedicated to the spectroscopy of transfermium nuclei are described elsewhere in this article. 2.2.2. The SACRED spectrometer A particular problem in γ -ray spectroscopic studies of high-Z nuclei is the fact that internal conversion becomes the dominant process in the decay of low-energy transitions. The total internal conversion coefficient for a typical rotational band E2 transition energy of 200 keV in a Z = 102 nucleus is close to 1.6, meaning that the transition is 62% converted. The corresponding number for an M1 transition with the same energy is approximately 7.7, i.e. the transition is 89% converted.

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Fig. 8. Schematic drawing of the sacred electron spectrometer, used in recoil-decay tagging studies at the ritu gas-filled recoil separator.

This means that when studying such heavy nuclei, the transitions between low-spin states may not be observed through γ ray spectroscopy (especially in odd-mass nuclei). In order to attempt the study of such states, a novel electron spectrometer known as sacred [71] was constructed at the target position of ritu. A detailed technical description and overview of the performance of sacred can be found in the work of Kankaanpää et al. [72]. A schematic drawing of the spectrometer is shown in Fig. 8. The spectrometer is operated in a geometry which is close to collinear with the beam direction. The beam passes through the spectrometer on route to the target, and a solenoidal magnetic field transports the emitted electrons back upstream to a multi-element silicon detector located close to the beam axis. The recoiling nuclei continue in the forward direction into ritu. The multi-element silicon detector allows the detection of electron–electron coincidences of electrons emitted in a cascade, for example from a rotational band. The efficiency for detecting single 200 keV electrons is of the order of 10%.

2.3. Facilities at gsi One of the most successful centres for the production and study of superheavy elements has been the ship velocity filter located at gsi, Darmstadt, Germany [104,105]. ship became operational in 1976 and used in the discovery of new elements 107–112 from 1981 to 1996, using the high intensity beams from the unilac linear accelerator. For details of these discovery experiments, see the review of Hofmann and Münzenberg [19]. Unlike a classical ‘‘Wien’’-filter, ship has separated electric and magnetic fields, which improves efficiency and primary beam suppression. The overall configuration is QQQEMMMMEQQQ where Q is a magnetic quadrupole, E is an electric deflector, and M is a magnetic dipole. An additional magnetic dipole with a bending angle between 0 and 15◦ and typically operated at an angle of 7.5◦ was added after the final quadrupole triplet in 1994, further aiding background reduction in some cases, see Fig. 9. The focal plane of ship is instrumented with a 16-strip position-sensitive PIPS PAD silicon detector with an active area of 80 × 35 mm2 . A resistive layer provides position sensitivity in the vertical direction through charge division. This detector acts as a ‘‘stop’’ detector into which the recoiling nuclei are implanted. The detector is 300 µm thick and has approximately 2800 effective pixels. An array of six identical detectors surrounds the stop detector in a hemisphere on the upstream side. This array is used to detect α particles or fission fragments which escape the stop detector, with a geometrical efficiency of 80% of 2π . Several large-volume germanium detectors can be placed in close geometry to the stop detector in order to detect X-rays or γ -rays emitted from the implanted nuclei. Time-of-flight (TOF) measurements are provided by up to three transmission detectors: ions passing a thin, large area carbon foil stimulate the emission of secondary electrons, which are deflected by a magnetic field onto a microchannel plate acting as a multiplier [106]. The detectors have a reasonable time resolution (' 700 ps) allowing E-TOF measurements for a rough mass estimation of nuclei implanted into the stop detector. Each detector has an efficiency of 99.8 % allowing for sufficient discrimination between implantation of nuclei and decays (alpha decay or spontaneous fission) in the stop detector detected in anticoincidence with the TOF detectors. The number of detectors used in specific experiments is taken as a compromise between maximising the anticoincidence efficiency and losses of nuclei due to scattering in the foils. Despite the fact that ship is now over 30 years old, the separator remains at the forefront of superheavy element research. In addition to the extremely successful superheavy element production program, the group working at ship has been very productive in decay spectroscopic studies of lighter nuclei in the transactinide region. A review of some of these experiments can be found in the work of Leino and Hessberger [30].

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Fig. 9. Schematic drawing of the velocity filter ship at gsi, Darmstadt.

2.4. Facilities at FLNR The majority of recent work on decay spectroscopy in the transfermium region at the Flerov Laboratory for Nuclear Reactions flnr has been carried out using the kinematic separator vassilissa [107,108]. Using beams from the U-400 cyclotron at flnr, vassilissa was built in 1987 and is an E /q separator, with the configuration QQQEEEQQQM (Q = magnetic quadrupole, E = electric deflector, M = magnetic dipole). The three electrostatic deflectors are all operated at the same electric rigidity and allow spatial separation of the fusion products from transfer products and the primary beam. The solid angle acceptance of vassilissa is 15 msr with energy and charge acceptance of ±15%. In the original configuration, background suppression factors of 1011 –1013 were measured. As at ship, the addition of a magnetic dipole behind the last quadrupole triplet and before the focal plane gave further improvement in the background suppression factors. The first change was to add a dipole with a bending angle of 8◦ , which was later replaced with one of 37◦ degree bending angle. The latter magnet has enabled some mass analysis to be performed and has reduced the background by a further factor of 10-50. Time-of-flight information is provided by a system of microchannel plates with plastic emitter foils of thickness 30–70 µg/cm2 and area 70 × 140 mm2 [109]. The typical timing resolution is 700 ps and efficiency is 99.95%. In order to obtain detailed spectroscopic data from the decay of implanted nuclei, a new focal plane detection system known as gabriela (Gamma Alpha Beta Recoil Investigations with the ELectromagnetic Analyser vassilissa) has been designed and constructed [110]. The recoiling ions are implanted into a sixteen strip 58 × 58 mm2 position-sensitive silicon detector of thickness 300 µm. Surrounding the implantation detector is an array of seven eurogam Phase-I type germanium detectors which were also obtained from the UK–France loan pool. Six of these detectors are Compton-suppressed and placed at a distance of 130 mm from the implantation detector in a ring. The seventh is placed directly behind the implantation detector, as close as possible. The efficiency of the array is approximately 7% for photons of energy 200 keV. Measurement of internal conversion electrons emitted during the decay process is made possible with an array of four four-strip silicon detectors mounted in a tunnel on the upstream side of the implantation detector. Each detector has an active area of 50 × 50 mm2 and the array has a simulated efficiency of around 16% for electrons of energy 50–400 keV. gabriela has mainly been used in studies of reactions involving a 48 Ca beam, some of the results of which are discussed in Section 4. 2.5. Facilities at ANL Argonne National Laboratory (anl) is another long-standing centre for research into the structure of heavy elements, providing a wealth of spectroscopic data on transactinide nuclei in the 1970’s. More recently, research into transfermium nuclei has been carried out using the Fragment Mass Analyser (fma) [111] using beams from the atlas heavy-ion accelerator. The fma is a recoil-mass spectrometer with the configuration QQEMEQQ, where Q is a magnetic quadrupole, E is an electric dipole, and M is a magnetic dipole, see Fig. 10. The symmetric combination of two electric dipoles and one magnetic dipole separates the fusion products from primary beam and then disperses them at the focal plane according to their A/q (mass/charge) ratio. The angular acceptance of the fma is 8 msr with A/q acceptance of ±7% and energy acceptance of ±20%. When coupled to the gammasphere array (see below) the angular acceptance is reduced as the target position must be moved. The mass resolving power is approximately 1/340 at 8 msr and with an energy acceptance of ±10%. As with

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Fig. 10. Schematic drawing of the ion-optical layout of the Fragment Mass Analyzer (FMA) at ANL.

ritu at jyfl, the fma has been coupled to a number of germanium detector arrays over the past decade or so. A number of measurements were performed in the early 1990’s with the Argonne-Notre Dame array of ten Compton-suppressed germanium detectors, an example of which is the study of the prolate rotational band in 186 Pb [112]. Following these early measurements, the efficiency of the germanium array was improved with the introduction of the (Argonne-Yale-European) AYE-Ball array [113]. AYE-Ball was used at the fma in late 1995. The array could house up to 15 Eurogam Phase-I germanium detectors and up to 10 tessa-type detectors. For the experimental campaign, nine 70% and ten 25% detectors were used, giving a total photopeak efficiency of 1.1% at 1.3 MeV. Two themes of this experimental campaign were the study of N = Z nuclei and shape co-existence in the region of the Z = 82 shell closure [114,115]. In 1998, the gammasphere array of 110 Compton-suppressed germanium detectors was installed at the fma. gammasphere is arguably the most powerful γ ray spectrometer to be constructed so far, with a photopeak efficiency approaching 10% for 1.3 MeV γ -rays [116]. Since conception in the early 1990’s, gammasphere has been tremendously successful in studies of exotic nuclei, in particular for the investigation of high-spin phenomena. gammaspehere has been used at the fma from 1998 to 2000 and from 2003 onwards. From 2001–2003 it was relocated to the Lawrence Berkeley National Laboratory. The coupling of gammasphere to the fma has been another tremendously productive venture. Examples from studies at the fma, which are discussed in this review, are the first observations of the rotational band sequence in 254 No, and the studies of K-isomerism in the No isotopes [117,118,78]. 2.6. Facilities at GANIL A relatively new participant in the field of superheavy elements is the Grand Accelerateur National D’ions Lourds, or ganil. The program of experiments employs beams provided by the css1 cyclotron and the lise3 spectrometer in the fulis configuration. lise has operated at ganil since 1984 and is designed to separate exotic nuclei produced in fragmentation reactions with primary beam energies of 20 to 100 MeV/nucleon [119]. The separation of these high-energy fragments is performed by a large dipole magnet which gives separation according to magnetic rigidity (A/Z ) and then by taking advantage of differential energy loss in an achromatic degrader and a second magnetic dipole, which gives a final selection depending on A3 /Z 2 . This selection was later improved with the addition of a Wien filter following lise, the full spectrometer being known as lise3 [120]. The Wien filter was then adapted to make it possible to study fusion–evaporation reactions, which is known as the fulis configuration [121]. A reaction chamber housing a rotating target wheel system was added, and slight modifications were made to the construction of the Wien filter to improve background suppression and dumping of the primary beam. For decay spectroscopy, the focal plane can be equipped with ‘‘Galotte’’ detectors (emissive foils plus microchannel plates) for time-of-flight determination, a double-sided silicon strip detector (dssd) and a tunnel of fourfold segmented silicon detectors for detection of conversion electrons known as best (Box for Electron Spectroscopy after Tagging). The dssd has 48 × 48 strips with dimensions of 50 × 50 mm2 and thickness 300 µm. best has an efficiency of 15% for 200 keV electrons and can be surrounded by a number of germanium detectors in close geometry. If four exogamtype Clover detectors are installed, the photopeak efficiency is estimated to be at a maximum of 22% at 120 keV [122]. The facilities at ganil have been used in a study of seaborgium isotopes (Z = 106), an attempt at element 118 using the 86 Kr + 208 Pb reaction and a study of the decay properties of 255 Lr, which is reported in Section 5 [121–123]. 2.7. Facilities at JAEA In recent years, a number of interesting new results have come from the work carried out using the tandem accelerator of the Japan Atomic Energy Agency (jaea), formerly known as jaeri. Several new isotopes have been produced and decay spectroscopic studies performed using a gas-jet coupled online to an isotope separator (see Ref. [124] and references therein for details). A schematic of the separator layout is shown in Fig. 11. Reaction products are stopped in He gas and transported by an aerosol jet via a capillary to a surface ionisation thermal ion source. The ions are then accelerated with an extraction voltage of 30 kV and mass separated with a dipole magnet. The dipole magnet has a mass resolving power (M /∆M) of 800. Coincidence measurements of α particles with conversion electrons or γ rays can be made with a collection of silicon pin diode detectors and various germanium detectors. Examples from the experiments carried out include spectroscopic studies of 257 No, and of the new isotopes 237 Cm and 241 Bk [83,125,126]. In-beam γ -ray spectroscopic studies have also been carried out at the jaea-Tokai tandem facility. Heavy (stable and radioactive) targets have been used with light-ion beams (e.g. 18 O) to populate the ground-state bands of more neutron-rich nuclei through few particle transfer reactions. A system of silicon ∆E − E telescopes is used to identify outgoing beam-like

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Fig. 11. Outline of the jaea gas-jet coupled online isotope separator.

transfer products in coincidence with γ -rays detected in a small array of six or seven germanium detectors. The array has an efficiency of around 3% for 1.33 MeV γ rays. The system has been used to identify the ground-state band transitions in 236 Th, 240,242 U and 250 Cm [127–129]. 3. Structure of even–even nuclei In this section, the structure of even–even nuclei in the transfermium region is presented. The first part presents the systematics of the known ground-state rotational bands from curium to nobelium, along with brief descriptions of how the data has been obtained and relevant references. For the ground-state bands beyond the nobelium isotopes, only the excitation energy of the 2+ state in 256 Rf is listed in the evaluated data, with a large error bar (51(35) keV [130]). This assignment was based on one event from the α decay of 260 Sg, which was subsequently not confirmed in later measurements where greater statistics were obtained [131]. Following this is a discussion of the energy level systematics and the behaviour of the moments of inertia. The second part of the section deals with the recently observed K -isomers and non-yrast states. 3.1. Systematics of ground-state rotational bands 3.1.1. Curium isotopes The systematics of known excited states in the curium isotopes are shown in Fig. 12. The energies of the 2+ states in 238,240 Cm were determined from measurements of fine structure in the α decay of 242,244 Cf. The californium isotopes were produced through bombardment of uranium targets with 12 C ions at Oak Ridge and Berkeley and collected using the helium gas-jet technique [132,133]. The α -decay activities are assigned to a particular isotope on the basis of excitation function and half-life analyses. As the typical resolution in α decay spectroscopy is of the order of 20 keV, the associated error bars are rather large. The ground-state band of 242 Cm has recently been extended to a spin of 24h¯ through one-proton transfer to a 241 Am target irradiated by a 209 Bi beam at an energy 10%–15% above the Coulomb barrier. The γ rays emitted were detected by the gammasphere array (see Section 2.5) [134]. Prior to this most recent study, only states up to the 6+ state were assigned through α decay of 246 Cf. A β − decay study of the 6− ground state in 244 Am has allowed the ground-state band of 244 Cm to be determined up to a spin of 8+ . The 6− ground state decays solely to a K π = 6+ state in 244 Cm and then to the ground-state K π = 0+ band. Samples of 244 Am were prepared by neutron capture onto 243 Am targets in the High Flux Reactor of the Institut Laue-Langevin, and subsequently studied by γ -ray and internal conversion electron spectroscopy [135]. A similar approach was used to study 246 Cm, though interestingly in this case a sample of 246 Pu was gathered from the site of the ‘‘Hutch’’ event, an underground nuclear explosion intended to produce heavy elements. The decay of 246 Pu proceeds by β − to a 7− state in 246 Am and then again via a K π = 8− isomer to the ground-state band [136–138]. Again using coincident γ -ray and electron spectroscopic techniques, it was possible to establish the ground-state band to a spin of 8+ . The most wellstudied curium isotope is 248 Cm, which is known to a spin of 30h¯ . Most recently, the structure of 248 Cm has been investigated through Coulomb excitation using a 209 Bi beam, using the gammasphere array of germanium detectors [139]. Also reported in the work of Hackman et al. is a sequence of γ rays with energies 153, 205, 253, 298, 338, 374, 405, and 434 keV which are attributed to be the continuation of the ground-state band in 246 Cm. These levels are marked with dashed lines in Fig. 12, and the level energies shown for 246,248 Cm are those of the unevaluated data from the work of Abu Saleem [140]. The most

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Fig. 12. Systematics of the ground-state rotational bands in the curium isotopes. The mass number is marked along the x-axis.

recent addition to the systematics of the curium isotopes has come from a measurement of 250 Cm via two-neutron transfer reactions with a 248 Cm target and a 18 O beam. The experiment was carried out at the Tokai tandem facility of the jaea (see Section 2.7) and employed a system of δ E − E telescopes operated in coincidence with a small array of germanium detectors [129].

3.1.2. Californium isotopes As can be seen from Fig. 13, the systematic data for the ground-state rotational bands of californium isotopes are much less extensive than that of the curium isotopes. The excitation energies of the 2+ states in 244,246 Cf have been determined from α -decay spectroscopy of 248,250 Fm, respectively [141,142]. The structure of 248 Cf has been studied through α decay of 252 Fm produced from reactions of α particles with a 249 Cf target. The α decays populated excited states up to a spin of 6+ [143]. Extensive studies have been made of 250 Cf, through the α decay of 254 Fm, β − decay of 250 Bk and the electron capture (EC) decay of 250 Es [143–145]. The β − decay of 250 Bk proceeds from a 2− state and therefore only populates low-spin states, whilst the EC decay of 250 Es is from a 6+ state which predominantly feeds high-lying 6− and 5− states which in turn decay via several higher K bands to the ground state K π = 0+ band. Similarly, 252 Cf has been studied through the α decay of 256 Fm and from the EC decay of 252 Es [146,147]. The (5− ) ground state of 252 Es decays via high-lying low spin states, populating the ground-state band up to a spin of 4+ .

3.1.3. Fermium isotopes Fig. 14 shows the level energy systematics of the ground-state rotational bands in the fermium isotopes. The most recently studied case is that of 248 Fm, which has been studied in a recoil-decay tagging measurement at jyfl using the jurogam, ritu and great system (see Section 2.2). The 248 Fm nuclei were produced in reactions of a 48 Ca beam with a 202 HgS target. Preliminary analyses have allowed the ground-state band to be established up to a spin of 14h¯ [148]. Prior to the measurement only the excitation energy of the 2+ was known from α decay studies of 252 No produced in the bombardment of 241 Am with a 15 N beam and the helium jet technique [149]. The structure of 250 Fm has been studied in several recoil-decay tagging experiments carried out at jyfl. An initial study of the ground-state band was performed using the jurosphere array coupled to ritu, allowing the band to be established up to the 18+ state. A measurement of the internal conversion electrons emitted in the decay of 250 Fm using the sacred spectrometer allowed the energy of the 4+ to 2+ transition to be determined, and showed that the observed transitions were indeed E2 in nature [98]. The latest study employed the jurogam array and allowed the ground-state band to be extended to a spin of 22h¯ . The structure of a band built upon a K π = 8− isomer was also investigated (see Section 3.2) [81,82]. In 252 Fm, only the excitation energy of the 2+ band member is known, determined through α -decay spectroscopy of 256 No. The 256 No was produced using reactions of 12 C on 248 Cm at the 88-inch cyclotron

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Fig. 13. Systematics of the ground-state rotational bands in the californium isotopes. The mass number is marked along the x-axis.

Fig. 14. Systematics of the ground-state rotational bands in the fermium isotopes. The mass number is marked along the x-axis.

in Berkeley, and extracted using the helium-jet technique [150]. Using the β − decay of the 2+ isomer in 254 Es, it has been possible to populate the ground-state band of 254 Fm up to the 4+ member [151]. Until the recent measurements at jyfl, 256 Fm was the best known of the fermium isotopes. The level scheme of 256 Fm was investigated via the β − decay of 256m Es. The β decay proceeds to an isomeric K π = 7− state which then decays both directly to the ground-state band and through several other lower K bands. The 256 Es was produced through (t , p) reactions on a 254 Es target and then radiochemically separated [69].

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Fig. 15. Systematics of the ground-state rotational bands in the nobelium isotopes. The mass number is marked along the x-axis.

3.1.4. Nobelium isotopes The only isotopes of nobelium for which the ground-state band structure has been investigated are 252,254 No, as shown in Fig. 15. Of these, 254 No was first investigated in a pioneering experiment carried out with the gammasphere array coupled to the fma at anl. The production cross section for 254 No through the 208 Pb (48 Ca, 2n)254 No reaction is of the order of 3 µb [152], which is anomalously high compared to the reactions for production of neighbouring nuclei. This high cross section occurs due to the fact that both projectile and target are doubly-magic, leading to a very favourable reaction Q -value. The initial study at anl allowed the ground-state band to be established up to a spin of 14h¯ and showed that 254 No was an excellent example of a rotational nucleus [117]. Subsequent studies at jyfl using the sari array and again at anl extended the groundstate band to a spin of 16h¯ and then 22 h¯ [96,153]. The latter experiment used two different bombarding energies (215 and 219 MeV) in order to investigate the reaction mechanism through measurement of the entry distribution. The entry distribution enables the height of the fission barrier to be estimated and gives a constraint on the shell energy at high spin. At jyfl, 254 No has been subsequently studied in several experiments using jurogam, ritu and great. The first of these led to the observation of high-energy γ -rays from the decay of a low-spin non-yrast state and extension of the ground-state sequence to a spin of 24 h¯ . It was not possible to give an unambiguous assignment to the non-yrast band-head, but the state was tentatively assigned a spin 3 h¯ [154]. Following this, attempts have been made to determine the level structure above the K π = 8− isomeric state, the configuration of which was determined in experiments both at jyfl and anl [77,78] (see Section 3.2). A spectrum of recoil-gated γ -rays emitted from 254 No is presented in Fig. 16. To create this spectrum, the data from two of the experiments using jurogam has been combined. The rotational band of 254 No can be seen up to a spin of 24h¯ , along with several less intense peaks which have not yet been placed in the level scheme. Of particular interest is the regular sequence of peaks with energies 199, 224, 247, 270 and 294 keV, which do not correspond to any structure which has so far been identified. The spectrum of internal conversion electrons emitted from 254 No has also been measured using the sacred electron spectrometer coupled to ritu (see Section 2.2.2). A recoil-gated conversion-electron spectrum is shown in Fig. 17. Inspection of Fig. 16 shows that the 4+ to 2+ transition is not visible in the γ ray spectrum, due to the internal conversion competition. The L- and M- conversion electrons from the 4+ to 2+ transition are clearly visible in Fig. 17. The additional intensity under the peaks in the spectrum was attributed to be due to the decay of low-energy transitions in high-K bands populated with an intensity corresponding to about 40% of that of the ground-state band [155,156]. This speculation was subsequently proved correct following the delineation of the level scheme below the K π = 8− isomer. The other nobelium isotope to be studied at jyfl, 252 No, has a much shorter history. The ground-state band was studied using the jurosphere array coupled to ritu

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Fig. 16. Spectrum of recoil-gated γ rays from 254 No, showing the rotational band up to a spin of 24 h¯ . The regular sequence of peaks with energies 199, 224, 247, 270 and 294 keV has not yet been placed in the level scheme.

Fig. 17. Recoil-gated internal conversion electron spectrum from 254 No. The spectrum was obtained using the sacred electron spectrometer at jyfl.

through the 206 Pb (48 Ca,2n)252 No reaction. The production cross section is of the order of 200 nb and the rotational band could be observed up to a spin of 20h¯ [99]. As 252 No has a significant spontaneous fission branch, the same data set was later analysed and the emitted fission fragments were used as an alternative ‘‘tag’’ for the prompt γ rays. This procedure improved the statistics in the tagged γ -ray spectrum and showed evidence for weak high-energy transitions, which were speculated to come from a low-spin band-head [157]. This was proved correct when a K π = 8− isomer was later discovered (see Section 3.2).

3.1.5. Systematics of the moments of inertia In this section, the systematic behaviour of the experimental moments of inertia is discussed along with the systematics of the level energies presented in the previous section. A plot of the dynamic moments of inertia for isotopes of plutonium to curium with neutron number N = 148–154 is shown in Fig. 18. The kinematic (J (1) ) and dynamic (J (2) ) moments of

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Fig. 18. Systematic behaviour of the experimental kinematic moment of inertia as a function of rotational frequency for nuclei with N = 148–154 and Z = 94–102.

inertia can be extracted from the experimental data using the following relations (for K = 0 and E2 transitions):

J (1) (I ) = h¯ 2

2I − 1 E (I + 1) − E (I − 1)

J (2) (I − 1) = h¯ 2

4 Eγ 1 − Eγ 2

=

= h¯ 2

4 h¯ 2

∆Eγ

.

2I − 1 Eγ 1

,

(4)

(5)

In the above expressions I is the spin of the initial level, and Eγ 1 , Eγ 2 are the energies of successive γ rays in the E2 cascade. It should be noted that the dynamic moment of inertia J (2) is calculated for (I − 1), and the associated rotational frequency should also be calculated at (I − 1). In the plutonium isotopes 242,244 Pu, a sharp alignment is seen at a rotational frequency of around 0.25 MeV. This upbend is due to the alignment of a pair of π i13/2 protons. The same sharp upbend is not seen in the lighter plutonium isotopes, which is attributed to the fact that the octupole correlations are stronger in those isotopes [158]. New data obtained for 246 Pu from two-neutron transfer reactions do not extend to high enough rotational frequency to determine whether the alignment persists at neutron number N = 152 [159]. In the curium isotopes, a smooth upbend and then a downturn is observed for the highest spins in 248 Cm. In the work of Piercey et al., this behaviour is suggested to be due to gradual alignment of a neutron ν j15/2 pair at low spins, followed by alignment of a proton π i13/2 pair at spins above 10h¯ . The alignment of the π i13/2 is smoothed by the ν j15/2 pair [160]. As discussed in Section 3.1.1 and shown in Fig. 12, new data are available for 246 Cm and 250 Cm [139,129]. The data for 246 Cm extend up to a spin of 26 h¯ , just below the maximum spin observed in 248 Cm. For the spin range observed, the moment of inertia of 246 Cm tracks closely that of 248 Cm, but is a little lower at the highest frequencies. It would be of interest to extend further the ground-state band of 246 Cm and to determine the behaviour through the expected turnover region. As only limited data exist for 244 Cm and for the californium isotopes, they are not discussed further. In the fermium and nobelium isotopes, data exist for 248,250 Fm and for 252,254 No. Comparison of the N = 150 and N = 152 isotones shows that the rotational alignment is faster in the N = 150 nuclei than in N = 152. The observation of rotational bands in 252,254 No combined with this difference led to a number of theoretical works which attempted to reproduce the behaviour through various approaches. An example is shown in Fig. 19, which is reproduced from the work of Bender et al. [161] which followed that of Duguet et al. [162]. The calculations are cranked Hartree–Fock–Bogoliubov using the SLy4 parameterization of the Skyrme interaction. A zero-range density-depending pairing force is used along with the Lipkin-Nogami prescription (see [161] and references therein for details).

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Fig. 19. Calculated kinematic, J (1) , and dynamic, J (2) , moments of inertia for nuclides with Z = 100–104 and N = 150, 152. Empty (full) symbols are for calculations (experiment). Reproduced from Bender et al. [161].

Overall, the reproduction of the behaviour of the moments of inertia is very good, though the alignment is slightly underestimated in 252 No. Another extensive and systematic study was performed by Afanasjev et al., using cranked relativistic Hartree–Bogoliubov theory with various parameterisations of the relativistic mean field [56]. Again the general trends of the moments of inertia were reproduced, though in comparing the N = 150 and N = 152 isotones it was found that experimental moments of inertia were lower than those from calculation at low spin. This was attributed to the fact that the deformed shell gaps are calculated to be at N = 148, 150, rather than N = 152. Also of interest was the prediction that a simultaneous alignment of a proton π i13/2 pair and a neutron ν j15/2 pair should occur at a rotational frequency of '0.3 MeV in 254 No. This is just above the highest spin which has currently been observed experimentally. However, the simultaneous alignment of two high-j orbitals would result in a much more gradual upbend, in agreement with the observed behaviour of 254 No. The work of Egido and Robledo investigated the fission barrier of 254 No at high angular momentum in the framework of Hartree–Fock–Bogoliubov theory with the D1S Gogny force. It was predicted that the stability of 254 No may persist up to 40 h¯ or higher and that there should be a backbend at 38 h¯ [163]. An alternative way to show the moment of inertia systematics is shown in Fig. 20, which is reproduced from the work of Ishii et al. [129], with additional data added for the recently-studied 248 Fm and 242 Pu [148,159]. The plot shows values of 2J0 / h¯ 2 , where J0 is the so-called Harris parameter [164]. The Harris parameters can be extracted from a fit of the kinematic moment of inertia, J 1 , with the rotational frequency, ω. The kinematic and dynamic moments of inertia and the rotational frequency are related as follows:

J (1) = J0 + ω2 J1 J

(2)

(6)

= J0 + 3ω J1 . 2

(7)

In cases where the energies of the low-spin states are not known, the higher-lying levels and a fit of the Harris parameters can be used to extrapolate to the energies of the 4+ and 2+ states using the formula: I = J0 ω + J1 ω3 + 1/2,

(8) +

252,254

where I is the spin of the initial state. The procedure has been used, for example, to extrapolate the 2 energies in No, 248,250 Fm, 250 Cm and 246 Pu. The work of Ishii is the first in-beam study beyond N = 152 and highlights the observation that the moments of inertia for isotopes of Cm are smaller for N > 152 than for N ≤ 152. This lends further support to the

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Fig. 20. Systematic behaviour of the Harris parameter, J0 , as a function of neutron number for elements from Pu to No. Reproduced from figure of Ishii et al. [129].

existence of a deformed shell gap for N = 152. It is interesting to note that the moments of inertia for the N = 150 isotones of Cf and Cm are also larger than those for the N = 152 isotones, as one would expect a maximum moment of inertia at the shell gap. The trend for the Cm isotopes is reasonably well reproduced in the calculations of Sobiczewski et al. (using the cranking approximation), with values of 133.0, 132.6 and 128.0 MeV−1 for 246,248,250 Cm, respectively [165]. The latest data shows that in the Fm isotopes the values at N = 148 are lower than for N = 150. Unfortunately the calculations of Sobiczewski et al. stop at N = 150 for the Fm isotopes, so a comparison cannot be made. For No, the value is higher for N = 152 than for N = 150. It would be of extreme interest to investigate the moment of inertia for 252 Fm and the nobelium isotopes at N = 148 and N = 154 to determine whether a maximum can be located. Also of interest is the latest data in the Pu isotopes, which shows that the moment of inertia continues to decrease at N = 152. This, along with extended systematics of the one-quasiparticle energies, shows that the size of the N = 152 deformed shell gap is reduced with decreasing atomic number [159]. 3.2. K-Isomerism and non-yrast states A little over thirty years ago, Ghiorso et al. reported the discovery of isomeric states in 250 Fm and 254 No which were observed in an experiment to study the α -decay properties of these isotopes [166]. The activities were transferred to a ‘‘carousel’’ system by a helium gas jet, and the α particles detected with a set of Si(Au) detectors. The experiments found evidence for decays which occurred prior to the α decays in detectors which should not have been facing the activity. From this it was deduced that: The transfer of the 250 Fm atoms from the wheel onto the movable detectors must then be caused by the feeble recoil resulting from the isomeric transition or other accompanying γ rays and conversion electrons in the cascade that leads to the ground state. For a 500 keV γ ray the recoil energy of a 250 Fm atom is about 0.5 eV. Ghiorso et al. then went on to discuss possible explanations in terms of high-spin two-quasiparticle configurations (the most likely configurations are 8− [9/2− [734]ν ⊗ 7/2+ [624]ν ] or 8− [7/2− [514]π ⊗ 9/2+ [624]π ]). No radiation emitted directly from the isomeric states was observed. The hypothesis went untested for several decades, until the suggestion of Jones for a new experimental technique (discussed in Section 1.3.2). Using the new technique, the first data confirming the existence of the isomer in 254 No was obtained in jyfl and then at anl [167,168]. Subsequent experiments with much improved focal plane detection systems then allowed the decay scheme of the isomer to be fully delineated to the ground state [77,78], and showed the existence of a new isomeric state. In the following, the data obtained at jyfl are discussed [77]. Fig. 21 shows spectra obtained at the focal plane of ritu using the great spectrometer. Panels (a,b) show the calorimetric electron signals from the decay of the two isomeric states and associated decay curves, whilst panels (c,d) show the spectra of γ rays observed in prompt coincidence with the internal conversion electrons. The inset to panel (c) shows the high-energy part of the γ -ray spectrum, revealing that the decay of the isomer does indeed proceed via several high-energy transitions and confirming the speculation of Ghiorso et al. quoted above. The level scheme deduced from the experiment is shown in Fig. 22, where it can be seen that the K π = 8− isomer decays via a 53 keV E1 transition to the 7+ member of a K π = 3+ band. The K π = 3+ band-head is the state originally observed by Eeckhaudt et al. in the in-beam study of 254 No [154]. A determination of the M1/E2 γ -ray intensity ratios for transitions in the K π = 3+ band firmly established that the band-head was a proton two-quasiparticle state with the configuration 3+ [1/2− [521]π ⊗ 7/2− [514]π ]. The configuration of the K π = 8− isomer could in turn be assigned the 8− [7/2− [514]π ⊗9/2+ [624]π ] configuration. The half-life of the isomer was determined to be T1/2 = 266(2) ms, in excellent agreement with the original value given by Ghiorso et al. It was not possible to fully determine the decay path of the new 184 µs isomer, but it was speculated that this could be a four-quasiparticle state constructed from the two possible protonand neutron- two-quasiparticle 8− states. The data allowed the position of the important 1/2− [521]π Nilsson orbital to be

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695

Fig. 21. Experimental data illustrating the decay of the two isomeric states observed in 254 No. a, b, Main panels, the calorimetric electron signals from the two isomer decays; insets, the time distribution between the recoil implantation and the decay of the isomer. c, d, Main panels, the γ rays observed in prompt coincidence with these electron signals. Insets, the high-energy regions of the spectra (taken from Ref. [77]).

Fig. 22. Partial level scheme of 254 No (taken from Ref. [77]).

determined, which is of particular interest as the level originates from the spherical f5/2 orbital from above the possible Z = 114 shell gap. The separation and position of the f7/2 − f5/2 spin-orbit partners plays a crucial role for calculations of

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Table 1 Table of known K -isomers in even–even nuclei in the heavy and superheavy elements Nucleus 244

Cm 246 Cm 248 Fm 250 Fm 256 Fm 250 No 252 No 254 No 254 No 270 Ds

Kπ

T1/2

Ex

Decay Mode

Configuration

Reference

6+ 8− – 8− 7− (6+ ) 8− 8− – 9− ,10−

34 ms – '8 ms 1.92 s 70 ns 42 µs 110 ms 266 ms 184 µs 6 ms

1.040 MeV 1.179 MeV – 1.195 MeV 1.425 MeV – 1.254 MeV 1.293 MeV '2.5 MeV '1.13 MeV

γ γ γ γ γ ,SF SF,γ ? γ γ γ α

5/2+ [622]ν ⊗ 7/2+ [624]ν 7/2+ [624]ν ⊗ 9/2− [734]ν 7/2+ [624]ν ⊗ 9/2− [734]ν 7/2+ [633]π ⊗ 7/2− [514]π (5/2+ [622]ν ⊗ 7/2+ [624]ν ) 7/2+ [624]ν ⊗ 9/2− [734]ν 7/2− [514]π ⊗ 9/2+ [624]π – 11/2− [725]ν ⊗ 7/2+ [613]ν 11/2− [725]ν ⊗ 9/2+ [615]ν

[135,171] [138] [148] [82] [69] [118] [169] [77,78] [77,78] [22]

In some cases the K π or configuration assignments are tentative and have not been made on the basis of unambiguous experimental data. See relevant references for details.

the structure of superheavy elements. The excitation energy of the K π = 3+ state is also rather low for a two-quasiparticle state, which indicates that the 1/2− [521]π and 7/2− [514]π levels must be close in energy. Following these successful studies of 254 No, a further experiment was carried out at jyfl in order to attempt confirmation of the isomer in 250 Fm [82]. The experiment again employed the ritu and great combination, but in this case the jurogam array was also coupled to ritu. This allowed prompt radiation from transitions above the isomeric state(s) to be extracted, using a variation on the same technique of Jones. The existence of the isomer in 250 Fm was confirmed with a half-life of 1.92(5) seconds, again in excellent agreement with the original value of Ghiorso et al.. The focal plane data showed that the K π = 8− isomer decayed via an unobserved 23 keV M1 transition to the 7− member of a K π = 2− band. In this case, it was possible to measure M1/E2 γ -ray intensity ratios in the strongly-coupled band based on the K π = 8− state. The intensity ratios indicated that the configuration of the isomer must be the two-quasineutron 8− [9/2− [734]ν ⊗ 7/2+ [624]ν ] configuration. At gsi and anl, the same technique was applied to a search for K -isomers in 252 No [169,170]. Both experiments were successful and discovered an isomer with a half-life of 110 (10) ms. The decay pattern of the isomer was very similar to that of 250 Fm and it was concluded that the configuration of the isomer must be the same as that of the isotone (8− [9/2− [734]ν ⊗ 7/2+ [624]ν ]). A study of the spontaneous fission activities produced in the reaction of 48 Ca with an enriched 204 Pb target carried out at the fma in anl provided evidence for an isomer in 250 No [118]. Two different spontaneous fission half-lives were observed, one of which was tentatively attributed to the decay of a K π = 6+ isomer in analogy to the isotone 244 Cm. The configuration of the K π = 6+ isomer in 244 Cm is assigned as 6+ [5/2+ [622]ν ⊗ 7/2+ [624]ν ]. The recent study of 248 Fm carried out at jyfl has also revealed evidence for an isomer with a half life of approximately 8 ms [148]. Possibly one of the most well-known K isomers is that of 270 Ds, discovered at gsi [22]. The isomer decays by emission of an α particle and is suggested to have a configuration of either 9− [11/2− [725]ν ⊗ 7/2+ [613]ν ] or 10− [11/2− [725]ν ⊗ 9/2+ [615]ν ]. Details of known K -isomers in the region of Cm isotopes and above are presented in Table 1. The existence of K isomers in these heavy nuclei raises an interesting question concerning the stability of the superheavy elements. In some cases it may be possible that an inversion of stability occurs, meaning that the high-K isomer in a particular nucleus has a lifetime longer than that of the ground state. This was investigated in the work of Xu et al., through configuration-constrained potential energy surface calculations [172]. It was found that the multi-quasiparticle configurations increase the barrier to fission and reduce the probability of α decay, leading to enhanced stability. Indeed, +8.2 this is the situation found in 270 Ds [22], where the isomeric state has a half-life of T1/2 = (6.0− 2.2 ) ms compared to the

140 ground-state half-life of T1/2 = (100+ −40 ) µs [22,172]. The systematics of the known K isomers and lowest-lying non-yrast states in the N = 150 and N = 152 isotones is shown in Fig. 23. The data for the N = 152 isotones is somewhat limited, the only known isomer being the proton twoquasiparticle 8− [7/2− [514]π ⊗ 9/2+ [624]π ] state in 254 No. The lowest-lying non-yrast state is the proton two-quasiparticle 3+ [1/2− [521]π ⊗ 7/2− [514]π ] state involving deformed configurations derived from spherical orbitals above and below the predicted Z = 114 spherical shell gap. A low-lying 2− state is known in 250 Cf and the lowest-lying non-yrast state in 248 Cm is either a vibrational 2+ or octupole-vibrational K = 0 J π = 1− state. More extensive systematics are available for the N = 150 isotones, where the 8− states are known in all isotones. In 248 Cf an assignment of the 8− energy has been made from a re-analysis of the data from the 249 Cf(d, t ) reaction [170,68]. The lowest-lying non-yrast state in all the N = 150 isotones is a 2− state. The systematic behaviour of the N = 150 isotones has been discussed in the work of Robinson et al. [170], the salient points of which are repeated here. The energies of the 8− states are very similar with neutron number, indicating that they all have the 8− [9/2− [734]ν ⊗ 7/2+ [624]ν ] configuration, as assigned in 250 Fm. The energies of the 2− states are too low to be pure two-quasiparticle states, suggesting that additional octupole collectivity brings them lower in energy. In 250 Cf, the 2− band has been populated in the 249 Cf(d, t ) reaction showing that a major component of the wave function is the 9/2− [734]ν ⊗ 5/2+ [622]ν configuration [68]. The energy of the 2− state in 248 Cf is much lower than in the other N = 150 isotones, which is attributed to the fact that both proton and neutron configurations can contribute to the 2− octupole collectivity at Z = 98. Detailed discussion of the systematics along with qrpa calculations can be found in the work of Robinson et al. It is also of interest to question why in the Z = 102 isotopes 252,254 No a neutron

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697

Fig. 23. Left: Systematics of known K isomers and lowest-lying non-yrast states in the N = 150, 152 isotones. Right: Single-particle energies calculated using a Woods-Saxon potential with ‘‘Universal’’ parameterisation for 250 Fm. The Fermi level 250 Fm is marked with a dashed line.

two-quasiparticle 8− isomer is observed for N = 150, whilst a proton two-quasiparticle isomer is seen at N = 152 (as discussed in Ref. [82]). This can be understood with reference to the spectrum of single-particle energies calculated using a Woods-Saxon potential with ‘‘Universal’’ parameterisation for 250 Fm shown in Fig. 23. Due to the deformed shell gap at N = 152, enclosed by the 1/2+ [620]ν and 9/2− [734]ν single-particle states, one would expect that in 254 No, the states based on neutron configurations are at much higher excitation energy. In going to 252 No (N = 150), the energy of the neutron 8− state is lowered dramatically as the Fermi surface moves below the N = 152 gap between the 9/2− [734]ν and 7/2+ [624]ν states, whilst that of the proton states should remain rather constant. One can extend the discussion to 250 Fm, where one would expect that the states based on proton configurations move to much higher energies, as the Fermi surface now moves into the deformed shell gap at Z = 100 between the 1/2− [521]π and 7/2+ [633]π states. This systematic comparison can therefore give valuable information concerning the location of the deformed shell gaps and single-particle levels in the deformed region. The single-particle energies calculated with Woods-Saxon potentials give a good reproduction of the excitation energies of the known K -isomer in 254 No [78]. As yet, there are very few calculations of these two-quasiparticle states using self-consistent methods. An extensive and systematic study using Hartfree-Fock–Bogoliubov theory with the Gogny D1S interaction was perfomed by Delaroche et al. [58], and calculations using the Skyrme SLy4 interaction yield the single-particle spectra shown in Fig. 24 (taken from the work of Chatillon et al. [122]). It can be seen that the deformed shell gaps are predicted at N = 150 and Z = 98 or 104, rather than N = 150 and Z = 100 indicated by experiment. The 1/2− [521]π and 7/2− [514]π configurations originating from the 2f5/2 and 1h9/2 shells are close together at the deformation expected for nuclei in this region, which means that the excitation energy of the 3+ level in 254 No is probably reasonably reproduced. However, the 9/2+ [624]π level from the 1i13/2 shell is probably too high, which would result in a very high excitation energy for the K π = 8− isomer. A lowering of the i13/2 level would open up the gap at Z = 100 and give a better reproduction of the experimental data, though how to achieve this in a self consistent theoretical manner is not clear. A similar argument could be made for the neutron 1j15/2 shell, which if lowered would bring the 9/2− [734]ν and 7/2+ [624]ν states closer together and open up the N = 152 gap. On the proton side, recent data on the α decay of mendelevium and lawrencium isotopes also suggest a lowering of the 1i13/2 shell would give better reproduction of the data (see Section 5). 4. Structure of odd-N , even-Z nuclei In this chapter we will first discuss recent in-beam experimental work on 253 No, the only odd-neutron nucleus beyond fermium studied in in-beam work. Then we review the growing body of experimental data for the neutron numbers N = 145 − 157. 4.1. In-beam studies of 253 No In-beam spectroscopy of

253

No is a very challenging task. The cross section of the

207

Pb (48 Ca,2n)253 No reaction is

σ = 1 µb and thus among the largest cross sections in this region, making 253 No an obvious choice for the first in-beam

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Fig. 24. Single-particle spectra of 250 Fm for protons (top) and neutrons (bottom) obtained with the SLy4 interaction. The vertical grey bar indicates the range of ground-state deformation predicted for this and neighboring nuclei. Taken from the work of Chatillon et al. [122].3

experiments on an odd-neutron transfermium nucleus. An experiment aimed at in-beam conversion electron spectroscopy using sacred [173] has not yielded a level scheme. However, the branching ratio between interband mixed M1/E2 transitions and intraband stretched E2 transitions is governed by the interplay of the quadrupole moment Q0 , the collective g-factor of the rotating deformed core, usually taken as gR = Z /A and the g-factor gK of the single particle configuration upon which the band is built. The γ ray branching ratio is then proportional to the square of the ratio of (gK − gR )/Q0 [174]: I (M1/E2; J → J − 1) I (E2; J → J − 2)

=

(gK − gR )2 Q02

· f (J ).

The spectral shape clearly preferred the main flow of intensity through bands with strong M1 transitions built on the 9/2− [734] configuration with a g-factor g = −0.25. A flow of intensity through bands without strong M1 transitions was expected for the 7/2+ [624] configuration with a g-factor g = +0.28, see Fig. 25. The first γ ray experiment aimed at unveiling the rotational structure of 253 No was performed at anl using the combined gammasphere and fma setup [175,176]. Although the available statistics was low, the large coincidence efficiency of gammasphere allowed the construction of a level scheme which tentatively placed the two observed bands as excited bands built on the 7/2+ [624] configuration. These in turn decayed to the ground state built on the 9/2− [734] configuration expected from systematics. The detected γ rays were all interpreted as stretched in-band E2 transitions. The expected interband M1 transitions are of lower energy and thus highly converted, so it was not expected to be able to observe any of the M1 transitions in this experiment. Fig. 25 shows the level scheme deduced in [175]. The placement of the observed bands as excited bands was mostly due to the observed very large intensity of a broad gamma peak at 350–355 keV. The low statistics and the uncertain placement of the bands prompted a new experiment performed at Jyväskylä using the jurogam/ritu/great combination with the same reaction [177,178]. The total gamma ray spectrum of 253 No is shown in Fig. 26. The large number of low-lying M1 transitions is clearly seen. The assignments of transitions to two bands from [175] are confirmed, and the newly observed interband transitions fix the relative excitation energy of the bands. Note that the strikingly large intensity around 350 keV cannot be confirmed in this experiment and must therefore be put down to an artifact of the low statistics in the earlier gammasphere experiment.

3 A. Chatillon et al., Eur. Phys. J. A 30, 397 (2006), Fig. 14. Reprinted with kind permission of Springer Science and Business Media.

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699

Fig. 25. Left: The top panel shows the electron spectrum for 253 No after an appropriate background has been subtracted. The two lower panels show the results of two simulations based on the configurations 9/2− [734] (g = −0.25) and 7/2+ [624] (g = +0.28). Taken from [173].4 Right: Proposed tentative level scheme for 253 No taken from [175].5 The observed bands are suggested to be built on the excited 7/2+ [624] configuration. Note the occurrence of several transitions with energies between 350 and 355 keV, especially in the decay out of the bands to the ground-state band.

Fig. 26. Left: Gamma ray spectrum of 253 No taken with jurogam. The stretched intraband E2 transitions are marked, a number of low-lying M1 transitions can be seen. Right: Proposed level scheme for 253 No as discussed in the text. Reproduced from work shown in [177,178].

After the main argument to place the bands on top of the excited 7/2+ [624] structure has been weakened, one has to query if the placement of the observed bands is still appropriate or if they can indeed be built on the 9/2− [734] ground-state configuration, as suggested earlier [173]. To this end one can compare the observed branching ratios to predictions based on the two different configurations. Furthermore one can compare the moment of inertia to calculations performed in the relativistic mean field model by Afanasjev et al. [56], shown in Fig. 27. Both clearly favour an assignment of the 9/2− [734] configuration for both bands, which must now be seen as the two signature partners of the ground-state rotational band [177,178]. The finally proposed level scheme is shown in Fig. 26. Spin assignments remain tentative, as they require the placement of a 132 keV 11/2− → 9/2− transition which is fully obscured by the intense No X-rays. 4.2. Systematics of single-particle states When discussing data relating to a certain neutron number, it is difficult to restrict the discussion to the region of Cm and heavier nuclei, as clearly for the lower neutron numbers there exist several well studied nuclei in the lighter actinide region, 4 R.-D. Herzberg et al., Eur. Phys. J. A 15, 205 (2002), Fig. 3. Reprinted with kind permission of Springer Science and Business Media. 5 P. Reiter et al., Phys. Rev. Lett. 95 032501 (2005) Fig. 2. Reprinted with permission. Copyright (2007) by the American Physical Society.

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Fig. 27. Left: Branching ratios of the interband and intraband transitions compared to the ratios expected for the two configurations 9/2− [734] (blue, top) and 7/2+ [624] (red, bottom). The former is clearly favoured. Reproduced from work shown in [177,178]. Right: Comparison of the moments of inertia of the bands to those calculated by Afanasjev [56]. To obtain the correct low-spin behaviour we postulate a transition at 132 keV, obscured by the large No X-rays. This fixes the spins of the assigned levels (From [177,178]).(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

especially around the technologically important U and Pu isotopes. While a detailed review of the data is beyond the scope of this article, they provides a much-needed anchoring point for the assignment of Nilsson labels to states along alpha-decay chains. We have therefore chosen to start the discussion of systematics at N = 145, which is the lowest neutron number of any Cm isotope for which definite Nilsson assignments have been made. We also limit our more detailed discussions to data that have been published after the relevant cutoff dates for entry into the Evaluated Nuclear Structure Data File (ENSDF) data base, and refer the reader to the evaluated data where they are available. This work also builds on the recent review of experimental work for elements with Z ≥ 100 [30]. It is always instructive to compare the experimentally assigned levels to theoretical predictions. Indeed, the ultimate goal of this programme of research is to pin down the detailed shell structure of the heaviest nuclei. To this end a large theoretical effort is currently under way in many groups, which in itself would fill the pages of an entire review article with ease. Thus for the current work we will firmly focus on the experimental work, and only compare systematic trends rather than giving detailed criticisms of the various approaches. A few words of caution. The last large scale efforts to establish the single-particle structure of heavy nuclei were undertaken in 1990 by Jain, Sheline, Sood and Jain [179] and earlier by Chasman [62]. There, the authors use different pairing models to extract intrinsic single-particle levels from the experimentally observed states and caution that this procedure introduces a model dependency into the extracted single-particle levels. We will therefore not attempt a similar approach, but limit our discussion to the systematics of the experimental levels so as to not introduce any arbitrary bias into this review of experimental progress. A lot of effort has been spent to determine the single particle structure in this region theoretically in self-consistent approaches, see e.g. the recent reviews by Bender [55] and Afanasjev [56] and references therein. For consistency we shall show the comparisons to the calculations of Parkhomenko and Sobiczewski [48] only, which are available for all nuclei studied here and show comparisons to other approaches where they are available. This is in no way intended to prefer one set of calculations over the others, but as a choice to have a common baseline for all nuclei as a starting point for discussion. 4.2.1. N = 145 The N = 145 nucleus 241 Cm has been studied through the EC decay of 241 Bk [126] and α decay of 245 Cf [181,182] and reviewed by Martin in [183]. The ground state is tentatively assigned as the 1/2+ [631] Nilsson configuration [182], with the 5/2+ [622] and 7/2+ [624] configurations at 267.8 keV and 420.2 keV, respectively [126,183]. The N = 145 nucleus 243 Cf has recently been studied through the α decay of 255 Rf → 251 No → 247 Fm → 243 Cf [182,184]. The entire decay sequence is reproduced in Fig. 28. Here α –γ –γ coincidences support the assignments of single-particle levels based on systematics. The ground state of 247 Fm has previously been assigned as the 7/2+ [624] configuration. From the favoured α decay one concludes that the state populated in 243 Cf also has this configuration and decays via set of gamma rays 166.8, 141.8, 121.8 and 82.2 keV. The 166.8 and 141.8 keV transitions are assigned M1 character from the observed K X-ray intensities. From the systematic trends of the rotational energies found in bands built on the 1/2+ [631] and 5/2+ [622] states in neighboring nuclei, the 166.8 and 121.8 keV transitions were interpreted as feeding rotational states 5/2+ and 7/2+ built on the 5/2+ [622] configuration, while the 141.8 and 82.2 keV transitions were interpreted as populating the 3/2+ and 5/2+ rotational states built on the 1/2 [631] ground state. However, the energy difference between the 1/2+ ground state

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Fig. 28. Alpha decay sequence of 255 Rf →

251

No →

Fig. 29. Systematics of the experimental single-neutron levels in N = 145 nuclei lines.

247

237

701

Fm → 243 Cf (taken from [184]6 ).

U,

239

Pu,

241

Cm and

243

Cf. Tentative levels are shown with dashed

and the first rotational 3/2+ level is typically less than 10 keV and has not been observed directly but taken from systematics as (7 ± 2) keV. This introduces an uncertainty in the assignment of excitation energies in 243 Cf. The assigned configurations are in agreement with the assignments of the lighter N = 145 isotopes 239 Pu [185] and 237 U [186]. We show the experimental levels in Fig. 29. 4.2.2. N = 147 The N = 147 isotone 243 Cm has been studied through the α decay from 247 Cf [187],  decay [188] and through the 244 Cm(d, t ) pickup reaction [66]. Its ground-state spin and parity have been determined as J π = 5/2+ via paramagnetic resonance [189], and thus the assignment of the 5/2+ [622] Nilsson configuration to the ground state is straightforward. The use of the 244 Cm(d, t ) pickup reaction allowed assignments of a number of Nilsson configurations to excited levels. The assignment of the 133 keV level as the 7/2+ [624] configuration determines the ground-state spin of 247 Cf. Fig. 30 shows all assigned Nilsson levels of all available N = 147 isotones. The nucleus 245 Cf was populated in α decay [190,182]. A discrepancy of 40 keV between the α energies for the decay of 249 Fm of [190] E = 7.52(3) MeV and those measured in [182] was attributed to the summing of the α line with conversion electrons. Its ground-state configuration is assigned on the basis of an unhindered α transition at 7142 keV which is interpreted as a ground-state to ground state decay from 245 Cf to 241 Cm, as no emitted γ rays or summing with

6 F.P. Hessberger et al., Eur. Phys. J. A 30, 561 (2006), Fig. 5. Reprinted with kind permission of Springer Science and Business Media.

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Fig. 30. Systematics of the experimental single-neutron levels in N = 147 nuclei 239 U [185], 241 Pu[183], 243 Cm, 245 Cf and 247 Fm. Tentative levels are shown with dashed lines.

conversion electrons were observed. This indicates that the ground-state configuration of 245 Cf should also be 1/2+ [631], thus establishing a strongly decreasing trend for the energy difference between the 5/2+ [622] and 1/2+ [631] Nilsson orbitals [182]. The structure of 247 Fm was also studied in [182,184] in the α decay of 251 No, see Fig. 28. The observation of a narrow α line at 8612 keV suggests that the ground states of 251 No and 247 Fm are connected by an unhindered decay with no electron summing. The isomeric state in 251 No is assigned the 1/2+ [631] configuration based on an estimate of the necessary change in K -value for such a long lifetime. Thus, unhindered α decays to the 4.3 s isomer in 247 Fm suggests the same structure for the isomer there. A comparison with the well studied 1/2+ [631] isomers in 241 Pu and 243 Cm with half-lives T1/2 = 0.88 µs and T1/2 = 1.08 µs which decay to the 5/2+ [622] configuration shows a difference in half-life of six orders of magnitude, suggesting that in 247 Fm the 5/2+ [622] configuration cannot lie below the isomeric state [182]. Thus the authors suggest a ground-state configuration of 7/2+ [624] for both ground states in 247 Fm and 251 No. No structure information is available on heavier N = 147 isotones. The isotope 249 No had been previously reported [191], but the observed activity has been reassigned to 250 No [118,192]. The nucleus 253 Rf was studied in [193], but no structure information was obtained.

4.2.3. N = 149 The nucleus 245 Cm has been well studied through α decay from 249 Cf [194,195],  decay of the 3/2− ground state of 245 Bk [196,188], β − decay of the (5/2)+ ground state of 245 Am [197,198] and the 246 Cm(d, t ) pickup and 244 Cm(d, p) stripping reactions [66]. It has recently been reviewed and evaluated with a cutoff date of 1993 (see [199] and references therein). The only spectroscopy work after the cutoff date has been the α decay work of Ardison [194,195], which modifies the existing level scheme in several places, but leaves the assignments of the low-lying Nilsson configurations intact. Importantly, spin assignments are on a very firm footing as the ground-state spin has been measured as 7/2 in paramagnetic resonance [200]. We show the systematics of the Nilsson states in the N = 149 isotones in Fig. 32. Data for 247 Cf has recently been evaluated [201]. The ground-state configuration is expected to be 7/2+ [624]. Support for this assignment comes from the unhindered α decay of the ground state to the 133 keV level in 243 Cm, which is assigned as 7/2+ [624] in 244 Cm(d, t ) [66]. Other Nilsson configurations have mainly been assigned on the basis of systematics and similarity of rotational properties [201]. The nucleus 249 Fm has been the subject of intense study since the last evaluation [202]. It has been studied through the α decay of 253 No [203–207,182,29,173,190], and the associated level scheme is shown in Fig. 31. The main α decay from the 9/2− ground state of 253 No populates the 9/2− [734] state at 280 keV, which in turn decays to the rotational band built on the 7/2+ ground state of 249 Fm. The multipolarity of the observed γ transitions at 280, 222 and 151 keV has been determined as E1 from internal conversion coefficient measurements [29,204]. In addition, a highly-converted transition at 209 keV has been observed as a γ ray [208] and internal conversion electrons [204], which is interpreted as the decay of the 5/2+ [622] level. We expect an isomeric half-life of 20–30 µs for this state from systematics, but no value is given in the literature. An additional γ transition at 670 keV has been tentatively assigned to the decay of the 7/2− [743] configuration in analogy to the decay pattern in 247 Cf [208,209]. The nucleus 251 No has also recently been studied [184,210,182] both through the α decay of 255 Rf and through the decay of isomeric states in 251 No produced directly in the reaction 206 Pb (48 Ca, 3n) 251m No. In both cases γ transitions at 143 and 203 keV were observed, which are interpreted as the decay from the 9/2− [734] configuration into rotational states built on the ground state 7/2+ [624] configuration in analogy to the situation in 249 Fm. The entire decay sequence is shown in Fig. 28.

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703

Fig. 31. Left: Gamma rays observed in prompt coincidence with α decays of 253 No. The transition at 209 keV is clearly observed. Right: Decay systematics of N = 151 isotones into excited states of N = 149 isotones, taken from [208].7

Fig. 32. Systematics of the experimental single-neutron levels in N = 149 nuclei 243 Pu [213], 245 Cm, 247 Cf, 249 Fm and 251 No. Tentative levels are shown with dashed lines.

We correct a small error in the figure taken from [184] where the arrows for the transitions at 143 and 203 keV were drawn from the wrong level. The isomeric 1/2+ [631] configuration is also placed in the level scheme at E = 106 ± 6 keV, obtained as the difference 251g in α decay Q -values Qα (251m No − 247m Fm) − Qα ( No − 247m Fm). The long half-life of T1/2 = 1.02 s again rules out the + presence of the 5/2 [622] configuration below this energy (see discussion of 247 Fm). A second isomeric state is observed in 251 No with a half-life of ' 2 µs at an excitation energy above 1.7 MeV [184], but the discussion remains tentative. Data on 253 Rf is sparse. The nucleus was produced only recently [193] and found to decay by spontaneous fission. No assignments of its ground-state spin were made. Model calculations for the ground state [180,48] indicate a near degeneracy of the 7/2+ [624] and 9/2− [734] configurations to within 20 keV. 4.2.4. N = 151 The nucleus 247 Cm is available for study via α decay [211], beta decay from 247 Am [212,136] as well as through singleparticle transfer reaction studies [66]. Its structure has recently been re-investigated by Ahmad through the α decay of 251 Cf [214]. Its ground-state spin has also been determined through paramagnetic resonance [189], putting spin assignments on a firm basis. All data prior to 2003 has been evaluated in [201]. The ground-state configuration is firmly established as 9/2− [734] and it is straightforward to interpret the isomeric level at 227 keV with a half-life T1/2 = (26.3 ± 3) µs as the 5/2+ [622] configuration from the assignment of M2 character in (d, t ) data [66]. The 7/2+ [624] configuration is established at 285 keV as the 285.4 γ ray is determined as E1 in (d, p) and (d, t ) data [66]. Beyond this level the assignments of excited configurations are more tentative. The evaluators tentatively place

7 F.P. Hessberger et al., Eur. Phys. J. D 45, 33 (2007), Fig. 5+6. Reprinted with kind permission of Springer Science and Business Media.

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Fig. 33. Proposed level scheme of 251 Fm from α decay work of [220,222]. Reproduced from [222].8

the 1/2+ [620] and 1/2+ [631] levels at 405 and 506 keV respectively [201]. The 405 keV level is an isomer with a half-life T1/2 = (100.6 ± 6) ns. The isotope 249 Cf has a half-life of T1/2 = (251 ± 2)yr and is therefore available for inelastic (d, d0 ) scattering studies [68] in addition to the β − decays from 249 Bk [215] and EC decay from 249 Es [216]. Alpha decays from 253 Fm have also been studied [217] and evaluated [202]. The ground-state configuration is determined as 9/2− [734] from the observed, unhindered α decay to the analogous state in 245 Cm. A low-lying isomeric state at 144 keV is identified with the 5/2+ [622] configuration based on systematics and the measured M2/E3 character of the γ transition to the ground state [216]. The 7/2+ [624] configuration was assigned on the basis of the log ft value in the EC decay from 249 Es [216]. None of these configurations were observed in the (d, d0 ) measurement, which interpreted all excitations as collective excitations coupled to the ground state [68]. The isotope 251 Fm has been studied through the α decay of 255 No [218–220] and evaluated recently [221]. One further study has been made after the cutoff date for [221], again through the α decay of 255 No [222] produced. Prompt and delayed α –γ coincidences were measured. The use of implanted α decays, however, results in significant electron-α summing which did not allow an observation of fine structure seen in earlier work [220]. The ground state is given as 9/2− [734] in agreement with systematics. The isomeric state observed earlier is confirmed as 5/2+ [622] from the systematics of its energy and halflife of T1/2 = (21 ± 3) µs. The earlier observed γ ray at 191 keV is seen in prompt coincidence with 255 No α decays, whereas a γ transition at 200 keV is seen in delayed coincidence. Thus the placement of the isomeric level at 191 keV in [221] must be corrected. The 191 keV transition feeds the isomer, which in turn decays by a 200 keV γ ray [222]. The conversion coefficient for the 200 keV transition is determined to be in agreement with a mixed M2/E3 multipole character, again confirming the assignment of the 5/2+ [622] level. The level scheme proposed in [222] is shown in Fig. 33. The assignment of the 7/2+ [624] level is much more tentative. The level at 353.8 keV decays via a 353.8 keV gamma ray to the ground state. Only M1 multipolarity is excluded for this level from the non-observation of K X-rays with α events at an energy corresponding to the full summing of the alpha energy and the fully converted 353.8 keV transition at 8165 keV [222]. It is thus tentatively assigned E1 multipolarity and the 7/2+ [624] configuration based on comparison with systematics and calculations [180,48]. It should be noted, that in earlier work [220] a 7/2+ [613] configuration was assigned to a level at 378 keV, which is not seen in this study. The 1/2+ [620] level at 558 keV is tentatively assigned as the same configuration as the ground state of 255 No on the basis of an unhindered α decay. However, the ground state of 255 No is assigned on the basis of systematics only. A great amount of effort has been spent on the study of 253 No. We have discussed the in-beam spectroscopy in the previous section and are confident that the ground-state configuration is indeed 9/2− [734] [175,177,178]. Additional information on single-particle levels in 253 No again comes from decay work either through the α decay of 257 Rf or direct observation of the decay of isomeric states [223,193,224–226,203]. In earlier work an isomeric state was observed through 8 F.P. Hessberger et al., Eur. Phys. J. A 29, 165 (2006), Fig. 1. Reprinted with kind permission of Springer Science and Business Media.

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705

Fig. 34. Systematics of the experimental single-neutron levels in N = 151 nuclei 245 Pu [159], 247 Cm, 249 Cf, 251 Fm, 253 No and 255 Rf. Tentative levels are shown with dashed lines, isomers with thicker lines. The data for 245 Pu has only very recently been obtained and added here for completeness.

the observation of delayed K X-ray emission [223]. However, in [193] the energy of the isomeric state was tentatively determined via α decay to be only 124 keV, less than the K binding energy EBK = 149 keV of electrons in nobelium, and thus incompatible with the earlier measurement. This was realized in a later experiment where the decays from the 261 Sg → 257 Rf → 253 No sequence were analysed resulting in a placement of the isomeric 5/2+ [622] configuration at ' 170 keV. In α –γ coincidences the γ decay from this isomer was observed via a 167 keV gamma ray [224,225]. Recently the situation has been corroborated through the isomer spectroscopy work of [177,203]. The energy of the isomer was determined to be 167 keV in agreement with [224,225]. Through direct measurement of the internal conversion electrons, the multipolarity of the 167 keV line was determined to be M2, confirming assignment of the 5/2+ [622] configuration to the isomer in agreement with systematics. The half-life has been measured to be T1/2 = (31.1 ± 2.1) µs, in agreement with the value given by [223] of T1/2 = (31.3 ± 4.1) µs. A second isomeric state with half-life T1/2 = (970 ± 200) µs has been observed [226,203] and no firm decay path or structure were assigned. The 7/2+ [624] configuration was placed at 355 keV from earlier in-beam work [175] and is not confirmed in later work (see Section 4.1), although the energy would nicely fit into the systematics. We therefore do not assign an experimental energy to the 7/2+ [624] orbital in this nucleus. The nucleus 255 Rf has been subject to a number of recent studies [193,210,184]. In earlier work indications for an isomeric state with a half life of one second was reported [193], but could not be confirmed in subsequent work with higher statistics [210]. Thus only the ground state is tentatively assigned the configuration 9/2− [734] based on systematics. We show the systematics of all experimentally assigned single-neutron configurations in N = 151 isotones in Fig. 34. 4.2.5. N = 153 The nucleus 249 Cm is only one neutron away from the long-lived 248 Cm isotope and is thus well studied in a number of different reactions, including thermal neutron capture (n, γ ) [227], α decay from 253 Cf [228] and the (α, 3 He) single-particle transfer reaction [67]. It has been reviewed in 1999 [202] and not been revisited experimentally since that time. We show the experimentally assigned Nilsson configurations in Fig. 35. The tentative assignment of a 3/2− [752] state at 730 keV is not confirmed in the (d, p) data of [229] and remains unidentified in both 249 Cm and 251 Cf. One must also query the assignments of configurations to the 1/2− states observed, especially the 1/2− [501] state at 917 keV assigned mainly from (n, γ ) work [227]. There, the authors find an anomalously low energy for this configuration which they attribute to large single-particle phonon coupling, lowering the energy significantly. Thus, this state contains strong admixtures and is not a good state to compare to calculated pure single-particle levels. The nucleus 251 Cf has been studied extensively in the (d, p) reaction [229] and recently been revisited in the EC capture from 251 Es [70,230]. Alpha decay studies from 255 Fm [230–236] and β − decay from 251 Bk [238] also provided a full set of spectroscopic data with reliable assignments of Nilsson configurations. The data are fully evaluated in [221]. Once one gets further away from suitably long-lived isotopes that can be fashioned into targets for pickup or stripping reactions, the data becomes much more sparse. The only studies of 253 Fm have been made through α decays from 257 No with a gas-jet technique [83]. The decay from the ground state of 257 No, with a probable configuration of 3/2+ [622], proceeds via an unhindered α decay to the 124 keV level in 253 Fm, which decays via three M1 transitions to rotational states built on the ground state, which is in good agreement with the 1/2+ [620] assignment expected from systematics [239]. No α decays have been observed into excited states of 255 No, and thus only the ground state is assigned the 1/2+ [620] configuration from systematics [240]. The situation is similar in 257 Rf [241]. However, new data have been taken and should be published soon [225].

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Fig. 35. Systematics of the experimental single-neutron levels in N = 153 nuclei 249 Cm, 251 Cf, 253 Fm, 255 No and 257 Rf. Tentative levels are shown with dashed lines, isomers with thicker lines.

4.2.6. N = 155 and 157 Structural information on N = 155 and N = 157 isotopes is very sparse. Most ground-state spins are assigned tentatively on the basis of systematics only. A systematic experimental reinvestigation of single-particle levels in this area would be a challenging but fruitful and rewarding task. The ground state of the 251 Cm nucleus is tentatively assigned (1/2+ ) on the basis of observed β decay patterns rather than the 7/2+ [613] configuration expected from systematics [221]. However, it becomes increasingly difficult to argue on the basis of systematics if the corroborating datasets are just as tentative. Excited states in 253 Cf have been populated through α decays from 257 Fm [242,239]. The ground state is assigned the 7/2+ [613] configuration based on the observed β decays to the ground state and first excited states in 253 Es where spins are known from optical spectroscopy [243]. The excited state at 241 keV is tentatively assigned as 9/2+ [615] in agreement with earlier work [244]. For 255 Fm, again only the ground-state configuration is assigned as 7/2+ [613] based on the favoured α decay to the same structure identified in 251 Cf [230,232,231,233–236], but no further excited configurations were assigned. In a recent work by Ahmad et al. [237], the EC decay of 255 Md was studied and two γ rays at 2231.1 and 169.5 keV were observed. These transitions were interpreted as the decay to the 7/2+ [613] ground state and the first rotational 9/2+ state built on it. The 231.1 keV level was tentatively assigned as the 9/2+ [615] configuration, based on the analogy with 253 Cf [237]. The ground state of 257 No was tentatively assigned 7/2+ [613] in the literature [241]. However, a recent study by Asai et al. has assigned the ground state of 257 No as the 3/2+ [622] configuration, based on the observed α –γ and α -electron coincidences in the decay into excited states in 253 Fm [83]. The ground state of 259 Rf is predicted to be 1/2+ [620] [180], but the alpha decay does not populate the (1/2+ ) ground state of 255 No [241], and is thus an unlikely assignment. Alpha decays from 263 Sg have recently been observed [246], but the authors make no attempts to deduce 259 Rf structure information. Information on N = 157 isotones is very sparse. Only the ground-state configurations of 255 Cf and 257 Fm are assigned as (7/2+ [613]) and (9/2+ [615]), respectively [240]. In 257 Fm, this assignment is based on an unhindered α decay to the tentatively assigned 9/2+ [615] configuration in 253 Cf. The α decay of 261 Rf has recently been studied [247], but no information about excited states in 257 No is deduced. The recent studies of Asai of the α decays of 259 No and 261 Rf, however, assign a probable ground-state configuration of 9/2+ [615] to both nuclei [245]. 4.2.7. Summary It is instructive to look at the growing wealth of data reviewed above with a view to find the best strategies to expand them further, i.e. to identify the ‘‘best’’ production mechanisms to study excited states. Obviously, data are most reliable if information from several experimental techniques can be combined to give a coherent picture. However, that usually requires long-lived isotopes in close vicinity to the nucleus to be studied, so that targets can be made for the various light ion induced reactions, ideally including single-particle transfer measurements and inelastic scattering, e.g. of deuterons, to identify collective levels. The comparison of the experimental data presented above to model calculations is slightly unfair, as the experimentally assigned states are subject to pairing and mixing with other configurations and collective states with the same spin and parity. One should therefore be careful not to overstate any perceived discrepancies, but concentrate on the systematic behaviour across a range of isotopes. In Fig. 36, we show as an example the calculated single-particle energies of Parkhomenko and Sobiczewski for N = 149 and N = 151 isotones [48] lying below 600 and 800 keV, respectively. Similar comparisons can be found for a variety of the-

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707

Fig. 36. Calculated single-neutron spectra for N = 149 and N = 151 isotones shown as examples of the smoothly varying energy systematics expected from macroscopic–microscopic approaches. The data are taken from [48].

oretical approaches: see e.g. the work by Cwiok [180] which compares macroscopic microscopic and Skyrme Hartree–Fock approaches and the extensive work by Bender and Heenen using Skyrme Hartree–Fock approaches, e.g. [161,55]. For systematic calculations using the Gogny interaction see, e.g., the work of Delaroche et al. [58]. For systematic relativistic mean field calculations in this region, see the work of Afanasjev et al. [56]. A great wealth of calculations are available on a number of individual nuclei. However, a detailed comparison of each case would go beyond the scope of this article. The most striking feature is the very smooth variation of the single-particle states with proton number, even strongly varying orbitals such as the 1/2− [501] orbital do so in a systematic manner. This is in contrast to the experimentally observed behaviour, where variations between neighbouring nuclei are often quite pronounced. This can be for several reasons; firstly, it may reflect the fact that the spectroscopic factor of the assigned configuration may well be significantly less than unity, with no easy experimental way to determine them except in lucky cases. Secondly, the assigned configuration may have been assigned wrongly. The more tentative assignments given above are often those expected from systematics, or through guidance from theory. Thirdly, the model calculations may not include all of the physics that governs the behaviour of the single-particle levels. It is therefore imperative to achieve a fully self-consistent theoretical framework with sufficient accuracy and predictive power to allow the data obtained in the deformed heavy actinide and transfermium region to be used in extrapolations to heavier, more spherical systems, and ultimately to the island of stability. Such theoretical efforts are currently under way in several groups worldwide. 5. Structure of odd-Z , even-N nuclei In the following section the structure of odd-Z , even-N nuclei is reviewed. As in Section 4, focus is firmly placed on experimental data, with limited comparisons to theoretical data. For the main part, the systematic data have been taken from the available tables of evaluated data, with some additions from recent publications. The data available for odd-proton nuclei are clearly more sparse than for the odd-neutron cases. In the first part of this section the systematics of single-particle states from the isotopes of berkelium to dubnium are reviewed, followed by discussion of the two cases studied in-beam, 251 Md and 255 Lr. 5.1. Systematics of single-particle states 5.1.1. Berkelium Isotopes The systematics of known single-particle states in the berkelium isotopes with mass numbers from 239 to 251 are shown in Fig. 37. Inspection of the Nilsson scheme shown in Fig. 2 shows that the 97th proton can be expected to occupy either the

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Fig. 37. Systematics of single-particle states in the berkelium isotopes. The mass number is marked along the x-axis.

3/2− [521] or the 7/2+ [633] state, which is borne out by the assignments shown in the figure. Hatsukawa et al. studied the α -decay systematics of the light einsteinium isotopes and, in general, observed several groups of α decays for each of the isotopes from 243−249 Es [249]. The starting point for their assignments was that in 249 Es the ground state had been denoted a Nilsson configuration of 7/2+ [633] on the basis of the EC capture decay to 249 Cf, and that the ground state of 245 Bk was assigned the 3/2− [521] configuration. It was concluded that the favoured α -decay that they observed was 7/2+ [633] to 7/2+ [633], and the transition to the (suggested) 3/2− [521] ground state was not observed. Three α groups were observed from the decay of 247 Es, which were deduced to populate a rotational band with the 7/2+ [633] configuration based on the rotational parameter extracted for the band. No decays to the possible 3/2− [521] state were observed. In the evaluated data, the ground state is nevertheless assigned to 3/2− [521] in analogy with 245 Bk. The excitation energy of the 7/2+ [633] state is estimated to be around 46 keV, as shown in Fig. 37. In the decay of 245 Es, four α groups were observed, three to a rotational band and one unfavoured decay. On the basis of the rotational parameter, the band was assigned to the 3/2− [521] configuration, and the unfavoured decay to the 7/2+ [633] 241 Bk ground state. This lead to the conclusion that the ground state of 245 Es must be 3/2− [521]. In the decay of 243 Es, two α decay groups were seen, and on the basis of hindrance factors and intensity ratios it was concluded that the favoured decay was 3/2− [521] to 3/2− [521]. This suggests that the ground state of 243 Es is 3/2− [521] and that of 239 Bk 7/2+ [633]. An extensive study of 247 Bk has been made by Ahmad et al., via the 246 Cm(α, t ) reaction, EC of 247 Cf and alpha decay of 251 Es [248]. The ground state of 247 Bk had previously been assigned to the 3/2− [521] configuration on the basis of favoured α decay to a 3/2− state in 243 Am [250]. The transfer reaction data and favoured α decay from 251 Es were suggested to support this assignment. A level at 40.8 keV was assigned to the 7/2+ [633] state on the basis of the (α, t ) data, along with consistent α decay hindrance factors and log ft values. It was also possible to identify states attributed to the 5/2+ [642], 5/2− [523], 1/2+ [400] and 1/2− [521] configurations. Detailed discussion of these assignments can be found in [248]. The most well-studied berkelium isotope is 249 Bk, in which the ground state spin and parity have been determined to be 7/2 + through electron paramagnetic resonance studies [251]. Using a pure sample of 253 Es extracted from 253 Cf source material produced in the High Flux Isotope Reactor at Oak Ridge, another extensive study was performed by Ahmad and coworkers. The α decay of 253 Es was analysed along with the β − decay of 249 Cf, together with data from previous 248 Cm(α, t ) and (3 He, d) reactions [252]. The 3/2− [521] state was identified at an excitation energy of only 8.8 keV, along with the following single-particle levels: 1/2+ [400] at 377.6 keV, 5/2+ [642] at 389.2 keV, 1/2− [530] at 569.2 keV, 1/2− [521] at 643 keV, 5/2− [523] at 672.9 keV and 9/2 + [624] at 1075.1 keV. Again, detailed discussion of the assignments can be found in the relevant reference [252]. In 251 Bk the ground state has been established as 3/2− [521] on the basis of log ft values for the decay to 251 Cf and from 251 Cm, which rule out the possibility of 7/2. The excited 7/2+ [633] state has been assigned on the basis of favoured α decay from 255 Es [253–256] and the deduced rotational properties [256]. 5.1.2. Einsteinium isotopes A plot of the known single-particle states in the einsteinium istopes is shown in Fig. 38. In 241 Es two states separated by ∆E = 41 ± 28 keV have been suggested from the α decay of 245 Md [257], but as the 3/2− [521] and 7/2+ [633] states are both expected [180] at low excitation energy, no assignment has been made and the levels are not shown in the figure. A thorough discussion of the systematics of the einsteinium isotopes can be found in the work of Hessberger et al., where detailed α –γ coincidence spectroscopy of the mendelevium isotopes 247−253 Md has been performed [258]. A plot of the deduced partial decay schemes from that work is reproduced in Fig. 39 including a γ ray transition into the first rotational 9/2+ state in 249 Es [224]. It was shown that the γ rays coincident with favoured α decays emitted from the mendelevium isotopes had E1 character. The only pair of single-particle states which can be realistically connected by such transitions are the 7/2− [514] and 7/2+ [633] proton configurations.

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Fig. 38. Systematics of single-particle states in the einsteinium isotopes. The mass number is marked along the x-axis.

Fig. 39. Systematic picture showing the decays of mendelevium isotopes 247−255 Md into excited states in einsteinium isotopes. Observed γ ray transitions are indicated. The structural assignments are discussed in the text. Taken from [258].9

The assignment of 7/2− [514] to the γ decaying level in the einsteinium isotopes in turn establishes that configuration as the ground state in 247−253 Md. Ground-state spins in the einsteinium isotopes are harder to assign. The favoured α decay into 239 Bk observed by Hatsukawa suggested that the ground state of 243 Es is 3/2− [521] — this possibility cannot be ruled out on the basis of the data obtained by Hessberger et al. [258]. In fact, there is weak evidence based on Q-value balances that this may indeed be the case [259,260]. Similar arguments can be made for the decay of 245 Es, hence the 3/2− [521] levels are drawn tentatively below the 7/2+ [633] states in Fig. 39. This is not strictly necessary for 247 Es, as Hatsukawa et al. did not observe an unfavoured decay to the 3/2− [521] state and their data are consistent with a 7/2+ [633] ground state in 247 Es [249]. On the basis of log ft values, the ground states of 249 Es and 251 Es have been assigned to 7/2+ [633] and 3/2− [521], respectively [261,237]. In 251 Es the 7/2+ [633] state is deduced to be at an excitation energy of 8.3 keV, with the 1/2− [521], 7/2− [514] and 1/2+ [400] at energies of 411.0, 461.5 and 661 keV, respectively. In 253 Es, a firm assignment of 7/2+ [633] exists for the ground state from optical spectroscopy [243] and also from atomic-beam magnetic-resonance [262]. The 3/2− [521] state has been established at an energy of 106 keV along with the 7/2− [514] state at 371 keV [263]. The ground state of 255 Es has also been tentatively assigned to the 7/2+ [633] configuration based on the preferred β − decay feeding pattern from the similarly tentative 7/2+ [613] ground state configuration in 255 Cf [264], but, as no γ rays have been measured in the β decays, this assignment must be seen as very tentative.

9 F.P. Hessberger et al., Eur. Phys. J. A 26, 233 (2005), Fig. 3. Reprinted with kind permission of Springer Science and Business Media.

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5.1.3. Mendelevium, lawrencium and dubnium isotopes For the isotopes of elements mendelevium and above we do not present plots of the systematics, as the available data are very sparse. In mendelevium, all isotopes from 247−257 Md have been assigned the ground state configuration 7/2− [514] [258,210,122,237,263]. Recent measurements of Chatillon et al. to study the α -decay scheme of 255 Lr assigned a level at 55 keV in 251 Md to the 1/2− [521] configuration. The 1/2− [521] level is also assigned as an excited state in 247 Md [265,259, 260] which has α and fission branches (bSF ' 23%) [260]. However, its excitation energy is not fixed. In 249 Md a tentative assignment of the excited 1/2− [521] level is made [210]. Assignment of the 1/2− [521] configuration 257 in Db and 253 Lr is based on the isomeric character which suggests a low-spin isomeric state above a high-spin ground state [210]. Due to the low statistics in that experiment, it is unclear whether the state populated by α decays from 253m Lr is also isomeric. The level schemes of 249 Md, 253 Lr and 257 Db as constructed from the α decays [266,210] must be regarded as tentative, with more experimental work to follow [225]. In 255 Lr, the 1/2− [521] configuration was tentatively assigned to the ground state with the 7/2− [514] state at an excitation energy of 35 keV. The level ordering is reversed in 253 Lr, where the ground state is assigned to be 7/2− [514] and the 1/2− [521] level an excited state [210]. It was not possible to determine the excitation energy of the 1/2− excited state in 253 Lr and all these assignments are tentative. 5.2. Discussion The systematics of the einsteinium and mendelevium isotopes provide a nice test for current theories. In the work of Hessberger et al., the systematic behaviour of the einsteinium level energies is compared to the macroscopic–microscopic calculations of Cwiok and also the more recent calculations of Parkhomenko [180,47]. It was noted that there is a maximum in the separation of the 7/2+ [633] and 7/2− [514] states for 251 Es, with N = 152. This maximum can be correlated with the deformation, which should be at a maximum at N = 152. This is related to the fact that the 7/2+ [633] state originates from the 1i13/2 orbital and is downsloping with deformation, whilst the 7/2− [514] state originates from the 1h9/2 orbital and is strongly upsloping with deformation. Both sets of calculations generally reproduce the trend, but the location of the maximum is displaced, and less pronounced than in the experimental data. Further details and discussion can be found in ref. [258]. The work of Chatillon et al. compared the experimental data available for einsteinium isotopes to self-consistent calculations using Hartree–Fock–Bogoliubov (HFB) theory with the Skyrme SLy4 interaction and densitydependent pairing [122]. Calculations of the level energies of 245−257 Md and 247−259 Lr were also presented. The HFB calculations also reproduced the general trend of the separation of the 7/2+ [633] and 7/2− [514] states, but predicted that the ground states of most of the einsteinium isotopes and all the mendelevium isotopes have the 1/2− [521] configuration, which in in disagreement with the available data. Extensive discussion of the location of the 1/2− [521] state and the consequences for the 2f5/2 shell can be found in Chatillon et al. Here we simply state the conclusion that in the HFB calculations the splitting between the 2f spin-orbit partners should be reduced by around 500 keV and the centroid of the 2f levels shifted relative to the 1i13/2 level, such that the Z = 114 gap is opened up slightly. 5.3. In-beam spectroscopy of 251 Md and 255 Lr The structure of 251 Md and 255 Lr has also been investigated in in-beam γ -ray spectroscopic studies using the jurogam array coupled to ritu and great. At Z = 103, 255 Lr is the heaviest nucleus which has so far been studied in-beam. The first experiment to be carried out was the study of 251 Md, which was populated in the 205 Tl (48 Ca,2n)251 Md reaction [267]. The production cross section for 251 Md is of the order of 800 nb. As discussed in Section 4, in-beam γ -ray spectroscopic studies of high-Z nuclei are strongly influenced by the gK factor of the odd particle and the magnitude of (gK − gR ). For K = 1/2, an additional complication comes from the decoupling parameter, a, which can also effect the level structure and M1 transition rates. In the mendelevium isotopes, one expects the 7/2− [514], 1/2− [521] and 7/2+ [633] at low excitation energy. In the work of Chatillon et al., the ratio of M1 to E2 transition rates was calculated and is reproduced in Fig. 40. One can see that for the 7/2− [514] band, one expects that the decay is dominated by E2 transitions, whilst for the 7/2+ [633] band, one expects that M1 transitions dominate. For the 1/2− [521] band, the two signatures are almost degenerate, showing that the decoupling parameter, a, has a value close to 1. The decoupling parameter of this orbital has been determined in 247 Bk and 251 Es, with values of 0.9 and 1, respectively [268,269]. In this case, one expects to only observe a single rotational band of the favoured signature. The experimental recoil-gated γ -ray spectrum obtained in the experiment is shown in Fig. 41, which is rather complex. Limited γ -γ coincidence data was only obtained which showed that only one signature of the rotational band was observed. This lead to the conclusion that the band was due to the 1/2− [521] orbital, with a decoupling parameter close to 1, in agreement with theory. The moment of inertia of the band was also well-reproduced by mean-field theory. No clear candidates for the other K = 7/2 bands could be extracted from the data. Following this successful study, a further experiment was carried out to study 255 Lr in a similar manner. The 255 Lr nuclei were produced using the 209 Bi (48 Ca,2n)255 Lr reaction, with a cross section of the order of 300 nb [270]. The recoil-gated γ -ray spectrum obtained in the experiment is shown in Fig. 42. Experiments of this type are extremely challenging, and the statistics obtained are somewhat lower than those for 251 Md. Despite this, a sequence of γ rays with energies of 197, 247, 295, 341 and 383 keV can be seen. The transition energies are very similar to the K = 1/2 band energies in 251 Md, and the

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Fig. 40. Schematic decay patterns for the three configuration candidates for rotational bands in 251 Md. The numbers labelling the states indicate the ratio T (M1)/T (E2). Taken from [267].10

Fig. 41. Gamma-ray spectrum of a rotational band in 251 Md. Panel (a) shows the data obtained by recoil tagging, while in panel (b) the available coincidence information confirms the band structure. Taken from [267].11

assignment to a rotational band is supported by a limited set of mutually consistent gamma-gamma coincidences. Again, no clear indication of a signature partner for this band can be observed, leading to the conclusion that the band is also based on the 1/2− [521] configuration. Also seen are weaker sequences of γ rays with energies 214, 239, 264, 289, 313, 337, 359 and (383) keV which have (for the two sequences 214, 264, 313, and 239, 289, 337 and (383) keV) similar spacings, and therefore moments of inertia, as some of the ground-state bands known in the even–even nuclei. It is suggested that these sequences are the signature-partner strongly-coupled rotational bands built on the 7/2− [514] state. Further experiments would be desirable (for both 251 Md and 255 Lr) to confirm the assignments. Indeed, these are perfect cases for study with the new sage spectrometer to be constructed in jyfl (see Section 7). 6. Structure of odd-N , odd-Z nuclei The following section briefly reviews the current situation concerning experimental data on odd–odd nuclei in the region. As will be shown, the difficulties in making experimental assignments are further exasperated in odd–odd nuclei due to the additional complexity of having two unpaired nucleons and the residual p–n interaction between them. The angular

10 A. Chatillon et al., Phys. Rev. Lett. 98, 132503 (2007) Fig. 4. Reprinted with permission. Copyright (2007) by the American Physical Society. 11 A. Chatillon et al., Phys. Rev. Lett. 98, 132503 (2007) Fig. 4. Reprinted with permission. Copyright (2007) by the American Physical Society.

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Fig. 42. Gamma-ray spectrum of 255 Lr obtained with jurogam. Transition energies discussed in the text are indicated [270].

Fig. 43. Schematic summary of evaluated nuclear data available in the ENSDF data base in November 2007 for odd–odd nuclei in the region covered by this review. Each isotope is labelled in the same manner as in Fig. 1.

momenta of the unpaired nucleons can be coupled according to the rules suggested by Gallagher and Moszkowksi [271], which state that the parallel spin triplet state should be energetically favoured over the antiparallel singlet state, or: I = Ωp + Ωn

if Ωp = Λp ±

1

and Ωn = Λn ±

2

I = |Ωp − Ωn | if Ωp = Λp ±

1 2

1 2

and Ωn = Λn ∓

, 1 2

(9)

.

(10)

The coupling leads to pairs of isomeric states with different K , which may have a large difference in angular momentum if a high-j orbital is involved in the configuration. The ordering of states and band-heads can also be influenced by rotational effects and due to the residual p–n interaction between the unpaired nucleons. In bands where the spins are coupled to K = 0, the odd and even spin members are shifted in energy relative to each other (Newby shifts [276]). These effects further complicate the analysis, even if the single-particle structure of the neighbouring odd-A nuclei is well-known. The data shown in earlier chapters highlight the fact that this is rarely true, especially for odd-Z nuclei beyond mendelevium. As in the case of odd-A nuclei, a reliable determination of spins and parities may not be possible using a single experimental technique. The reliability of spin assignments increases if a number of observables can be determined, for example through (n, γ ) reactions which provide a particularly powerful probe. A demonstration of the limited experimental progress in these studies can be obtained from inspection of Fig. 43, which shows the experimental assignments for the ground states of odd–odd nuclei in the region covered by this review. This figure should be compared to Fig. 1 of the review of ‘‘Intrinsic and Rotational Level Structures in Odd-Odd Actinides’’ carried out by Sood et al., in 1994 [272] and shows that the majority of the ground-state assignments are identical and that very few new assignments of ground-state spins and parities have been made. The work of Sood et al. and references therein contains rather extensive discussion of experimental techniques, systematics of Gallagher–Moszkowksi splittings and Newby shifts, to which we direct the interested reader [272]. As already stated, little progress has been made in these studies and the ENSDF tables also discuss level assignments in some detail. In

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a similar manner to that for the odd-N nuclei, we mainly focus the following discussion on isotopes which have been given spin and parity assignments (N > 145 and isotopes of Bk and above). 6.1. Bk isotopes The lightest odd–odd Bk isotope which has a ground-state spin and parity assignment is 244 Bk, which was studied by bombarding Am targets with α particles [28] and through the α decay of 248 Es [249]. The ground-state spin and parity assignment is simply based on analogy to the neighbouring odd-A nuclei for the 97th proton and 147th neutron. The assignment given by Sood et al. is (1− ) ([3/2− [521]π ⊗ 1/2+ [631]ν ]), whereas that given in the ENSDF table is (4− ) ([3/2− [521]π ⊗ 5/2+ [622]ν ]). Inspection of Fig. 30 for the N = 147 isotones, shows that the 1/2+ [631] neutron state becomes the ground state in 245 Cf. The 5/2+ [622] neutron state is likely to be at low excitation energy [182], thus either assignment could be correct. Configurations involving the proton 7/2+ [633] state, which should be below 100 keV in 243,245 Bk, are also not discussed. The ground-state spin of 246 Bk is rather firmly assigned to be 2(−) on the basis of log ft values for decays to 2− , 3− and 1− states in 246 Cm [196]. This is consistent with the configuration [3/2− [521]π ⊗7/2+ [622]ν ] expected from the neighbouring odd-mass nuclei, though the Gallagher–Moszkowksi rule would suggest that the 5− state of this combination should be lower in energy, thus the observed isomeric state may not necessarily be the ground state. A rather extensive ENSDF entry exists for 248 Bk, in which 22 levels and 2 bands have been identified. Despite this comparatively extensive level of knowledge, it has still not been possible to assign a definite spin and parity to the ground state. In 1965, Milsted et al. deduced the presence of a long-lived isomer in 248 Bk, with a half-life of greater than 9 years [273]. A detailed study of the α and EC decay of 252 Es, from which most of the level assignments in 248 Bk come, was made by Fields at al. in 1973 [147]. On the basis of the log ft value for the decay to the two-neutron 3+ state in 252 Cf ([7/2+ [613]ν ⊗ 1/2+ [620]ν ]), the ground state of 252 Es was assigned a spin and parity (5− ) with configuration [7/2+ [613]ν ⊗ 3/2− [521]π ]. Favoured α decay from 252 Es was found to populate a level at 590 keV which was assumed to have the same configuration as the 252 Es ground state ([7/2+ [613]ν ⊗ 3/2− [521]π ](5− )). This state then decays via an E1 transition to a (6+ ) state with assumed configuration [9/2− [734]ν ⊗ 3/2− [521]π ], which was denoted as the ground state in that work. A further isomeric state with a half-life of 23.7 hrs has been assigned a spin and parity of 1(−) on the basis of log ft values decays to low-spin states in 248 Cm and 248 Cf (see e.g. [274]). A probable configuration for this state is [9/2− [734]ν ⊗ 7/2+ [633]π ]. It is suggested that the state with a half-life greater than 9 years could be the Gallagher–Moszkowski 8− partner of this configuration. It is, however, also possible that this longer-lived isomer is the (6+ ) observed by Fields et al. For a more in depth discussion and detailed calculations of the locations of a large number of configurations in 248 Bk, see the work of Sood and Singh [275]. An attempt to resolve these ambiguities was proposed in the review of Sood et al. [272], by re-assigning the ground state of 252 Es to have a spin and parity of 7+ and configuration [7/2+ [613]ν ⊗ 7/2+ [633]π ], though this seems to ignore the observed log ft value for the decay to 252 Cf. 248 Bk is therefore a very good example of the difficulty presented by making assignments in odd–odd nuclei. The situation in 250 Bk is somewhat clearer, with a firmly established ground-state spin and parity of 2− based on log ft values (configuration [1/2+ [620]ν ⊗ 3/2− [521]π ]). The excited state structure of 250 Bk has been studied through the α decay of 254 Es and through the 249 Bk(n, γ ) reaction, though the data for the latter is marked as being ‘‘tentative’’ in the ENSDF table. 250 Bk is the best known of the odd–odd nuclei in the region of this review, with 44 levels and 9 bands known. Of particular interest in 250 Bk is the observation of several Gallagher–Moszkowski partners, which allow a systematic investigation of the p–n interaction for a number of configurations via the observed Gallagher–Moszkowski splittings and Newby shifts. A detailed investigation of the residual p–n interaction in odd–odd deformed nuclei has been performed by Nosek et al. [277]. The Newby shifts in a wide range of K = 0 bands have been studied by Frisk [278]. 6.2. Es isotopes According to Fig. 1 of the review of Sood et al. and the ENSDF table, the ground state spin of 246 Es should be 4− or 6+ based on inspection of the single-particle systematics of the neighbouring nuclei. These arise from the coupling of a 5/2+ [622] neutron (N = 147) to either a 7/2+ [633] or 3/2− [521] proton. As 246 Es has only been populated via the α decay of 250 Md, an assignment based on this data or the α decay properties of 246 Es cannot be made [249,279]. A similar assignment simply based on the expectations from neighbouring single-particle states is made for 248 Es, whose decay proceeds almost entirely by EC [261]. Again either the 7/2+ [633] or 3/2− [521] proton is involved, and coupled to the 7/2+ [624] neutron this yields a spin and parity of either 2− or 0+ . Whilst there is little data available concerning the excited state structure of 250 Es, the EC decay has been exploited to good effect in detailed studies of 250 Cf [145,280]. Two isomeric states are known, the first assigned a spin and parity of (6+ ) and the second with 1(−) . Both assignments are made based on log ft values for decays to excited states in 250 Cf, which suggest 5 or 6 for the spin of the first isomer and 1 for the second. The configuration of the (6+ ) state is likely to be [9/2− [734]ν ⊗ 3/2− [521]π ], and that of the 1(−) state [9/2− [734]ν ⊗ 7/2+ [633]π ]. In the latter case, the Gallagher–Moszkowski rule suggests that the possible 8− state should be energetically favoured, thus the 1(−) state is not likely to be the ground state.

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As mentioned in the discussion of Bk isotopes, the ground state of 252 Es has been assigned a spin and parity of (5− ) with configuration [7/2+ [613]ν ⊗ 3/2− [521]π ] on the basis of log ft values [147]. Another possible configuration discussed in the ENSDF table is [1/2+ [620]ν ⊗ 7/2+ [633]π ]. This configuration can be ruled out on the basis of the observed hindrance factors in the α decay of 256 Md [237,263]. These α -decay data also provide some information on the excited state structure of 252 Es, though even with coincident γ -ray data it has been difficult to draw conclusions [237]. No assignments have been made for many of the populated levels. A level at 536 keV has been assigned a spin and parity of (1− ), on the basis of the fact that it is fed by a favoured α decay from 256 Md. The configuration is proposed to be K = 0, J π = 1− [7/2+ [613]ν ⊗ 7/2− [514]π ], the same as that proposed for the ground state of 256 Md. The assignment in 256 Md is supported by the EC decay properties to 256 Fm presented in the work of Ahmad et al. [237]. The EC decay feeds only low-spin states in 256 Fm, indicating that the ground state of 256 Md is also of low spin. The structure of 254 Es is comparatively well-known, with four of the nine excited levels having a spin assignment. The ground state of 254 Es is assigned to (7+ ) with the configuration [7/2+ [613]ν ⊗ 7/2+ [633]π ]. This is consistent with data from a recent study of the angular distribution of α emission from oriented nuclei [281], and with weak β − and EC branches to 254 Fm and 254 Cf, respectively [28]. An isomeric state with a half-life of 39.3 h at an excitation energy of 84.2 keV is firmly assigned with a spin and parity of 2+ . The firm assignment is possible as the spin has been measured by the atomicbeam magnetic-resonance method [262]. The same measurement allows a determination of the magnetic moment, which is consistent with that expected for the [3/2+ [622]ν ⊗ 7/2+ [633]π ] configuration. The majority of the remaining level assignments in 254 Es come from the 258 Md α decay data and analysis of Moody et al. [263]. As yet, no assignments for Gallagher–Moszkowksi partner states have been made. 256 Es has been studied by thermal neutron capture onto 255 Es and via (t , p) reactions with a 254 Es target [282,69]. The 25.4 min half-life ground state of 256 Es has a tentatively assigned spin and parity of (1+ , 0− ). The assignments made in 253,255 Es and 257 Fm suggest the configuration [9/2+ [615]ν ⊗ 7/2+ [633]π ] (1+ ), with another possibility being the 0− [3/2+ [622]ν ⊗ 3/2− [521]π ] configuration. For both of these configurations, the Gallagher–Moszkowski rule suggests that the low-spin state should be energetically favoured. No experimental evidence exists to confirm that the low-spin isomer is the ground state. The other observed isomeric state in 256 Es is assigned a spin and parity of (8+ ), which is known to β − decay to a 7− two-quasiparticle isomer in 256 Fm [69]. The excitation energy of the high-spin isomer is not known, but the configuration is likely to be [9/2+ [615]ν ⊗ 7/2+ [633]π ] meaning that this is the Gallagher–Moszkowski partner for the (1+ ) state. 6.3. Md isotopes In the mendelevium isotopes, only for 256,258 Md are experimental data available which can constrain the possible spin and parity assignments. For 250,252,254 Md, the ENSDF table includes some speculation of ground-state and low-lying configurations based on the systematics of single-particle states in neighbouring odd-A nuclei [28]. As discussed above, the ground state of 256 Md is assigned to (K = 0, 1− ) on the basis of EC decay to 256 Fm and α decay to 252 Es [237,263]. The α -decay data lead to the conclusion that the 0− and 1− levels are inverted, in a similar way to that observed in 242 Am [283]. In 258 Md, it is speculated that the ground state has the configuration [9/2+ [615]ν ⊗ 7/2− [514]π ] coupled to 8− . Moody et al. determined an upper limit for the EC and β decay branches which is consistent with the assignment to a high-spin state [263]. Also known in 258 Md is another isomer which decays predominantly by EC. It is speculated that this state should have a low spin, with a number of possibilities to create 0− , 1− , or 2− states discussed [28,263]. 6.4. Lr and Db isotopes As in the case of odd-Z nuclei, the data beyond mendelevium are extremely sparse. No assignments of ground-state configurations have been made for any of the odd–odd lawrencium or dubnium isotopes. Most of the data available has been obtained through α decay studies with low statistics, and has only provided decay half-lives, branching ratios, α decay energies and so on. Without additional data (for example from log ft values) it is very difficult to make assignments. As was stated in the introduction to this chapter, progress in studies of odd–odd nuclei in the region has been very limited. The only data in the XUNDL unevaluated nuclear data list which exists for odd–odd nuclei in the region comes from nuclei populated in the decay chains of 260 Bh, which was recently studied in Berkeley, and for the elements 113 and 115 produced in Dubna [284–286]. 6.5. Summary It has been shown that reliable data for odd–odd nuclei in the region is very sparse. In cases where configurations can be deduced, the data often provide nice confirmation of the configurations assigned in neighbouring odd-A isotopes. The data can also provide interesting information concerning the residual p–n interaction when the relative energies of the Gallagher–Moszkowksi partners are known. It is essential to obtain more data on the odd–odd nuclei in the region, though this will certainly be an extreme challenge for future experiments.

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Fig. 44. Schematic design of the sage Spectrometer together with the JUROGAM II Ge detector array coupled to RITU.

7. Current and future developments 7.1. Instrumentation One key problem for in-beam spectroscopy studies of transfermium nuclei is the strong competition from internal conversion processes. As a rule of thumb, in a nucleus with Z ' 100 an M1 transition below 400 keV and an E2 transition below 200 keV will be dominated by internal conversion, i.e. have a total conversion coefficient αtot ≥ 1. This means, that both in in-beam γ ray and in-beam conversion electron spectroscopy experiments one only sees one side of the coin. The sage spectrometer aims to combine internal conversion electron spectroscopy and γ ray spectroscopy. The design concept of sage is shown schematically in Fig. 44. Although such approaches have been tried before, it was always found problematic to simultaneously satisfy the essentially complementary experimental conditions encountered in gamma ray spectroscopy versus those in conversion electron spectroscopy. The sage concept builds on the successful sacred conversion electron spectrometer with its near 180◦ geometry [71,72], see Section 2.2.2. It consists of a split solenoid with a maximum on-axis field of B0 = 0.4 T at an angle of 177◦ with the incoming beam. Thus the beam can pass the detector while the Doppler broadening of the emitted electrons is minimised. The design ensures that the germanium detectors have an unhindered view of the target. The Si detector is highly segmented into 90 elements which are read out by digital electronics capable of running each detector pixel at rates up to at least 30 kHz. A High Voltage barrier inside the solenoid allows to cut the very large background from atomic delta-electrons down to manageable levels, so that both germanium and silicon parts of the system can run at optimal count rates simultaneously. Another great opportunity to further the in-beam spectroscopy of transfermium nuclei is the use of the next generation germanium array AGATA (see e.g. [287]) where the path of all gamma rays is tracked through a complete shell of germanium resulting in unprecedented efficiency and sensitivity. AGATA will be a key instrument for these studies in the future. 7.2. Facilities Currently one is limited to experiments with stable beams (or at least beams from long-lived isotopes, such as 14 C, available from conventional ion sources). More symmetric reactions with stable beams and targets will always produce neutron-deficient isotopes. However, the slope of the valley of stability in the upper regions of the nuclear chart is such, that α decay chains tend to move closer to the valley of stability for the lower members of the chain. The price to pay is that the cross sections for the production of the top ends of such chains are so small that it becomes very challenging to gather enough statistics for meaningful spectroscopy and requires the highest intensity stable beams. It is thus important that the developments of stable beam facilities are pushed forward. An initiative for a dedicated high intensity stable beam facility is given by the ecos (European Collaboration on Stable ion beams) initiative. The low production cross sections that dominate experimental considerations in this region of the nuclear chart clearly require the highest beam currents. For in-beam spectroscopy the current limitations for the count rates in germanium detectors limit the beam currents to 30 pnA, but with digital electronics capable of running a factor 3–5 faster without deterioration of spectral quality one can expect that limit to be pushed to at least 100 pnA. It is, however, in the decay experiments that the use of rotating targets allows the use of beam currents of several particle microampere. These kinds of beam intensities are currently achievable with stable beams, yet beams of these intensities are rare. To ensure a ready supply of high intensity stable beams the ecos has identified the need for high intensity stable beams in a number of areas of

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nuclear physics, such as, e.g., superheavy element research, nuclear structure studies at low, medium and high spin, ground state properties, nuclear astrophysics, and ion–ion collisions in a plasma. A report of their findings is available from the NuPECC web site [288]. The current suite of instrumentation at gsi is extended by the gas-filled separator tasca (Trans Actinide Separator and Chemistry Apparatus) [289] which has recently been commissioned. Although designed primarily for chemical studies of heavy actinides and transactinides, it is also a powerful tool for nuclear decay spectroscopy experiments. It will allow the use of heavy actinide targets and therefore allow studies of more neutron rich systems than those accessible with stable beam/target combinations at ship. An upgrade of the unilac accelerator at gsi, and therefore an increase of the beam intensity available both for tasca and ship, is one of the recommendations of the ecos report, and will continue to push the boundaries ever outwards. The other promising avenue to extend these studies in the future, though, comes from the prospect of high intensity radioactive beams, see e.g. [290]. Especially when taken together with heavy actinide targets, it becomes possible to create target/projectile combinations with sufficient neutron numbers to extend the experimental systematics closer to the extrapolated valley of stability of the nuclear chart. Another way to reach more neutron-rich systems is the use of intense neutron-rich radioactive beams available in the fair facility. Projected intensities will allow studies of more neutron rich nuclei in the transfermium region. The facilities offered by the spiral2 project at ganil in France should provide a unique opportunity to extend studies of heavy and superheavy nuclei. spiral2 will primarily be a radioactive beam facility, driven by a deuteron beam from a superconducting linac, known as the linag. The linag is also designed to deliver (stable) heavy-ion beams, coupled with next-generation ion sources. Initially with A/q = 3 injection and later to be upgraded to A/q = 6, the ion-source linag combination should provide stable beams with unprecedented intensities (up to 1014 pps). Coupled with these highintensity beams will be a new recoil separator/spectromer known as S3 (Super Separator Spectrometer). The spectrometer is expected to have a high transmission efficiency for fusion–evaporation reaction products, leading to very high yields of nuclei at the focal plane. A state-of-the-art detection system will be constructed around the focal plane for decay studies, and there will also be the possibility to collect the nuclei into a gas cell, for possible mass measurements in traps, or laser spectroscopy measurements. It is expected that the first beams from linag will be available in 2012. Another interesting aspect is the possibility to use the radioactive beams of spiral2 in order to extended systematic studies over a wider range of nuclei, particularly in neutron number for a given element. While the expected intensities will not initially allow studies of superheavy nuclei at the same level of detail as with stable beams, they will allow access to nuclei which are simply not available by other means. Coupling of the upgraded exogam 2 or agata array to the vamos spectrometer is also of interest. vamos has an extremely large acceptance, which makes it ideal to study nuclei produced in very asymmetric reactions. Initial studies suggest that the transmission efficiency is a factor of 3–4 greater than that possible with, e.g., ritu for such reactions. eurisol is planned to be a next-generation radioactive beam facility providing intense beams of a wide range of ions. At present, eurisol is in the design study stage and should bring at least an order of magnitude over the intensities expected with spiral2. Such an increase will certainly make a wider range of nuclei accessible, though performing experiments with such intense radioactive beams will be an extreme technical challenge. 8. Summary and conclusions In the past decade a great deal of progress has been made in both in-beam and decay spectroscopic studies of very heavy nuclei. The in-beam studies have been driven by extensive use of the recoil-decay tagging technique, coupled to focal plane developments which have substantially lowered the spectroscopic limit. This is largely due to the fact that the focal plane devices allow much cleaner selection of the events of interest. These focal plane developments have also led to significant improvements in the quality of data obtained in coincidence measurements either following α decay or from the decay of isomeric states. In-beam measurements have shown that the nuclei in the region of 254 No are indeed deformed, that the fission barrier is robust up to high spins, and that following the moments of inertia over a range of neutron and proton number, can yield information about the underlying structure, deformed shell gaps and pairing in these nuclei. Experiments to study the α decay properties, along with coincident γ ray and conversion electrons have allowed the single-particle levels in odd-mass nuclei to be traced systematically. These coincidence measurements have also allowed transition multipolarities to be determined unambiguously, giving credence to level schemes which would have previously only relied on α decay hindrance factors. Again, the systematic tracing of single-particle levels over a wide range of neutron number reveals interesting effects which a single measurement cannot give, the einsteinium isotopes being a nice example. The most recent measurements of K isomers and the non-yrast structures which their decays populate have also given valuable data on the location of single-particle states, in particular the interesting 1/2− [521] state which stems from the 2f5/2 orbital above the possible Z = 114 shell gap. Again by performing systematic studies, information concerning the location of deformed proton and neutron shell gaps has been obtained, along with knowledge of the ordering of singleparticle levels. A detailed re-analysis of this dataset is beyond the scope of the present work, as is an in-depth review of theoretical progress in this region. Both tasks, however, are very worthwhile, and are in progress in a number of groups.

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The data are already providing a stringent test for modern self-consistent theories, which have been reasonably successful in describing properties such as the moments of inertia, but which struggle to reproduce the correct ordering of singleparticle levels. It is not yet known which components of the effective interaction (spin-orbit, tensor, pairing) need to be modified or how to modify them without destroying the other properties of the interactions. It can be expected that over the next decade our knowledge of this part of the nuclear chart will be further enhanced, with new facilities and instrumentation coming online. The push to higher proton number will be aided by high intensity stable beams, and wider neutron number will be covered by the possibilities at next generation radioactive beam facilities. In short, there remains a great deal still to be learned. Acknowledgments We would like to thank F.P. Hessberger for many helpful discussions and a thorough reading of the manuscript. We thank all our collaborators for their input, insights and hard work over the years, namely Peter Butler, Graham Jones, Rauno Julin, Matti Leino, Dieter Ackermann, Joe Bastin, Audrey Chatillon, Sarah Eeckhaudt, Craig Gray Jones, Fritz Hessberger, Rich Humphreys, Pete Jones, Harri Kankaanpää, Steffen Ketelhut, Teng-Lek Khoo, Wolfram Korten, Robert Page, Tom Page, Amy Pritchard, Panu Rahkila, Peter Reiter, Danielle Rostron, Cath Scholey, Sujit Tandel, Christophe Theisen, Juha Uusitalo, and Martin Venhart. We also thank Michael Bender, Paul-Henri Heenen, Adam Sobiczewski, Witek Nazarewicz, Heloise Goutte, Anatoli Afanasjev, Yang Sun, Masato Asai and Phil Walker for many insightful discussions and their patience when we were slow to grasp the point. This work was supported by the UK STFC and by the Academy of Finland under the Finnish Center of Excellence Programme 2006–2011, the EU-FP6-I3 Project EURONS (No. 506065). PTG gratefully acknowledges the receipt of an Academy of Finland Research Fellowship. RDH wishes to thank his Finnish collaborators for their kind hospitality during the many years of their collaboration. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46]

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