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Towards far from stability with euroball
Progress in Particle and Nuclear Physics PERGAMON
Progress in Particle and NuclearPhysics46 (2001) 253-268 http://www.elsevier.nl/locate/npe
Towards Far from Stability with Euroball S. L U N A R D I Dipartimento di Fisica dell'Universita' and INFN, Sezione di Padova, Padova, Italy
Abstract The Euroball 7-detector array has been built with the main purpose of studying high angular momentum phenomena in nuclei. When coupled with powerful ancillary detectors it has proved to be an excellent instrument to explore the properties of very exotic nuclei far from j3-stability. A large fraction of the experiments has been therefore devoted to study both proton-rich and neutron-rich nuclei populated with very low cross sections by using the stable beams provided by the Leguaxo and Strasbourg accelerators. In this talk the main emphasis will be on nuclei lying close to the N = Z line where fundamental properties of the nuclear force can be tested with high precision.
1
Introduction
The current projects to build more powerful radioactive beams facilities plan, as a main purpose, to explore the structure of nuclei very far from the valley of/~-stability where new phenomena are predicted to occur and where one may learn about new facets of the nuclear interaction. Such facilities will indeed allow to go into the so called "terra incognita" of the nuclei which are still bound with respect to the emission of their nucleonic constituents, but are outside the reach with present stable beam facilities. The physics of "exotic nuclei" has anyway a long tradition, since it has been always the dream of nuclear physicists to go into unexplored regions of the nuclear landscape and to extend the knowledge of nuclear properties much further with respect to the few stable nuclei present in nature. The increasing sophistication of detection systems in terms of efficiency and selectivity has allowed to study, by using stable heavy ions,~more and more exotic nuclei on both sides of the valley of stability. The Euroball detector is one of such detectors [1, 2]. It has been built in the second half of the 90 's, in the frame of a European collaboration, as an high spin instrument to study mainly superdeformed nuclear shapes at high angular momentum but it has proved to be an excellent instrument also for spectroscopy at the limits of stability using available stable beams facilities. Indeed, until radioactive beams reach good intensities, large 0-array detectors coupled to selective ancillary devices and using stable beams will still be competitive. Fig. 1 shows a chart of the nuclides where the proton- and neutron-rich nuclei that have been studied recently at Euroball are indicated. The physics issues that have been addressed are: neutron-proton pairing interaction, proton radioactivity, new shell gaps, new regions of deformation, isospin degree of freedom and isospin mixing. As just stated above, to perform such studies Euroball has to be combined with proper ancillary detectors which allows to select the weak channels dealing with exotic nuclei from the huge background of all other intense reaction channels. The proton-rich nuclei are produced in fusion evaporation reactions whereas the neutron-rich ones axe following deep-inelastic reactions or fission induced by heavy-ion bombardment. In order to study the N = Z nuclei up to the highest masses on the proton-rich side, charged particles and neutron detectors have been especially designed; to identify neutron-rich nuclei produced in heavy-ion induced fission new fission fragments detectors have been developed. Fig. 2 shows a photograph of the standard apparatus used for studying all the proton-rich nuclei close to the N -- Z line mentioned in Fig. 1. 0146-6410/01/$ - see front matter © 2001 Elsevier ScienceBV. All rights reserved PII: S0146-6410(01)00130-2
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Figure 1: Chart of the nuclides with indicated the N .~ Z nuclei far from B-stability studied via fusion-evaporation reactions with Euroball. Some of the neutron rich nuclei studied through deep-inelastic reactions or heavy-ions induced fission are also shown.
The spherical chamber containing the 40 AE-E Silicon telescopes [3] is visible in the centre surrounded by the composite germanium detectors (Clover and Cluster located around 90° and in the backward direction, respectively) and by the neutron detectors covering the forward lzr solid angle [4]. In this talk I will concentrate on the results obtained for the proton-rich nuclei located close to the N -- Z line by using the neutron-wall plus Silicon ball system shown in Fig. 2. The experiments have been performed with the heavy ions beams provided by the Tandem accelerator of the Legnaro National Laboratory during the stay of Euroball there in the period May 1997-November 1998. Later on Euroball has been moved to IReS Strasbourg where is now taking data since June 1999. For the Strasbourg phase the spectrometer, which is composed of 239 Ge-detectors (30 standard Tapered, 26 Clover and 15 Cluster detectors), has been implemented with an inner BGO ball of 210 detectors. The inner ball is mainly used to measure the total energy and multiplicity of the reaction and is extremely useful to select high spin states in nuclei. Before going therefore to illustrate some of the results on the N = Z nuclei I would like to stress the power of Euroball, combined with the inner BGO ball, for high spin studies by picking up one experiment performed at Strasbourg with the goal to prove definitely the existence of an elementary mode of excitation, the octupole vibration, built on the superdeformed (SD) minimum.
2
E v i d e n c e for O c t u p o l e V i b r a t i o n built on S u p e r d e f o r m e d States: the nucleus 19°Hg.
One of the unique capabilities of Euroball is the measurement of the linear polarisation of "y-rays (and therefore of their magnetic or electric character) by means of the Clover germanium detectors used as Compton polarimeters. Due to the high efficiency of Euroball, this experimental tool, which
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
255
Figure 2: The Euroball array (one half) during the Legnaro phase with the Silicon ball (inside the spherical chamber) and the neutron wall in the front part of the picture.
was substantially limited to the strongest transitions, can can now be applied also to extremely weak populated structures such as excited SD bands. To date more than 200 SD bands are known in different mass regions [5] and in almost all cases the excited bands are interpreted as single or quasi-particle excitations. Since SD nuclei have large single-particle shell gaps ( ~ 1 MeV), single or quasi-particle excitations are pushed to higher energy and one should expect to observe at lower energy collective vibrational excitations. Indeed, many theoretical predictions have been made about octupole vibration in the SD well, in particular for the A~190 region [6]. Few excited SD bands have been found in nuclei of this region which decay directly to the yrast SD states via a series of discrete transitions in competition with the highly collective in-band electric quadrupole transitions. They have been interpreted as bands built on the octupole vibration since the connecting transitions have a dipole character and in fact, associated to the charge asymmetry of the vibration, a large transition dipole moment is expected [7, 8, 9]. If the bands have really the expected octupole character, enhanced inter-band E1 transitions should compete with the highlycollective in-band E2 transitions. Anyway, the electric dipole nature of the inter-band E1 transitions could not be proved in previous experiments. An example is the nucleus :9°Hg whose relevant level scheme [7] in the SD minimum is shown in Fig. 3: the excited SD band 2 decays into the yrast band (band 1) through a series of dipole transitions at Ex~ 0.8 MeV. An experiment [10] has been performed at Eurobatl to measure angular distribution and linear polarisation of those transitions to prove definetely the octupole scenario in the mass 190 SD region.The :g°Hg nucleus has been populated in the :S°Gd+32S reaction at 158 MeV, the beam being delivered by the Vivitron accelerator in Strasbourg. The high statistics collected has allowed to measure, by using the Clover detectors as polarimeters, the linear polarisation of three transitions connecting the excited SD band and the yrast SD band in 19°Hg. Combined with the angular distribution data obtained in the same experiment this gives an electric dipole character for the inter-band transitions connecting the first excited band to the yrast band [10]. The branching ratios and the previously
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S. Lunardi/ Prog. Part.Nucl. Phys. 46 (2001)253-268
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Figure 3: Level scheme of 19OHgin the SD minimum from ref. [7]. In the Euroball experiment described in the text and in ref. [10] the multipolarity of three of the transitions connecting band 2 to band 1 has been measured, giving conclusive evidence of the octupole character of the excited band 2.
measured lifetimes [8] indicate transition strenghts corresponding to a significant charge asymmetry in the nucleus. With this experiment the existence of collective octupole excitations has been therefore definetely established in 19°Hg. This demonstrates also that, with large ~/-arrays like Euroball, it is possible to perform quantitative spectroscopic measurements in the second well.
3
N u c l e i w i t h N ~ Z in t h e A - - 5 0 - 6 0 m a s s r e g i o n
Spectroscopy of medium mass nuclei with N ~ Z has become feasible only recently and constitute nowardays an exciting field to study. The strongest motivation for studying these nuclei is given probably by the fact that only here we hope to be able to evidence effects of the neutron-proton pairing interaction. Since in these nuclei valence protons and neutrons occupy the Same single-particle orbitals, the effects of shell gaps axe very strong and determine rapid shape changes both with N, Z and spin. Strongly deformed bands have been observed which decays not only trough "r-radiation but also by particle emission [11]. In medium-mass N ~ Z nuclei there is also the possibility to test experimentally the isospin symmetry which is intimately related to the charge independence of the nuclear force. New doubly magic nuclei, such as l°°Sn, are along this line and the study of their neighbours provide unique information on shell structure and interaction of protons and neutrons at the proton drip-line. All these physics issues have been adressed in various experiments at Euroball which are described in the following. 3.1
Validity of the isospin selection rule: the case of the N = Z nucleus 64Ge
One of the most interesting possibilities offered by the study of N --- Z nuclei is the chance to estimate experimentally the amount of isospin impurity in the low-lying states. Isospin is strictly conserved by
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268 (16÷)
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S. Lunardi / Prog. Part. Nucl.
Phys. 46 (2001) 253-268
1510 keV E1 stretchedin 66Ge
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the strong interaction, but the Coulomb interaction mixes states of different isospin. Electric dipole transitions in N -- Z nuclei with AT = 0 are forbidden by isospin conservation [12]. Therefore, E1 transitions between low-lying states of even-even N -- Z nuclei can only proceed through the mixing of T -- 0 and T = 1 states induced by the Coulomb interaction. This is apparently the case of the 64Ge nucleus, where an intense 1665 keV transition, assigned as a pure El, was observed to connect the low-lying 5- and 4+ states [13]. In Fig. 4 the complete level scheme of the N = Z nucleus ~4Ge at it results from recent experiments performed at GASP and Euroball [14] is drawn. If one compares the lower part of this level scheme with that of the isotope 66Ge from ref. [15] (see left part of Fig. 7) one notices a great similarity between the two. In particular, the presence in both nuclei of the strong 5 - 4 4+El transition is rather surprising because in the self-conjugate nucleus 64Ge E1 transitions are forbidden by the isospin selection rule [16]. The "forbidden" 5-4-*4+ E1 transition in e~Ge is possible only through isospin mixing with T -- 1 states of similar spin which, anyway, lie 3 MeV higher in energy. Isospiu impurities in nuclear levels are expected to be small along the valley of stability; however, as the Coulomb mixing increases rapidly with mass, they can become large and have indeed been used in ref. [13] to explain such a strong E1 transition in 64Ge. On the other side, the previous experiment [13] did not determine the polarisation of the 1665 keV 5 - ~ 4 + transition; but such a measurement should definetely be done before making definite conclusion about "isospin mixing" or "isospin selection rule". The N = Z nucleus 64Ge has been therefore studied at Euroball by means of the 4°Ca+32S reaction
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
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at 125 MeV with the beam provided by the Leguaro Tandem. The 1 mg thick target was evaporated on a 12 mg/cm 2 foil. Both the ISIS silicon ball [3] and the array of neutron detectors were used in coincidence with v-rays detected by the germanium detectors. The level scheme deduced for the 64Ge nucleus populated after emission of 2a particles is drawn in Fig. 4. In the same reaction we could populate with much higher cross section the 66Ge nucleus: this is important since it allows to measure, in the same experiment, angular distribution and polarisation for the 5---*4+ 1510 keV transition in 6eGe and compare with the same quantities measured for the corresponding 1665 keV transition of 64Ge. The multipolarity of the 1665 and 1510 keV transitions was inferred through a directional correlation from oriented states analysis; then, the mixing ratio 6 and the alignment parameter a/J [17] were deduced simultaneously from a fit of the angular distribution data with the code MINUIT. The results of the fit for the 1510 keV line in eSGe and for the 1665 keV line in 64Ge are shown in Fig. 5. In the case of the 1665 keV "r-ray, the best fit gives 6= -3.9~+°T ' 5~_0.41with , a reduced chi square X~= 0.80, whereas it gives 6~0 for the 1510 keV transition in 66Ge. A polarisation correlation analysis was performed using the Clover detectors of Euroball. The asymmetry A = ~ for the 1510 keV transition in N±+NII SSGe was found positive (see Fig. 6), which, combined with the angular distribution results, confirms its stretched E1 character. A similar analysis for the 1665 keV line in 64Ge gives a negative asymmetry, as it is shown in Fig. 6. This result is only compatible with a predominantly M2 character of the transition (93%), with a very small E1 component and corresponds to the large 6 value solution of the angular distribution fit [14]. This is a nice confirmation of the validity of the isospin selection rule in N = Z nuclei. Despite the fact that the 64Ge and SSGe nuclei have almost equal level schemes, reflecting the same intrinsic structure for the excited states (see Fig. 7), their different isospin, T = 0 and T = 1
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respectively, induces a completely different character for the 5---*4+ transition. Even if small (~7%), a "forbidden" E1 component is present in the transition connecting the 5- and the 4+ states in 6aGe which can be explained trough mixing with high-lying T -- 1 states. It would therefore be interesting to derive from it an estimate of the isospin mixing and compare with recent calculations which were able to derive the degree of isospin impurities in N -- Z nuclei close to the proton-drip line [18]. In that paper an isospin mixing probability of ~2.4% is calculated for the 64Ge ground state. To derive the isospin mixing of the 5- state in e~Ge the knowledge of its lifetime is needed. At the moment, a lower limit of T < 1 ps is set by the absence of line broadening in the Euroball thick target experiment. An experiment with the plunger device and a new silicon ball (EUCLIDES) especially built for Euroball has been recently performed at the Vivitron in Strasbourg by using the same reaction as above. The analysis of the data is still in progress, but we expect to set at least an upper limit to the lifetime of the 5- level. From this Euroball experiment we can conclude that in e~Ge isospin is a much better quantum number than expected and that the amount of isospin impurity for the low lying states is much smaller than given by previous theoretical estimates. 3.2
The T -- 1 mirror nuclei 5°Fe and 5°Cr: charge independence of the nuclear interaction and Coulomb effects
The charge independence of the nuclear force can be verified also by studying mirror nuclei, i.e. nuclei with interchanged number of neutrons and protons. The nearly identical spectra of light mirror nuclei has confirmed the assumption that protons and neutrons may be viewed as two states of one particle, the nucleon. Thanks to the improvements in detection sensitivity, is has become now possible to explore the isospin symmetry of the mirror nuclei in the lf7/2 shell to very high angular momenta, allowing to test for the first time this symmetry under rotational stress. With increasing Z, already for mass A~50, one of the mirror partners lies very far from stability which makes very difficult its experimental study. With Euroball coupled to the n-wall we can do spectroscopy down to cross sections of ~ 10 microbarns. This allows to study excited states in nuclei lying on the left of the N -- Z line like the case of the N = Z - 2 S°Fe nucleus (see Fig. 8). This nucleus is the mirror partner of 5°Cr whose structure is known since more than 20 years [19]. The energy spectra of mirror nuclei, if the charge independence of nuclear interactions holds, are expected to be equal; when small differences between energy levels arise, these can be interpreted entirely in terms of Coulomb effects. With the term Coulomb Energy Displacement (CED) one indicates the energy difference between levels in mirror nuclei [20]. The angular momentum dependence of CED has been investigated recently in series of nuclei of the lf~12 shell allowing to study the spatial behaviour of the active valence nucleons [20, 21, 22, 23]. As a consequence, the smooth variation in the CED reflects in detail the change as a function of spin of the nucleus: from a deformed rotor ( which is typical of lf~/2 nuclei in the middle of the shell), through one or two particle alignment in the backbending region, to an almost spherical non-collective band termination state. Being the Coulomb energy due only to protons, it has been pointed out that when a J -- 0 proton pair recouples to another J configuration, the Coulomb energy would decrease [24]. In fact, in the J = 0 coupling the overlap of the wave functions (and therefore the Coulomb repulsion) is maximum. In an odd mass nucleus, the blocking effect due to the unpaired nucleon, favours the alignment of the other type of nucleon pairs. When a proton pair in the fT/~ shell changes from a coupled J = 0 state to an aligned J = 6 state, the repulsive Coulomb interaction decreases in the odd-neutron nucleus while in its odd-proton mirror no Coulomb effect is expected when a pair of neutrons align. Thus, at the backbending the corresponding transition energy in the odd-neutron partner will be smaller than that in its odd-proton mirror. For the case of even-even mirror nuclei the experimental information is very scarce. Recently, some theoretical predictions have been reported for odd-even and even-even mirror nuclei in the fv/2 shell in the framework of the cranked shell model [25]. One of the better rotors in the f7/2 shell is the nucleus S°Cr which presents a first backbending around spin I = 10 [26]. Different explanations have been given to this behavior such as a change of shape or a crossing with a band based on an oblate deformation [27]. Another description in terms of a bandcrossing
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
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with a high-K band has been also suggested. From the previous lifetimes measurements [28] performed at GASP, the ground state deformed band seems to continue above the I = 8+ yrast state up to the yrare I -- 12+ state. To have a stringest test of the mirror symmetry in nuclei and to look for an experimental fingerprint of the nucleon alignment at the backbending, high spin states in the N -- Z - 2 nucleus S°Fe, in which no gamma transitions were known previously, have been investigated. The 5°Fe nucleus was produced in the reaction 288i+288i at 110 MeV bombarding energy, after the evaporation of one aparticle and two neutrons. The beam was delivered by the XTU Tandem accelerator of the Legnaro National Laboratory. The target consisted of 0.8 mg/cm 2 of 2sSi (enriched to 99.9%) with a Au backing of 15 mg/cm 2. Gamma rays were detected with the EUROBALL array (Clovers and Clusters only), charged particles were detected with the ISIS silicon ball (40 E-AE telescopes) and the neutrons with the Neutron Wall. Events were collected when at least : a ) t h r e e Ge detectors plus one neutron detector fired in coincidence or b) two Ge detectors fired and one neutron was identified in coincidence in the Neutron Wall. Data were sorted in 7 - 7 matrices in coincidence with charged particles and neutrons. For the identification of 7-lines candidates to belong to S°Fe, we have looked at spectra taken in coincidence with neutrons, with only one a-particle and in anti-coincidence with protons. Six transitions have been found, in mutual coincidence with each other, which satisfy all conditions to be in S°Fe. The coincidence spectrum shown in Fig. 9 corresponds to a sum of gates on these transitions. In the same Fig. 9 a coincidence spectrum (with gates on all the relevant transitions) is shown also for the mirror nucleus (S°Cr) produced in the same reaction after a2p evaporation. The comparison of the two spectra illustrates clearly the rapid decrease of population for nuclei lying far from stability. From the present data a cross section of around 15 #b is estimatedfor the S°Fe nucleus.
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
263
Prom the coincidence data and the transitions intensity a level scheme has been built for S°Fe which is shown in Fig. 10 together with the one of the mirror nucleus 5°Cr. Spin and parity assignment for levels in 5°Fe are based on the great similarity of the two level schemes of Fig. 10. The energy difference among levels is ranging from few keV to a maximum value of ~40 keV, to be compared with absolute values of energy up to 7 MeV. This confirms, in a first approximation, the validity of the mirror symmetry which is connected to the charge independence of the nuclear force. Such small energy differences which, as stated above, can be understood as Coulomb effects are plotted in the right part of Fig. 10 as a function of spin as C E D ( I ) = E ~ ( I ) - Ebr(I ). The behavior of the C E D can be explained in the following way: a neutron pair is aligning at I = 8+ in ~°Fe while a proton pair aligns in ~°Cr; at spin I = 10+ a second alignment of the other type of nucleon pairs occurs, a proton pair in 5°Fe an a neutron pair in 5°Cr. The data is qualitatively well described by cranked shell model calculations of ref. [25]. Large shell model calculations are also reproducing with great precision [29] the shape and the absolute value of the C E D curve depicted in the right part of Fig. 10. The fact that such small energy differences are understood and reproduced with high accuracy in calculations is significant of the importance of mirror symmetry in nuclei. 3.3
P r o t o n - a n d v - d e c a y l i f e t i m e m e a s u r e m e n t s in the second m i n i m u m
o f 5SCu.
58
spherical
Figure 11: Schematic drawing of the proton-decay of the strongly deformed rotational band in 5SCu to spherical states in the daughter nucleus 57Ni.
One peculiar aspect of proton-rich nuclei around mass A--60 with N = Z is that, due to very low Coulomb barrier, proton emission can be an important mode of decay of their excited states. In fact, a new exotic decay mode was established recently in 5SCu, namely a prompt monoenergetic proton decay which connects the lowest state in the rotational band of 5SCu with the spherical states of the daughter nucleus 57Ni [11]. In Fig. 11 a schematic drawing of the process is shown. The excited rotational band of 5SCu built on a quadrupole deformed shape decays both via 7- and proton-emission to spherical states belonging to 58Cu and 57Ni respectively. This band is strongly deformed with a quadrupole deformation of/32=~0.4, which has been extracted from a residual Doppler shift measurement in a Gammasphere thin target experiment [11].
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
264
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Figure 12: Four selected regions of gamma-ray spectra obtained in the SSNi+~aFe reaction: the upper part is in coincidence with 2aln, the middle with 2 a l n l p and the lower part is from a cleaned SSGe spectrum from the contaminating reaction 58Ni+12C [32].
The proton decay of a well deformed band is an interesting quantum mechanical process which makes it possible to actress the problem of proton tunneling through a potential energy barrier in a deformed nucleus. One of the quantities wich are inportant in this respect is the lifetime of the proton-decaying state. In the previous Gammasphere experiment, where a thin target has been used, a safe upper limit of 3 ns could be derived. Using a target deposited on a Gold backing an experiment has been performed at Euroball (coupled with the n-wall and the ISIS silicon ball) with the goal to measure the lifetimes of the low lying states of the 5SCu rotational band and possibly of the band-head decaying by proton emission. The 58Cu nucleus has been produced in the reaction 4°Ca+24Mg at 96 MeV, following the evaporation channel l c d p l n . From the analysis of the lineshapes of the -y-rays deexciting the lowlying states in the well deformed rotational band the individual lifetimes of the four lowest states were determined [30]. The deduced transitional quadrupole moments show an increase towards the bottom of the band which is in agreement with the predictions [31]. In order to deduce a new upper limit for the lifetime of the proton decaying state, proton and -y-ray energy correlations have carefully been analized. A new upper limit of 0.5 ps has been obtained, to be compared with the previous value of 3 ns and with theoretical estimates of the order of 10-a ps for a deformed-to-deformed or for a spherical-to-spherical proton-decay [30]. New theoretical calculations for a deformed-to-spherical proton-decay are needed to understand the nature of this new process.
4
Towards doubly-magic l°°Sn: first e x c i t e d s t a t e s in 1°3Sn.
The nucleus l°°Sn is probably the heaviest N = Z nucleus which is stable with respect tO particle emission, corresponding to the doubly magic closure N = Z = 50. Here one has therefore the opportunity
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S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
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Figure 13: Coincidence spectrum with gate on the 168 keV transition assigned to 1°3Sn. All other transitions of the level scheme of Fig. 14 are visible. The data are from a matrix in coincidence with two alphas and one neutron.
to study nuclear magicity at the limits of nuclear existence. Spectroscopy of l°°Sn is not possible with the present available stable beams and will await long till radioactive beams reach enough intensity. The study of neighbouring nuclei is also very difficult, because of the very low cross sections involved in their population, but it is still achievable with present stable beams when using a powerful apparatus like Euroball coupled to its ancillaries. The energy levels in nuclei near x°°Sn define the single particle spectrum and the nuclear interactions around magic number 50, for both neutrons and protons. The neutron single-particle energies around l°°Sn would be best obtained by studying the 1 neutron nucleus l°lSn which is still out of present experimental possibilities; the best verification we can have now of the neutron single-particle energies may come from l°3Sn whose excited states have been identified for the first time in a Euroball experiment. The reaction 5aNi+r~Fe at 240 MeV has been chosen to produce the 1°3Sn nucleus. Being the compound nucleus ll2Xe, the evaporation channel leading to l°3Sn was 2 a l n requiring the simultaneus detection of two alphas and one neutron in the ISIS silicon ball and in the n-wall respectively. In the upper part of Fig. 12 selected regions are shown of a 7-spectrum in coincidence with two alphas and one neutron. For comparison, the same energy regions are displayed below for a spectrum with the additional requirement of a proton and for a cleaned 65Ge spectrum obtained in the reaction 58Ni+12C at 261 MeV [32]. This last spectrum is presented because the lines of 65Ge may arise in coincidence with 2 a l n from the reaction with the 160 contaminant in the target. A careful analysis of the three spectra just mentioned indicates the presence of four transitions at 168, 298, 578, and 1318 keV which fulfill the
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
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.
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Figure 14: Level scheme of l°3Sn from the Euroball experiment [33] (a) and the systematics of odd-A neutron deficient Sn isotopes. The widths of the arrows are proportional to the "y-ray intensities.
conditions for belonging to l°3Sn. In fact, they are present in the 2aln-gated spectrum but not in the 2 a l n l p - g a t e d spectrum and in the 85Ge spectrum. A prompt coincidence "r7 matrix has been created with the conditions that two a-particles and one neutron were detected. Despite the low statistics the analysis of the spectra in coincidence with the four lines assigned to l°3Sn gives clear indications of the coincidence relationships between them (see Fig. 13); this allows to construct the level scheme drawn in Fig. 14 [33]. The cross section for the production of I°3Sn is estimated to be around 10#b. Based on a systematic comparison with the other odd-A neutron deficient Sn isotopes (see Fig. 14b), spin and parity (5/2 +) is proposed for the ground state of 1°3Sn. The spins and parities for the states above have been suggested on the basis of DCO ratios obtained for some of the transitions and on the systematics of odd-A Sn isotopes (see Fig. 14b). These data on 1°3Sn are important since they give new constraints to shellmodel calculations around l°°Sn. In fact, various shell-model approaches try to obtain a good fit to the observed excitation energies in the long series of heavier Sn isotopes by varying the input parameters like single particle energies and two body matrix elements; the goal is to extract the best possible value for these quantities. New data, if coming from nuclei with fewer valence neutrons, put more stringent constraints on the parameters and may solve the many ambiguities present in such an approach. A shell model calculation of this kind has been performed on many odd-A Sn isotopes, including the new one l°3Sn, which, as a main result, has produced a more accurate estimate for the relative singleparticle energies of the neutron d5/2 and g7/2 with respect to l°°Sn, e(lgT/2) - e(2d~/2) = 0.11(2) MeV. Future experiments axe necessary in order to establish the complete set of single-particle energies in the d5/2, g7/2, 81/2, d3/2, hll/2 model space.
5
Future of Euroball with radioactive beams
The Eurobail array has been operating for one and half year at the Tandem-ALPI complex of Legnaro and is now taking data at IReS Strasbourg by using the heavy ions beams delivered by the Vivitron accelerator. It will continue the operation in Strasbourg, with emphasis on both high spin phenomena
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in nuclei and on properties of nuclei far from ]~-stability, up to the end of 2002. The EurobaU community is now discussing (end of 2000) about the new opportunities offered by the use of Euroball detectors in connection with radioactive beams. The proposal has therefore been made to move in 2003 the composite Clover and Cluster detectors (which are the most efficient part of the array) to GSI Darmstadt for experimental campaigns with the radioactive beams provided by the SIS-FRS facility [34]. By fragmentation or fission of relativistic heavy ions several hundred unstable rare isotopes can be generated with sufficient intensity for in-beam spectroscopy for the first time. Secondary beams can also be produced in high spin isomeric states. The beams can be used either at high energies (100-200 MeV/u), for Coulomb excitation and fragmentation reactions, or slowed down to Coulomb barrier energies,allowing :~;~perform fusion and direct reactions [35]. A spectrometer with the granularity of Euroball will be able, as an "example, to study high spin states produced in fusion reactions induced by n-rich short-lived nuclei. Many other ideas and perspectives for nuclear structure studies are expected that can be fulfilled by the coupling of Euroball with the FRS.
6
Summary
With the development of stable-beams accelerators and high precision detection systems an enormous quantity of information on the behaviour and structure of atomic nuclei has been achieved during the years. It has been possible to study the internal structure of stable and unstable nuclei, not only in their ground states but over a large range of excitation energy and spins. With the gain of efficiency and selectivity of modern ~-detector arrays, such as Euroball, one is able now to extend the methods of in-beam ~/-ray spectroscopy not only to extremely high spins but also to more exotic nuclei. In this talk I have reviewed only a small part of the physics that has been obtained recently with Euroball in the study of nuclei far from j3-stability. It has been demonstrated that, taking advantage of very powerful detectors, high intensity stable beams can still compete with low-intensity radioactive beams in their capability to extract crucial properties of nuclear interactions in "exotic" nuclei. We are confident that also the physics of radioactive nuclei will take great profit from such advanced and sophisticated instruments.
7
Aknolewdegments
Euroball is a collaboration involving six countries (Danemark, France, Germany, Italy, Sweden, UK) and around 200 physicists. What I have presented here is the result of the hard work, from the data taking to the data analysis, of many colleagues that are impossible to quote here. I would like to thank in particular all those who provided me with material and help in the preparation of the talk. They are A. Korichi, E. Farnea, S. Lenzi, D. Rudolph, M. Paiacz and C. Fahlander.
References [1] J. Simpson Z. Phys. A 358 (1997) 139 [2] C. Rossi Alvarez Nuovo Cimento A 111 (1998) 601 • [3] E. Farnea et al., gucl. Instr. Meth. A400 (1997) 87 [4] O. Skeppstedt et al., Nucl. Instr. Meth. A421 (1999) 531 [5] B. Singh, R. B. Firestone and S. J. Frank Chu, Table of Superdeformed Nuclear Bands and Fission Isomers, W W W edition, http://ie.lbl.gov/sdband/sdbindex.html [6] T. Nakatsukasa et al., Phys. Rev. C 53 (1996) 2213 [7] B. Crowell et el., Phys. Rev. C 5! (1995) R1599 [8] H. Amro et al., Phys. Lett. B 413 (1997) 15 [9] A.N. Wilson et al., Phys. Rev. C 54 (1996) 559
268 [10] [11] [12] [13] [14]
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A. Korichi et al., submitted to Physical Review Letters D. Rudolph et al., Phys. Rev. Left. 80 (1998) 3018 A..Bohr, B. Mottelson, Nuclear Structure, Vol. 1, p. 44. P.J. Ennis et al., Nucl. Phys. A 535 (1991) 392 ; Nucl. Phys. A 560 (1993) 1079 (erratum). E. Farnea et al., Proceedings of the International Workshop PINGST2000, Lund June 2000, p. 64; Proceedings of the International Conference Bologna 2000, May 2000. [15] V. Hermkens et al., Z. Phys. A 343 (1992) 371 [16] L. Ra~ticati, Phys. Rev. 87 (1952) 521 [17] H. Morinaga, T. Yamazaki, "In beam ~,-ray spectroscopy" North-Holland, Amsterdam 1976 [18] J. Dobacewski, I. Hamamoto, Phys. Lett. B 345 (1995) 181 [19] W. Kutchera et al., Phys. Rev. Lett. 33 (1974) 1108 [20] M. Bentley et al., Phys. Lett. B 437 (1998) 243 [21] J. A. Cameron et al., Phys. Lett. B 319 (1993) 58 [22] C.D. O'Leary et al., Phys. Rev. Lett. 79 (1997) 4349 [23] C.D. O'Leary et al., Phys. Lett. B 459 (1999) 73 [24] J. A. Cameron et al., Phys. Lett. B 235 (1990) 239 [25] J. A. Sheikh, D. D. Warner and P. Van Isaker, Phys. Lett. B 443 (1998) 16 [26] S. M. Lenzi et al., Phys. Rev. C 56 (1997) 1313 [27] G. Martfnez-Pinedo et al., Phys. Rev. C 54 (1996) R2150 [28] F. Brandolini et al., Nucl. Phys. A 642 (1998) 387. [29] S. M. Lenzi et al., Proceedings of the International Workshop PINGST2000, Lund June 2000, p. 240 and to be published. [30] D. Rudolph et al., submitted to Physical Review C [31] A. V. Afanasiev et al., Phys. Rev. C 59 (1999) 3166 [32] D. Sohler et al., Nucl. Phys. A 644 (1998) 141 [33] C. Fahlander et al., submitted to Phys. Rev. Lett. [34] H. Geissel et al., Nucl. Instr. Meth. BT0 (1992) 286 [35] J. Gerl et al., WWW adress: http://www-gsi-vms.gsi.de/eb/html/eb_at_gsi.html
Progress in Particle and NuclearPhysics46 (2001) 253-268 http://www.elsevier.nl/locate/npe
Towards Far from Stability with Euroball S. L U N A R D I Dipartimento di Fisica dell'Universita' and INFN, Sezione di Padova, Padova, Italy
Abstract The Euroball 7-detector array has been built with the main purpose of studying high angular momentum phenomena in nuclei. When coupled with powerful ancillary detectors it has proved to be an excellent instrument to explore the properties of very exotic nuclei far from j3-stability. A large fraction of the experiments has been therefore devoted to study both proton-rich and neutron-rich nuclei populated with very low cross sections by using the stable beams provided by the Leguaxo and Strasbourg accelerators. In this talk the main emphasis will be on nuclei lying close to the N = Z line where fundamental properties of the nuclear force can be tested with high precision.
1
Introduction
The current projects to build more powerful radioactive beams facilities plan, as a main purpose, to explore the structure of nuclei very far from the valley of/~-stability where new phenomena are predicted to occur and where one may learn about new facets of the nuclear interaction. Such facilities will indeed allow to go into the so called "terra incognita" of the nuclei which are still bound with respect to the emission of their nucleonic constituents, but are outside the reach with present stable beam facilities. The physics of "exotic nuclei" has anyway a long tradition, since it has been always the dream of nuclear physicists to go into unexplored regions of the nuclear landscape and to extend the knowledge of nuclear properties much further with respect to the few stable nuclei present in nature. The increasing sophistication of detection systems in terms of efficiency and selectivity has allowed to study, by using stable heavy ions,~more and more exotic nuclei on both sides of the valley of stability. The Euroball detector is one of such detectors [1, 2]. It has been built in the second half of the 90 's, in the frame of a European collaboration, as an high spin instrument to study mainly superdeformed nuclear shapes at high angular momentum but it has proved to be an excellent instrument also for spectroscopy at the limits of stability using available stable beams facilities. Indeed, until radioactive beams reach good intensities, large 0-array detectors coupled to selective ancillary devices and using stable beams will still be competitive. Fig. 1 shows a chart of the nuclides where the proton- and neutron-rich nuclei that have been studied recently at Euroball are indicated. The physics issues that have been addressed are: neutron-proton pairing interaction, proton radioactivity, new shell gaps, new regions of deformation, isospin degree of freedom and isospin mixing. As just stated above, to perform such studies Euroball has to be combined with proper ancillary detectors which allows to select the weak channels dealing with exotic nuclei from the huge background of all other intense reaction channels. The proton-rich nuclei are produced in fusion evaporation reactions whereas the neutron-rich ones axe following deep-inelastic reactions or fission induced by heavy-ion bombardment. In order to study the N = Z nuclei up to the highest masses on the proton-rich side, charged particles and neutron detectors have been especially designed; to identify neutron-rich nuclei produced in heavy-ion induced fission new fission fragments detectors have been developed. Fig. 2 shows a photograph of the standard apparatus used for studying all the proton-rich nuclei close to the N -- Z line mentioned in Fig. 1. 0146-6410/01/$ - see front matter © 2001 Elsevier ScienceBV. All rights reserved PII: S0146-6410(01)00130-2
254
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268 = i¸ i
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Figure 1: Chart of the nuclides with indicated the N .~ Z nuclei far from B-stability studied via fusion-evaporation reactions with Euroball. Some of the neutron rich nuclei studied through deep-inelastic reactions or heavy-ions induced fission are also shown.
The spherical chamber containing the 40 AE-E Silicon telescopes [3] is visible in the centre surrounded by the composite germanium detectors (Clover and Cluster located around 90° and in the backward direction, respectively) and by the neutron detectors covering the forward lzr solid angle [4]. In this talk I will concentrate on the results obtained for the proton-rich nuclei located close to the N -- Z line by using the neutron-wall plus Silicon ball system shown in Fig. 2. The experiments have been performed with the heavy ions beams provided by the Tandem accelerator of the Legnaro National Laboratory during the stay of Euroball there in the period May 1997-November 1998. Later on Euroball has been moved to IReS Strasbourg where is now taking data since June 1999. For the Strasbourg phase the spectrometer, which is composed of 239 Ge-detectors (30 standard Tapered, 26 Clover and 15 Cluster detectors), has been implemented with an inner BGO ball of 210 detectors. The inner ball is mainly used to measure the total energy and multiplicity of the reaction and is extremely useful to select high spin states in nuclei. Before going therefore to illustrate some of the results on the N = Z nuclei I would like to stress the power of Euroball, combined with the inner BGO ball, for high spin studies by picking up one experiment performed at Strasbourg with the goal to prove definitely the existence of an elementary mode of excitation, the octupole vibration, built on the superdeformed (SD) minimum.
2
E v i d e n c e for O c t u p o l e V i b r a t i o n built on S u p e r d e f o r m e d States: the nucleus 19°Hg.
One of the unique capabilities of Euroball is the measurement of the linear polarisation of "y-rays (and therefore of their magnetic or electric character) by means of the Clover germanium detectors used as Compton polarimeters. Due to the high efficiency of Euroball, this experimental tool, which
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
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Figure 2: The Euroball array (one half) during the Legnaro phase with the Silicon ball (inside the spherical chamber) and the neutron wall in the front part of the picture.
was substantially limited to the strongest transitions, can can now be applied also to extremely weak populated structures such as excited SD bands. To date more than 200 SD bands are known in different mass regions [5] and in almost all cases the excited bands are interpreted as single or quasi-particle excitations. Since SD nuclei have large single-particle shell gaps ( ~ 1 MeV), single or quasi-particle excitations are pushed to higher energy and one should expect to observe at lower energy collective vibrational excitations. Indeed, many theoretical predictions have been made about octupole vibration in the SD well, in particular for the A~190 region [6]. Few excited SD bands have been found in nuclei of this region which decay directly to the yrast SD states via a series of discrete transitions in competition with the highly collective in-band electric quadrupole transitions. They have been interpreted as bands built on the octupole vibration since the connecting transitions have a dipole character and in fact, associated to the charge asymmetry of the vibration, a large transition dipole moment is expected [7, 8, 9]. If the bands have really the expected octupole character, enhanced inter-band E1 transitions should compete with the highlycollective in-band E2 transitions. Anyway, the electric dipole nature of the inter-band E1 transitions could not be proved in previous experiments. An example is the nucleus :9°Hg whose relevant level scheme [7] in the SD minimum is shown in Fig. 3: the excited SD band 2 decays into the yrast band (band 1) through a series of dipole transitions at Ex~ 0.8 MeV. An experiment [10] has been performed at Eurobatl to measure angular distribution and linear polarisation of those transitions to prove definetely the octupole scenario in the mass 190 SD region.The :g°Hg nucleus has been populated in the :S°Gd+32S reaction at 158 MeV, the beam being delivered by the Vivitron accelerator in Strasbourg. The high statistics collected has allowed to measure, by using the Clover detectors as polarimeters, the linear polarisation of three transitions connecting the excited SD band and the yrast SD band in 19°Hg. Combined with the angular distribution data obtained in the same experiment this gives an electric dipole character for the inter-band transitions connecting the first excited band to the yrast band [10]. The branching ratios and the previously
256
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/
/
576
/ ~
-"'543
697 / /
/ /---;. Band 2
• Bandl
Figure 3: Level scheme of 19OHgin the SD minimum from ref. [7]. In the Euroball experiment described in the text and in ref. [10] the multipolarity of three of the transitions connecting band 2 to band 1 has been measured, giving conclusive evidence of the octupole character of the excited band 2.
measured lifetimes [8] indicate transition strenghts corresponding to a significant charge asymmetry in the nucleus. With this experiment the existence of collective octupole excitations has been therefore definetely established in 19°Hg. This demonstrates also that, with large ~/-arrays like Euroball, it is possible to perform quantitative spectroscopic measurements in the second well.
3
N u c l e i w i t h N ~ Z in t h e A - - 5 0 - 6 0 m a s s r e g i o n
Spectroscopy of medium mass nuclei with N ~ Z has become feasible only recently and constitute nowardays an exciting field to study. The strongest motivation for studying these nuclei is given probably by the fact that only here we hope to be able to evidence effects of the neutron-proton pairing interaction. Since in these nuclei valence protons and neutrons occupy the Same single-particle orbitals, the effects of shell gaps axe very strong and determine rapid shape changes both with N, Z and spin. Strongly deformed bands have been observed which decays not only trough "r-radiation but also by particle emission [11]. In medium-mass N ~ Z nuclei there is also the possibility to test experimentally the isospin symmetry which is intimately related to the charge independence of the nuclear force. New doubly magic nuclei, such as l°°Sn, are along this line and the study of their neighbours provide unique information on shell structure and interaction of protons and neutrons at the proton drip-line. All these physics issues have been adressed in various experiments at Euroball which are described in the following. 3.1
Validity of the isospin selection rule: the case of the N = Z nucleus 64Ge
One of the most interesting possibilities offered by the study of N --- Z nuclei is the chance to estimate experimentally the amount of isospin impurity in the low-lying states. Isospin is strictly conserved by
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268 (16÷)
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1510 keV E1 stretchedin 66Ge
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the strong interaction, but the Coulomb interaction mixes states of different isospin. Electric dipole transitions in N -- Z nuclei with AT = 0 are forbidden by isospin conservation [12]. Therefore, E1 transitions between low-lying states of even-even N -- Z nuclei can only proceed through the mixing of T -- 0 and T = 1 states induced by the Coulomb interaction. This is apparently the case of the 64Ge nucleus, where an intense 1665 keV transition, assigned as a pure El, was observed to connect the low-lying 5- and 4+ states [13]. In Fig. 4 the complete level scheme of the N = Z nucleus ~4Ge at it results from recent experiments performed at GASP and Euroball [14] is drawn. If one compares the lower part of this level scheme with that of the isotope 66Ge from ref. [15] (see left part of Fig. 7) one notices a great similarity between the two. In particular, the presence in both nuclei of the strong 5 - 4 4+El transition is rather surprising because in the self-conjugate nucleus 64Ge E1 transitions are forbidden by the isospin selection rule [16]. The "forbidden" 5-4-*4+ E1 transition in e~Ge is possible only through isospin mixing with T -- 1 states of similar spin which, anyway, lie 3 MeV higher in energy. Isospiu impurities in nuclear levels are expected to be small along the valley of stability; however, as the Coulomb mixing increases rapidly with mass, they can become large and have indeed been used in ref. [13] to explain such a strong E1 transition in 64Ge. On the other side, the previous experiment [13] did not determine the polarisation of the 1665 keV 5 - ~ 4 + transition; but such a measurement should definetely be done before making definite conclusion about "isospin mixing" or "isospin selection rule". The N = Z nucleus 64Ge has been therefore studied at Euroball by means of the 4°Ca+32S reaction
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
259
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Figure 7: Low lying excited states of the two nuclei S4Ge and e6Ge. Due to the isospin selection rule, forbidding E1 transitions in a N = Z nucleus, in 64Ge the transition connecting the 5- and the 4+ states is mainly of M2 character, contrary to the N -- Z + 2 nucleus SSGe.
at 125 MeV with the beam provided by the Leguaro Tandem. The 1 mg thick target was evaporated on a 12 mg/cm 2 foil. Both the ISIS silicon ball [3] and the array of neutron detectors were used in coincidence with v-rays detected by the germanium detectors. The level scheme deduced for the 64Ge nucleus populated after emission of 2a particles is drawn in Fig. 4. In the same reaction we could populate with much higher cross section the 66Ge nucleus: this is important since it allows to measure, in the same experiment, angular distribution and polarisation for the 5---*4+ 1510 keV transition in 6eGe and compare with the same quantities measured for the corresponding 1665 keV transition of 64Ge. The multipolarity of the 1665 and 1510 keV transitions was inferred through a directional correlation from oriented states analysis; then, the mixing ratio 6 and the alignment parameter a/J [17] were deduced simultaneously from a fit of the angular distribution data with the code MINUIT. The results of the fit for the 1510 keV line in eSGe and for the 1665 keV line in 64Ge are shown in Fig. 5. In the case of the 1665 keV "r-ray, the best fit gives 6= -3.9~+°T ' 5~_0.41with , a reduced chi square X~= 0.80, whereas it gives 6~0 for the 1510 keV transition in 66Ge. A polarisation correlation analysis was performed using the Clover detectors of Euroball. The asymmetry A = ~ for the 1510 keV transition in N±+NII SSGe was found positive (see Fig. 6), which, combined with the angular distribution results, confirms its stretched E1 character. A similar analysis for the 1665 keV line in 64Ge gives a negative asymmetry, as it is shown in Fig. 6. This result is only compatible with a predominantly M2 character of the transition (93%), with a very small E1 component and corresponds to the large 6 value solution of the angular distribution fit [14]. This is a nice confirmation of the validity of the isospin selection rule in N = Z nuclei. Despite the fact that the 64Ge and SSGe nuclei have almost equal level schemes, reflecting the same intrinsic structure for the excited states (see Fig. 7), their different isospin, T = 0 and T = 1
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respectively, induces a completely different character for the 5---*4+ transition. Even if small (~7%), a "forbidden" E1 component is present in the transition connecting the 5- and the 4+ states in 6aGe which can be explained trough mixing with high-lying T -- 1 states. It would therefore be interesting to derive from it an estimate of the isospin mixing and compare with recent calculations which were able to derive the degree of isospin impurities in N -- Z nuclei close to the proton-drip line [18]. In that paper an isospin mixing probability of ~2.4% is calculated for the 64Ge ground state. To derive the isospin mixing of the 5- state in e~Ge the knowledge of its lifetime is needed. At the moment, a lower limit of T < 1 ps is set by the absence of line broadening in the Euroball thick target experiment. An experiment with the plunger device and a new silicon ball (EUCLIDES) especially built for Euroball has been recently performed at the Vivitron in Strasbourg by using the same reaction as above. The analysis of the data is still in progress, but we expect to set at least an upper limit to the lifetime of the 5- level. From this Euroball experiment we can conclude that in e~Ge isospin is a much better quantum number than expected and that the amount of isospin impurity for the low lying states is much smaller than given by previous theoretical estimates. 3.2
The T -- 1 mirror nuclei 5°Fe and 5°Cr: charge independence of the nuclear interaction and Coulomb effects
The charge independence of the nuclear force can be verified also by studying mirror nuclei, i.e. nuclei with interchanged number of neutrons and protons. The nearly identical spectra of light mirror nuclei has confirmed the assumption that protons and neutrons may be viewed as two states of one particle, the nucleon. Thanks to the improvements in detection sensitivity, is has become now possible to explore the isospin symmetry of the mirror nuclei in the lf7/2 shell to very high angular momenta, allowing to test for the first time this symmetry under rotational stress. With increasing Z, already for mass A~50, one of the mirror partners lies very far from stability which makes very difficult its experimental study. With Euroball coupled to the n-wall we can do spectroscopy down to cross sections of ~ 10 microbarns. This allows to study excited states in nuclei lying on the left of the N -- Z line like the case of the N = Z - 2 S°Fe nucleus (see Fig. 8). This nucleus is the mirror partner of 5°Cr whose structure is known since more than 20 years [19]. The energy spectra of mirror nuclei, if the charge independence of nuclear interactions holds, are expected to be equal; when small differences between energy levels arise, these can be interpreted entirely in terms of Coulomb effects. With the term Coulomb Energy Displacement (CED) one indicates the energy difference between levels in mirror nuclei [20]. The angular momentum dependence of CED has been investigated recently in series of nuclei of the lf~12 shell allowing to study the spatial behaviour of the active valence nucleons [20, 21, 22, 23]. As a consequence, the smooth variation in the CED reflects in detail the change as a function of spin of the nucleus: from a deformed rotor ( which is typical of lf~/2 nuclei in the middle of the shell), through one or two particle alignment in the backbending region, to an almost spherical non-collective band termination state. Being the Coulomb energy due only to protons, it has been pointed out that when a J -- 0 proton pair recouples to another J configuration, the Coulomb energy would decrease [24]. In fact, in the J = 0 coupling the overlap of the wave functions (and therefore the Coulomb repulsion) is maximum. In an odd mass nucleus, the blocking effect due to the unpaired nucleon, favours the alignment of the other type of nucleon pairs. When a proton pair in the fT/~ shell changes from a coupled J = 0 state to an aligned J = 6 state, the repulsive Coulomb interaction decreases in the odd-neutron nucleus while in its odd-proton mirror no Coulomb effect is expected when a pair of neutrons align. Thus, at the backbending the corresponding transition energy in the odd-neutron partner will be smaller than that in its odd-proton mirror. For the case of even-even mirror nuclei the experimental information is very scarce. Recently, some theoretical predictions have been reported for odd-even and even-even mirror nuclei in the fv/2 shell in the framework of the cranked shell model [25]. One of the better rotors in the f7/2 shell is the nucleus S°Cr which presents a first backbending around spin I = 10 [26]. Different explanations have been given to this behavior such as a change of shape or a crossing with a band based on an oblate deformation [27]. Another description in terms of a bandcrossing
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
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261
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S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268 12+
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with a high-K band has been also suggested. From the previous lifetimes measurements [28] performed at GASP, the ground state deformed band seems to continue above the I = 8+ yrast state up to the yrare I -- 12+ state. To have a stringest test of the mirror symmetry in nuclei and to look for an experimental fingerprint of the nucleon alignment at the backbending, high spin states in the N -- Z - 2 nucleus S°Fe, in which no gamma transitions were known previously, have been investigated. The 5°Fe nucleus was produced in the reaction 288i+288i at 110 MeV bombarding energy, after the evaporation of one aparticle and two neutrons. The beam was delivered by the XTU Tandem accelerator of the Legnaro National Laboratory. The target consisted of 0.8 mg/cm 2 of 2sSi (enriched to 99.9%) with a Au backing of 15 mg/cm 2. Gamma rays were detected with the EUROBALL array (Clovers and Clusters only), charged particles were detected with the ISIS silicon ball (40 E-AE telescopes) and the neutrons with the Neutron Wall. Events were collected when at least : a ) t h r e e Ge detectors plus one neutron detector fired in coincidence or b) two Ge detectors fired and one neutron was identified in coincidence in the Neutron Wall. Data were sorted in 7 - 7 matrices in coincidence with charged particles and neutrons. For the identification of 7-lines candidates to belong to S°Fe, we have looked at spectra taken in coincidence with neutrons, with only one a-particle and in anti-coincidence with protons. Six transitions have been found, in mutual coincidence with each other, which satisfy all conditions to be in S°Fe. The coincidence spectrum shown in Fig. 9 corresponds to a sum of gates on these transitions. In the same Fig. 9 a coincidence spectrum (with gates on all the relevant transitions) is shown also for the mirror nucleus (S°Cr) produced in the same reaction after a2p evaporation. The comparison of the two spectra illustrates clearly the rapid decrease of population for nuclei lying far from stability. From the present data a cross section of around 15 #b is estimatedfor the S°Fe nucleus.
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
263
Prom the coincidence data and the transitions intensity a level scheme has been built for S°Fe which is shown in Fig. 10 together with the one of the mirror nucleus 5°Cr. Spin and parity assignment for levels in 5°Fe are based on the great similarity of the two level schemes of Fig. 10. The energy difference among levels is ranging from few keV to a maximum value of ~40 keV, to be compared with absolute values of energy up to 7 MeV. This confirms, in a first approximation, the validity of the mirror symmetry which is connected to the charge independence of the nuclear force. Such small energy differences which, as stated above, can be understood as Coulomb effects are plotted in the right part of Fig. 10 as a function of spin as C E D ( I ) = E ~ ( I ) - Ebr(I ). The behavior of the C E D can be explained in the following way: a neutron pair is aligning at I = 8+ in ~°Fe while a proton pair aligns in ~°Cr; at spin I = 10+ a second alignment of the other type of nucleon pairs occurs, a proton pair in 5°Fe an a neutron pair in 5°Cr. The data is qualitatively well described by cranked shell model calculations of ref. [25]. Large shell model calculations are also reproducing with great precision [29] the shape and the absolute value of the C E D curve depicted in the right part of Fig. 10. The fact that such small energy differences are understood and reproduced with high accuracy in calculations is significant of the importance of mirror symmetry in nuclei. 3.3
P r o t o n - a n d v - d e c a y l i f e t i m e m e a s u r e m e n t s in the second m i n i m u m
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58
spherical
Figure 11: Schematic drawing of the proton-decay of the strongly deformed rotational band in 5SCu to spherical states in the daughter nucleus 57Ni.
One peculiar aspect of proton-rich nuclei around mass A--60 with N = Z is that, due to very low Coulomb barrier, proton emission can be an important mode of decay of their excited states. In fact, a new exotic decay mode was established recently in 5SCu, namely a prompt monoenergetic proton decay which connects the lowest state in the rotational band of 5SCu with the spherical states of the daughter nucleus 57Ni [11]. In Fig. 11 a schematic drawing of the process is shown. The excited rotational band of 5SCu built on a quadrupole deformed shape decays both via 7- and proton-emission to spherical states belonging to 58Cu and 57Ni respectively. This band is strongly deformed with a quadrupole deformation of/32=~0.4, which has been extracted from a residual Doppler shift measurement in a Gammasphere thin target experiment [11].
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
264
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The proton decay of a well deformed band is an interesting quantum mechanical process which makes it possible to actress the problem of proton tunneling through a potential energy barrier in a deformed nucleus. One of the quantities wich are inportant in this respect is the lifetime of the proton-decaying state. In the previous Gammasphere experiment, where a thin target has been used, a safe upper limit of 3 ns could be derived. Using a target deposited on a Gold backing an experiment has been performed at Euroball (coupled with the n-wall and the ISIS silicon ball) with the goal to measure the lifetimes of the low lying states of the 5SCu rotational band and possibly of the band-head decaying by proton emission. The 58Cu nucleus has been produced in the reaction 4°Ca+24Mg at 96 MeV, following the evaporation channel l c d p l n . From the analysis of the lineshapes of the -y-rays deexciting the lowlying states in the well deformed rotational band the individual lifetimes of the four lowest states were determined [30]. The deduced transitional quadrupole moments show an increase towards the bottom of the band which is in agreement with the predictions [31]. In order to deduce a new upper limit for the lifetime of the proton decaying state, proton and -y-ray energy correlations have carefully been analized. A new upper limit of 0.5 ps has been obtained, to be compared with the previous value of 3 ns and with theoretical estimates of the order of 10-a ps for a deformed-to-deformed or for a spherical-to-spherical proton-decay [30]. New theoretical calculations for a deformed-to-spherical proton-decay are needed to understand the nature of this new process.
4
Towards doubly-magic l°°Sn: first e x c i t e d s t a t e s in 1°3Sn.
The nucleus l°°Sn is probably the heaviest N = Z nucleus which is stable with respect tO particle emission, corresponding to the doubly magic closure N = Z = 50. Here one has therefore the opportunity
265
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
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to study nuclear magicity at the limits of nuclear existence. Spectroscopy of l°°Sn is not possible with the present available stable beams and will await long till radioactive beams reach enough intensity. The study of neighbouring nuclei is also very difficult, because of the very low cross sections involved in their population, but it is still achievable with present stable beams when using a powerful apparatus like Euroball coupled to its ancillaries. The energy levels in nuclei near x°°Sn define the single particle spectrum and the nuclear interactions around magic number 50, for both neutrons and protons. The neutron single-particle energies around l°°Sn would be best obtained by studying the 1 neutron nucleus l°lSn which is still out of present experimental possibilities; the best verification we can have now of the neutron single-particle energies may come from l°3Sn whose excited states have been identified for the first time in a Euroball experiment. The reaction 5aNi+r~Fe at 240 MeV has been chosen to produce the 1°3Sn nucleus. Being the compound nucleus ll2Xe, the evaporation channel leading to l°3Sn was 2 a l n requiring the simultaneus detection of two alphas and one neutron in the ISIS silicon ball and in the n-wall respectively. In the upper part of Fig. 12 selected regions are shown of a 7-spectrum in coincidence with two alphas and one neutron. For comparison, the same energy regions are displayed below for a spectrum with the additional requirement of a proton and for a cleaned 65Ge spectrum obtained in the reaction 58Ni+12C at 261 MeV [32]. This last spectrum is presented because the lines of 65Ge may arise in coincidence with 2 a l n from the reaction with the 160 contaminant in the target. A careful analysis of the three spectra just mentioned indicates the presence of four transitions at 168, 298, 578, and 1318 keV which fulfill the
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
266
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Figure 14: Level scheme of l°3Sn from the Euroball experiment [33] (a) and the systematics of odd-A neutron deficient Sn isotopes. The widths of the arrows are proportional to the "y-ray intensities.
conditions for belonging to l°3Sn. In fact, they are present in the 2aln-gated spectrum but not in the 2 a l n l p - g a t e d spectrum and in the 85Ge spectrum. A prompt coincidence "r7 matrix has been created with the conditions that two a-particles and one neutron were detected. Despite the low statistics the analysis of the spectra in coincidence with the four lines assigned to l°3Sn gives clear indications of the coincidence relationships between them (see Fig. 13); this allows to construct the level scheme drawn in Fig. 14 [33]. The cross section for the production of I°3Sn is estimated to be around 10#b. Based on a systematic comparison with the other odd-A neutron deficient Sn isotopes (see Fig. 14b), spin and parity (5/2 +) is proposed for the ground state of 1°3Sn. The spins and parities for the states above have been suggested on the basis of DCO ratios obtained for some of the transitions and on the systematics of odd-A Sn isotopes (see Fig. 14b). These data on 1°3Sn are important since they give new constraints to shellmodel calculations around l°°Sn. In fact, various shell-model approaches try to obtain a good fit to the observed excitation energies in the long series of heavier Sn isotopes by varying the input parameters like single particle energies and two body matrix elements; the goal is to extract the best possible value for these quantities. New data, if coming from nuclei with fewer valence neutrons, put more stringent constraints on the parameters and may solve the many ambiguities present in such an approach. A shell model calculation of this kind has been performed on many odd-A Sn isotopes, including the new one l°3Sn, which, as a main result, has produced a more accurate estimate for the relative singleparticle energies of the neutron d5/2 and g7/2 with respect to l°°Sn, e(lgT/2) - e(2d~/2) = 0.11(2) MeV. Future experiments axe necessary in order to establish the complete set of single-particle energies in the d5/2, g7/2, 81/2, d3/2, hll/2 model space.
5
Future of Euroball with radioactive beams
The Eurobail array has been operating for one and half year at the Tandem-ALPI complex of Legnaro and is now taking data at IReS Strasbourg by using the heavy ions beams delivered by the Vivitron accelerator. It will continue the operation in Strasbourg, with emphasis on both high spin phenomena
S. Lunardi / Prog. Part. Nucl. Phys. 46 (2001) 253-268
267
in nuclei and on properties of nuclei far from ]~-stability, up to the end of 2002. The EurobaU community is now discussing (end of 2000) about the new opportunities offered by the use of Euroball detectors in connection with radioactive beams. The proposal has therefore been made to move in 2003 the composite Clover and Cluster detectors (which are the most efficient part of the array) to GSI Darmstadt for experimental campaigns with the radioactive beams provided by the SIS-FRS facility [34]. By fragmentation or fission of relativistic heavy ions several hundred unstable rare isotopes can be generated with sufficient intensity for in-beam spectroscopy for the first time. Secondary beams can also be produced in high spin isomeric states. The beams can be used either at high energies (100-200 MeV/u), for Coulomb excitation and fragmentation reactions, or slowed down to Coulomb barrier energies,allowing :~;~perform fusion and direct reactions [35]. A spectrometer with the granularity of Euroball will be able, as an "example, to study high spin states produced in fusion reactions induced by n-rich short-lived nuclei. Many other ideas and perspectives for nuclear structure studies are expected that can be fulfilled by the coupling of Euroball with the FRS.
6
Summary
With the development of stable-beams accelerators and high precision detection systems an enormous quantity of information on the behaviour and structure of atomic nuclei has been achieved during the years. It has been possible to study the internal structure of stable and unstable nuclei, not only in their ground states but over a large range of excitation energy and spins. With the gain of efficiency and selectivity of modern ~-detector arrays, such as Euroball, one is able now to extend the methods of in-beam ~/-ray spectroscopy not only to extremely high spins but also to more exotic nuclei. In this talk I have reviewed only a small part of the physics that has been obtained recently with Euroball in the study of nuclei far from j3-stability. It has been demonstrated that, taking advantage of very powerful detectors, high intensity stable beams can still compete with low-intensity radioactive beams in their capability to extract crucial properties of nuclear interactions in "exotic" nuclei. We are confident that also the physics of radioactive nuclei will take great profit from such advanced and sophisticated instruments.
7
Aknolewdegments
Euroball is a collaboration involving six countries (Danemark, France, Germany, Italy, Sweden, UK) and around 200 physicists. What I have presented here is the result of the hard work, from the data taking to the data analysis, of many colleagues that are impossible to quote here. I would like to thank in particular all those who provided me with material and help in the preparation of the talk. They are A. Korichi, E. Farnea, S. Lenzi, D. Rudolph, M. Paiacz and C. Fahlander.
References [1] J. Simpson Z. Phys. A 358 (1997) 139 [2] C. Rossi Alvarez Nuovo Cimento A 111 (1998) 601 • [3] E. Farnea et al., gucl. Instr. Meth. A400 (1997) 87 [4] O. Skeppstedt et al., Nucl. Instr. Meth. A421 (1999) 531 [5] B. Singh, R. B. Firestone and S. J. Frank Chu, Table of Superdeformed Nuclear Bands and Fission Isomers, W W W edition, http://ie.lbl.gov/sdband/sdbindex.html [6] T. Nakatsukasa et al., Phys. Rev. C 53 (1996) 2213 [7] B. Crowell et el., Phys. Rev. C 5! (1995) R1599 [8] H. Amro et al., Phys. Lett. B 413 (1997) 15 [9] A.N. Wilson et al., Phys. Rev. C 54 (1996) 559
268 [10] [11] [12] [13] [14]
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A. Korichi et al., submitted to Physical Review Letters D. Rudolph et al., Phys. Rev. Left. 80 (1998) 3018 A..Bohr, B. Mottelson, Nuclear Structure, Vol. 1, p. 44. P.J. Ennis et al., Nucl. Phys. A 535 (1991) 392 ; Nucl. Phys. A 560 (1993) 1079 (erratum). E. Farnea et al., Proceedings of the International Workshop PINGST2000, Lund June 2000, p. 64; Proceedings of the International Conference Bologna 2000, May 2000. [15] V. Hermkens et al., Z. Phys. A 343 (1992) 371 [16] L. Ra~ticati, Phys. Rev. 87 (1952) 521 [17] H. Morinaga, T. Yamazaki, "In beam ~,-ray spectroscopy" North-Holland, Amsterdam 1976 [18] J. Dobacewski, I. Hamamoto, Phys. Lett. B 345 (1995) 181 [19] W. Kutchera et al., Phys. Rev. Lett. 33 (1974) 1108 [20] M. Bentley et al., Phys. Lett. B 437 (1998) 243 [21] J. A. Cameron et al., Phys. Lett. B 319 (1993) 58 [22] C.D. O'Leary et al., Phys. Rev. Lett. 79 (1997) 4349 [23] C.D. O'Leary et al., Phys. Lett. B 459 (1999) 73 [24] J. A. Cameron et al., Phys. Lett. B 235 (1990) 239 [25] J. A. Sheikh, D. D. Warner and P. Van Isaker, Phys. Lett. B 443 (1998) 16 [26] S. M. Lenzi et al., Phys. Rev. C 56 (1997) 1313 [27] G. Martfnez-Pinedo et al., Phys. Rev. C 54 (1996) R2150 [28] F. Brandolini et al., Nucl. Phys. A 642 (1998) 387. [29] S. M. Lenzi et al., Proceedings of the International Workshop PINGST2000, Lund June 2000, p. 240 and to be published. [30] D. Rudolph et al., submitted to Physical Review C [31] A. V. Afanasiev et al., Phys. Rev. C 59 (1999) 3166 [32] D. Sohler et al., Nucl. Phys. A 644 (1998) 141 [33] C. Fahlander et al., submitted to Phys. Rev. Lett. [34] H. Geissel et al., Nucl. Instr. Meth. BT0 (1992) 286 [35] J. Gerl et al., WWW adress: http://www-gsi-vms.gsi.de/eb/html/eb_at_gsi.html