Super-asymmetric fission in the 245Cm(nth, f) reaction at the Lohengrin fission-fragment mass separator

Nuclear Physics A 735 (2004) 3–20 www.elsevier.com/locate/npe

Super-asymmetric fission in the 245Cm(nth, f) reaction at the Lohengrin fission-fragment mass separator ✩ D. Rochman a,b,∗ , I. Tsekhanovich a , F. Gönnenwein c , V. Sokolov d , F. Storrer e , G. Simpson a , O. Serot f a Institut Laue Langevin, 6 rue Jules Horowitz, BP 156, 38042 Grenoble, France b Los Alamos National Laboratory, LANSCE-3, Los Alamos, NM 87545, USA c Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany d PNPI, Gatchina, Russia e DRI, CEA Saclay, 91191 Gif-sur-Yvette Cédex, France f CEA Cadarache, 13108 Saint-Paul-Lez-Durance Cédex, France

Received 15 September 2003; received in revised form 21 November 2003; accepted 13 January 2004

Abstract Mass, isotopic yields and single-fragment kinetic energy measurements for thermal-neutron induced fission of 245 Cm at the Lohengrin fission-product mass separator are described. Using an ionization chamber coupled to the mass separator, we have measured the mass and isotopic yields from fragment mass A = 67 up to A = 77 over three yield decades. This considerably extends the data set previously known for the light peak. A full set of data is now available for this actinide in the super-asymmetric mass region. The results of mass and isotopic yields are compared with those of other compound nuclei to highlight the shell effect at mass 70 for the 246 Cm compound-nucleus system. Also, the present results are compared to the data from the European library JEF2 and the evaluation from Wahl’s Zp model.  2004 Elsevier B.V. All rights reserved. PACS: 25.85.Ec; 28.41.Kw

✩

This work, co-sponsored by CEA-DEN and ILL, forms a part of the PhD thesis of D. Rochman.

* Corresponding author.

E-mail addresses: [email protected] (D. Rochman), [email protected] (I. Tsekhanovich), [email protected] (F. Gönnenwein), [email protected] (V. Sokolov), [email protected] (F. Storrer), [email protected] (G. Simpson), [email protected] (O. Serot). 0375-9474/$ – see front matter  2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2004.01.121

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Keywords: N UCLEAR REACTIONS 245 Cm(n, f), E = thermal; measured fission fragment mass distribution, isotopic yields, kinetic energy spectra; deduced shell effects. Lohengrin mass separator.

1. Introduction Since the time of the discovery of nuclear fission through to the present day, investigations of the thermal-neutron induced fission have remained a dynamic field of nuclear physics [1]. Detailed studies on fission-fragment charge, mass and energy distributions for a large variety of fissile systems continue to be an important source of information about the mechanism of this process. The asymmetric-mass distributions of fission fragments have been known for a long time, and considerable data about these distributions for different fissile nuclei have been accumulated. It is generally recognized (see for instance Refs. [2–4]) that the mass distributions are governed by shell effects in both, spherical and in deformed nuclei. In general fission fragments are very neutron rich. Fission of heavy nuclei is hence one of the most efficient methods for production of very neutron-rich nuclides in the atomic number range from Z = 27 to Z = 65 [5]. By contrast to standard asymmetric fission, which is steered by stabilizing shell effects in the heavy fragment group, the term “super-asymmetric fission” has come into use to designate the phenomenon of enhanced yields in very asymmetric fission where shell stabilization of fragments from the light group appears to play a role [6]. The knowledge of the mass and isotopic distribution of the fragments in super-asymmetric fission is very important for several reasons. (1) The shell model recognizes magic shells at Z = 28 and N = 50 which could be of importance for fragments from the light mass group. The doubly magic nucleus 78 Ni which comes to mind is, however, much too neutron rich to be produced in notable quantities. It has recently been observed in experiments at the GSI [7] but at rates preventing spectroscopic studies. It is therefore anticipated that the influence of the above proton and neutron shells will be observed independently for fragments shifted in mass number. In particular, it should be interesting to see how the extra-stability of the Ni-isotopes with Z = 28 will influence the mass distributions. A recent spectroscopic analysis points to the isotope 68 Ni as having features in common with other magic nuclei [8,9]. In the present work the fission yields of Ni isotopes are compared. (2) Furthermore, for large neutron numbers, the characteristics of the neutron-rich nickel nuclei profoundly affect nuclear astrophysics through the r-process. The nuclear mechanism involved is the rapid capture of neutrons for the synthesis of elements in stars. The precise course of this reaction is rather difficult to establish, but it follows a path among the neutron-rich nuclides and is dictated by the magic numbers. In particular, it is generally suspected that the neutron-rich isotopes of nickel play a privileged role [10]. If the predicted 78 Ni magicity weakens or disappears, it may profoundly affect our understanding of the stellar nucleosynthesis through the r-process. (3) Also reliable fission data are needed for the technical applications of nuclear reactions and for the transmutation of nuclear waste in hybrid reactors [11]. From the Lohengrin fission-fragment spectrometer of the Institut Laue Langevin (Grenoble, France),

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reliable sets of data on the mass, charge and kinetic-energy distributions exist for the fragments of 235 U(nth, f) [12], 239 Pu(nth, f) [13], 249 Cf(nth, f) [14], 242m Am(nth, f) [15] and 237 Np(2n , f) [17] in the super-asymmetric or asymmetric fission region. Yields down to th 10−6 % have already been measured, which shows the possibility and reliability of this sort of measurements on Lohengrin. Singular characteristics at A = 70 have been observed in the mass distribution, with an enhanced yield being dominated by the 70 Ni isotope, in Refs. [12–16]. Furthermore, strong local odd–even effects for protons have been mentioned for the thermal-neutron induced fission of U, Pu, Cf and Am in the above references. Contrary to the results presented in these papers, evaluated data from the JEF2 and ENDF/B6 libraries, or calculated data from Wahl’s Zp model [18] do not show these enhanced yields at the mass A = 70 region neither for 235 U, 239 Pu nor for 245 Cm. Except for 249 Cf(nth , f), no evaluated data take into account the change of the gradient of the mass-yield curve, which takes place at mass A = 70. For 249 Cf(nth , f) only the ENDF/B6 library has evaluated data; it reproduces with a very good accuracy the Lohengrin mass yields. However, this nucleus has practically no importance for reactor physics, and is therefore not a priority for the evaluators [19]. New data for 245 Cm(nth, f) have recently been obtained for isotopic yields in the light mass peak from A = 76 to A = 115 [20,21] and for mass yields from A = 76 to A = 132 [21]. Measurements were performed at the Lohengrin spectrometer. Concerning superasymmetric fission, no data previously existed for 245 Cm(nth , f). Gamma-ray spectroscopy or radiochemical methods do not give access to the mass region A  70 because of the very low yields [22]. The peculiarities of mass A = 70 mentioned above were also expected to be found in our experiment with 245 Cm(nth, f), which aimed to extend the systematics on mass and isotopic yields into the super-asymmetric mass region. The present paper studies super-asymmetric fission of 245 Cm induced by thermal neutrons. The data on mass and isotopic fragment yields obtained are compared with those from experiments with other actinides as well as with the evaluated data given by libraries.

2. Experimental set-up and technique 2.1. Target preparation and experimental set-up The target material from PNPI in Gatchina, Russia, had an isotopic composition of 92% and 8% 244 Cm. The target preparation and fabrication procedures are described in Ref. [20]. Due to the difference of 3 orders of magnitude between the fission cross sections of 244 Cm and 245 Cm (1.2 barns and 2200 barns, respectively), the contribution of the 244 Cm was negligible compared with that of 245 Cm. Several targets were produced. The total mass per target was about 12 µg. Furthermore, each target was protected against sputtering by a nickel foil of 0.25 µm to avoid uncontrolled losses of the target material. All experiments were performed at the Lohengrin mass spectrometer [23], which is a mass separator for unslowed fission products. This device makes use of electric and magnetic deflection fields to separate fission products according to their mass A, their kinetic energy Ekin and their ionic charge q. This spectrometer is installed at the high-

245 Cm

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flux reactor of the Institut Laue Langevin (ILL), where a flux of 5 × 1014 n s−1 cm−2 of thermal neutrons is available for fission studies. The fission fragments selected according to given A/q and E/q ratios by the electromagnetic fields were detected as a function of their nuclear charge Z with a small ionization chamber [24]. The typical flight time of fragments from the target to the detector is about 2 µs. Hence, fragment charges are measured before β-decay. 2.2. Measurement technique In the range of fragment masses that was studied, the measurements provide both mass and isotopic yields, simultaneously as a function of ionic charge and kinetic energy of the fragments. The Z-resolution of the ( E, Erest ) ionization chamber allowed the fractionalindependent yields to be obtained with the method detailed in Ref. [14]. An example for the mass A = 73 is given in Fig. 1. Evidently, the nuclear charges of isobars are approximately

Fig. 1. Nuclear charge resolution obtained with the ionization chamber for the mass A = 73 at different kinetic energies. The measurements were fulfilled at the fragment ionic charge 19+ . For all energies, the nuclear charges are distinctly separated, as symbolically demonstrated by dotted lines.

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resolved. In the following, the kinetic energies given are corrected for the energy loss in the nickel foil protecting the targets. For a given mass A, different measurements were performed at several values of kinetic energy and ionic charge. Typically, three to seven kinetic energies from 90 to 117 MeV were measured per mass from A = 68 to A = 77. For mass A = 67, the measurements were, however, performed only for one energy near the mean kinetic-energy value of mass 68. As regards the ionic charge distributions, eight ionic charge configurations were measured at the mean kinetic energy for each fragment mass from A = 77 down to A = 72. For lighter masses from A = 67 to A = 71, the measurements were performed for only one ionic charge (because of the very low count rates), selected as the mean ionic charge calculated with the Nikolaev formula [25]. To evaluate mass and energy distributions of fragments the burn-up of the targets in the intense neutron flux had to be monitored. To that purpose the kinetic energy distribution for mass A = 135 was measured day-by-day under identical irradiation conditions from Ekin = 77 to Ekin = 95 MeV. In order to assess measurements at different kinetic energies the ionization chamber was calibrated as specified in Ref. [26]. Mass yields were then calculated as described in more detail in Ref. [15]. As usual the mass yields were normalized independently to 100 % for the light and heavy fragment group, respectively. Finally, by normalization of the fractional independent yields to the mass yields the absolute isotopic yields were obtained.

3. Results and discussion Tables 1–3 give the first and second moments for ionic charge (q¯ and σq ), kinetic energy ¯ ¯ (E¯ k and σE ), isotopic (A(Z) and σA;Z ) and isobaric (Z(A) and σZ;A ) distributions. All parameters were calculated with the usual statistical formula. Data for A = 67 were taken for only one energy, the error given is the energy window admitted by the setting of the separator. Mass and isotopic yields were measured for mass 67 up to 77 as explained above. The absolute mass and isotopic yields are presented in Table 4. The isotopic yields of Table 1 Single-fragment ionic charge and kinetic-energy distribution parameters. For A < 72, the ionic charge values were obtained as an integer value of the mean ionic charge calculated with the Nikolaev formula [25] Mass

q¯

σq

E¯ k (MeV)

σE (MeV)

67 68 69 70 71 72 73 74 75 76 77

18 18 18 18 19 19.0 ± 2.1 19.5 ± 1.6 19.2 ± 1.6 19.6 ± 1.6 19.5 ± 1.0 20.2 ± 0.7

– – – – – 0.7 ± 0.3 1.2 ± 0.3 1.0 ± 0.2 1.3 ± 0.3 1.1 ± 0.3 0.9 ± 0.3

103.8 ± 1.0 103.9 ± 6.1 102.6 ± 6.1 102.8 ± 5.1 103.9 ± 5.6 103.6 ± 4.8 103.3 ± 3.2 103.9 ± 4.6 103.9 ± 4.1 103.4 ± 3.3 102.8 ± 3.7

– 2.8 ± 0.8 3.0 ± 0.6 3.8 ± 0.5 3.7 ± 0.6 2.5 ± 0.5 4.4 ± 0.5 5.0 ± 0.4 4.5 ± 0.4 5.6 ± 0.5 4.9 ± 0.5

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Table 2 ¯ Mean mass A(Z) and width σA;Z of the isotopic distribution as a function of the fragment nuclear charge. Data for nuclear charges higher than Z = 31 are from Ref. [21]. The values in italic (Z = 27 where the isotopic yields for A < 67 are missing) are calculated for an incomplete distribution and have to be considered as preliminary Z

¯ A(Z)

σA;Z

Z

¯ A(Z)

σA;Z

27 28 29

68.03 ± 0.29 70.27 ± 0.21 73.16 ± 0.11

0.70 ± 0.11 1.14 ± 1.13 1.11 ± 0.05

30 31 32

75.66 ± 0.07 78.49 ± 0.10 80.54 ± 0.11

1.13 ± 0.07 1.16 ± 0.03 1.15 ± 0.04

Table 3 Mean nuclear charge Z¯ and width σZ;A of the isobaric distribution as a function of the fragment mass A

¯ Z(A)

σZ;A

A

¯ Z(A)

σZ;A

68 69 70 71 72

27.58 ± 0.31 27.83 ± 0.06 28.08 ± 0.03 28.38 ± 0.09 29.08 ± 0.07

0.49 ± 0.26 0.29 ± 0.08 0.26 ± 0.05 0.48 ± 0.09 0.64 ± 0.11

73 74 75 76 77

29.31 ± 0.07 30.02 ± 0.02 30.06 ± 0.06 30.31 ± 0.03 30.86 ± 0.04

0.53 ± 0.03 0.40 ± 0.03 0.40 ± 0.08 0.51 ± 0.05 0.55 ± 0.03

secondary fragments for eleven masses were measured over three yield decades. For mass A = 67, only one count for cobalt (Z = 27) was obtained after six hours of measurement. The uncertainties on isotopic yields in Table 4 and on the mean value and variance for a given mass or charge in Tables 1 to 3 have been calculated with the error propagation formula considering two independent values (mass yield and one of the isotopic yield) when two isotopes are found in one mass. In the case of three isotopes for one mass (A > 71), three independent variables are considered, following the same maximization of the uncertainties. The independent isotopic yield is thought to contribute the largest uncertainty. 3.1. Mass yields The mass yields obtained in the present study are compared in Fig. 2 with the mass yields from 235 U(nth, f) [12], 239 Pu(nth, f) [13], 242m Am(nth, f) [15], 249 Cf(nth, f) [14], as well as with evaluated data (JEF2 library [27] and Wahl’s Zp evaluation [28]) for 245 Cm(n , f). th The first discovery of a shoulder in the mass yield near A = 70 for reactor-neutron induced fission was reported in 1974 by Rao et al. [29] for U-isotopes where abnormally high yields for A = 66, 67 and 72 were measured by a radiochemical method. At the same time, a calculation based on the liquid-drop model with the inclusion of shell corrections disclosed mass super-asymmetric valleys corresponding to enhanced fission yields for 66 Ni and 67 Cu in fast-neutron fission of 238 U [30]. For 246 Cm analyzed in the present study, similar to the compound nuclei from 236 U to 243 Am , a pronounced hump in the mass yield is present at A = 70. As proposed in Ref. [15], this structure in the mass-yield distribution is again understood as a result of the influence of shell closure at Z = 28 which is the only magic proton shell to be expected in the light-fragment mass distribution. Indeed, it is seen in Table 4 that for A = 70 most of the yield is due to Z = 28. However, for

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Table 4 Absolute mass and isotopic yields, summed over the kinetic energies and ionic charges, with errors given in italic below each value A

Mass yield

Z = 27 (Co)

67 ±

2.78 × 10−6

2.78 × 10−6

2.78 × 10−6

Z = 28 (Ni)

Z = 29 (Cu)

Z = 30 (Zn)

68 ±

1.52 × 10−5 6.80 × 10−6

6.31 × 10−6 4.38 × 10−6

8.89 × 10−6 7.34 × 10−6

69 ±

3.85 × 10−5 7.86 × 10−6

3.18 × 10−6 2.26 × 10−6

3.52 × 10−5 2.60 × 10−5

70 ±

8.29 × 10−5 9.45 × 10−6

7.66 × 10−5 3.17 × 10−5

6.30 × 10−6 2.70 × 10−6

71 ±

6.85 × 10−5 1.04 × 10−5

4.26 × 10−5 1.06 × 10−5

2.59 × 10−5 7.54 × 10−6

72 ±

9.91 × 10−5 1.13 × 10−5

1.78 × 10−5 4.79 × 10−6

5.82 × 10−5 2.18 × 10−5

2.32 × 10−5 5.46 × 10−6

73 ±

3.29 × 10−4 2.16 × 10−5

8.42 × 10−6 3.45 × 10−6

1.94 × 10−4 1.66 × 10−5

1.26 × 10−4 5.35 × 10−5

Z = 29 (Cu)

Z = 30 (Zn)

Z = 31 (Ga)

Z = 32 (Ge)

74 ±

1.07 × 10−3 5.25 × 10−5

7.74 × 10−5 1.41 × 10−5

8.98 × 10−4 2.34 × 10−4

9.46 × 10−5 1.56 × 10−5

75 ±

1.95 × 10−3 8.83 × 10−5

5.97 × 10−5 1.55 × 10−5

1.62 × 10−3 8.05 × 10−5

2.67 × 10−4 7.14 × 10−5

76 ±

4.31 × 10−3 1.46 × 10−4

3.13 × 10−3 7.37 × 10−4

1.08 × 10−3 7.31 × 10−5

1.02 × 10−4 2.24 × 10−5

77 ±

6.72 × 10−3 1.81 × 10−4

1.41 × 10−3 1.62 × 10−4

4.58 × 10−3 1.47 × 10−4

6.77 × 10−4 5.75 × 10−5

2.78 × 10−6

compound nuclei heavier than 246 Cm , the enhancement effect becomes weaker and for the fissioning nucleus 250 Cf , the structure for the super-asymmetric mass region in question manifests itself only as a change in slope of the mass-yield curve [14]. The gradual fading of the nuclear structure effect for increasing fissilities of heavy nuclei is in line with the observed trend of increasing intrinsic-excitation energies at scission which should have a tendency to smooth out shell effects [31]. It can be noticed that on the left part of Fig. 2, the absolute yields in super-asymmetric fission for all reactions studied are close together from A = 80 down to A = 73. For A < 73, the mass yields for the reaction 235 U(nth, f) become different from the yields for the other systems. The similarity of mass yields in this mass region is a major result, to be compared to the stability of the heavy fragment yields for standard asymmetric fission related to the shell closure of the 132 Sn nucleus. Hence, both asymmetric and superasymmetric fission are governed by shell effects, either in the heavy or the light fragment, respectively.

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Fig. 2. Left: absolute fragment-mass yields for the reactions 235 U(nth , f), 239 Pu(nth , f), 242m Am(nth , f), 245 Cm(n , f) and 249 Cf(n , f) measured at Lohengrin (see text for references). Right: 245 Cm(n , f) data from th th th this work (A < 78) and Ref. [21] (A > 77), from the JEF2 library and the Wahl Zp evaluation. Half of the error bars for Wahl’s data and JEF2 data (positive and negative error bars respectively) are presented for the clarity of the figure.

As shown in the right panel of Fig. 2, in the case of 245 Cm(nth, f), the change in the mass-yield slope for A = 70 is not apparent in the evaluated data and for several masses the evaluated yields are at variance with experiment. The same phenomenon shows up in the evaluations of 235 U(nth, f) and 239 Pu(nth, f) for the change of slope at A = 70 which is not predicted. One can also observe in the right panel of Fig. 2 that, for 245 Cm(nth, f), the uncertainties which had to be ascribed to evaluated data are larger than those for the measured data. 3.2. Isotopic yields The isotopic yields from 245 Cm(nth , f) evaluated from the present measurements are shown in Fig. 3 along with the mass yields. The isotopic yield distributions in superasymmetric fission are comparable in shape to those of “standard” asymmetric fission. Similar to the results from Refs. [20,21] for masses from A = 77 up to A = 115, the isotopic and isobaric yields in super-asymmetric fission follow globally a Gaussian distribution as described by Wahl for instance in Refs. [18,32]. It is interesting to observe that the nuclear charge Z = 30 is dominant for three masses (from A = 74 to A = 76) at more than 70% of total yield. For the thermal-neutron induced fission of 235 U and 249 Cf, this characteristics was also seen, as presented in Fig. 3. Furthermore, the same phenomenon appears for Z = 28 where this nuclear charge is prevailing for four masses (from A = 68 to A = 71). For 235 U(nth , f), the Z = 28 contribution is also dominant between A = 69 to A = 71 (see Fig. 3). The yields of even charge fragments are hence strongly pronounced (see below). Concerning the increase of the mass yield for the masses around A = 70, no deviation from the Gaussian distribution is seen on the isotopic yields of the nuclear

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Fig. 3. Top: mass and isotopic yields for 245 Cm(nth , f). Data for A < 78 are from this work and the data for A > 77 are taken from Ref. [21]. Bottom: mass and isotopic yields for 235 U(nth , f) [12] and 249 Cf(nth , f) [14] previously measured at Lohengrin.

charge Z = 28. The isobaric distribution for the mass A = 70 shows that more than 90% of this mass are isotopes of nickel. The enhanced formation of mass A = 70 is thus clearly due to the proton shell closure at Z = 28. These results for the A = 70 distribution are in agreement with experiments for 30 MeV proton-induced fission of 238 U [33] measured at LISOL. Also no deviation from the Gaussian distribution has

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Fig. 4. Comparison of isotopic yields between Lohengrin, JEF2 and Wahl’s Zp model for 245 Cm(nth , f). The “Lohengrin” values for A > 77 are from Ref. [21].

been found, but a slight difference in the centroids exists [69.45 ± 0.07 for 238 U(p,f) and 70.27 ± 0.21 for 245 Cm(nth, f)]. In addition to the proton shell closure also the neutron subshell N = 40 may come into play, in particular for 68 Ni and 67 Co. Evidence for a magic N = 40 subshell in neutron-rich nuclei has recently been advocated [9]. Fig. 4 presents comparisons of isotopic yields in the super-asymmetric-fission region between data from the library JEF2, from Wahl’s Zp model and from the present experiment. In this figure, the values measured in this work (A < 78) are in good agreement with the evaluated ones, except for Z = 29 (A < 72) and Z = 28 (A > 71). No previous measurements exist for the super-asymmetric fission of 246 Cm , so evaluated data from the library JEF2 in this region stem from models which do not take into account any fine structure. The overestimate in isotopic-yield amplitude for Z = 29 and A < 72 for the JEF2 library and Wahl’s Zp model, partly compensated by the underestimation for Z = 28, is reflected in the mass yields where a larger difference is observed between the measurement and the evaluation for A = 72 (see Fig. 2 right panel). It is just these slight discrepancies, however, which instead of the smooth behavior predicted by evaluations give rise to a shoulder in the experimental mass yield at A = 70. Concerning the uncertainties on the nuclear charge Z = 27 yields, our data are characterized by large error bars due to the low count rate. For the other charge numbers the experimental errors are generally smaller than the uncertainties given by evaluators.

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Fig. 5. Left: average kinetic energy for different nuclear charges as a function of their mass numbers. Nuclear charges are displaced on the Y -axis to make the picture readable. Right: logarithm of the isotope yields as a function of the Q-values (keV) for 67 < A < 80.

On the whole, nevertheless, the agreement between the present data and in particular the predictions by Wahl’s model is rather good. Applying the same type of analysis which was introduced in Ref. [12] for 235 U(nth, f), the average kinetic energy of each nuclear charge has been calculated with the data for 245 Cm(n , f) as a function of its mass. The results are presented in the left part of Fig. 5. th As for thermal-neutron-induced fission of 235 U [12], 239 Pu [26] and 242m Am [15], the average kinetic energies of the isotopes increase strongly and regularly with the neutron number for Z > 30. For the lightest nuclear charges however, there is no dependence of kinetic energy on fragment mass, to be observed. For Z = 28, the measured statistics is low, which induced large uncertainties on the calculated averaged kinetic energies, as presented in the left part of Fig. 5. In consequence, the oscillations for this nuclear charge are not significant. This feature is surprising since for a given charge number one should expect that for decreasing mass numbers the kinetic energies also decrease, as indeed observed for the somewhat heavier charges. This correlation is simply due to neutron evaporation because for every neutron evaporated from the light fragments under discussion some 1.5 MeV of kinetic energy is lost for the fragments. The constancy of the kinetic energy of isotopes as a function of their mass is, therefore, a strong indication that super-asymmetric light fragments do not emit neutron at all. Neutron multiplicities near zero for magic superasymmetric light fragments should be seen in close analogy to those virtually vanishing multiplicities for magic asymmetric heavy fragments near 132 Sn. As demonstrated in Ref. [14], a linear correlation exists between the logarithm of the isotopic yields Y (A, Z) of single nuclides and the Q-values for their formation (see right part of Fig. 5). The Q-values are calculated from the ground state mass of 245 Cm plus an unbound neutron minus the mass of the two complementary fission fragments. As suggested above, it is assumed that light fragments in super asymmetric fission do not emit neutrons which allows one to find unambiguously the complementary heavy fragment.

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The mass excesses were obtained from the table of Audi [34]. A linear fit through the data points gives the following equation: log(Y (A, Z)) = 0.155 · Q − 31.57 with Q in MeV. The values of this fit are close to those obtained in Ref. [14] in the case of 249 Cf(nth , f): 0.149 for the slope and 31.744 for the intercept. This shows that the proton shell does not have any special influence on the linearity of the log(Y ) = f (Q) equation. Thus, the linear relationship between the log(Y ) and the corresponding Q-value can be used for a rough prediction of yield of masses below A = 70. 2 ¯ of the isobaric distribution 3.3. Mean nuclear charge Z(A) and variance σZ;A

It was mentioned in the above that the isobaric charge distributions for any fixed mass are well reproduced by Gaussians [32] modulated by odd–even factors:
2 ¯ FZ (A) (Z(A) − Z(A)) exp − Ym (Z; A) = √ . (1) 2 2 2σZ;A 2πσZ;A 2 ¯ In this equation, Z(A) is the most probable charge (not necessarily an integer), σZ;A is the variance of the distribution and FZ (A) is the odd–even factor. Table 3 presents the ¯ mean nuclear charge Z(A) and the square root of the variance σZ;A together with the ¯ uncertainties of these values. Figure 6 shows Z(A) and σZ;A for four thermal-neutron 235 239 245 induced fission reactions ( U, Pu, Cm and 249 Cf). On the left part of Fig. 6, all fissioning systems follow globally the same trend for the mean nuclear charge as a function of fragment mass. Similar to the width of the nuclear charge distributions, the mean nuclear charge calculated from the 245 Cm(nth , f) data follows very well the systematics defined by the other fissioning systems. Despite large error bars on the sigma values for A = 68 and 69, a common trend can be seen on Fig. 6 (right) for the four displayed fissioning systems: there is a minimum around A = 70 and A = 74–75 and a maximum at A = 72 for all the systems. Therefore the period

Fig. 6. Mean nuclear charge (left) and width (right) of the isobaric nuclear charge distribution from this work and Refs. [12–14].

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Table 5 Mean width σ¯ Z;A for different reactions and different mass regions A ∈ [68−77] 235 U(n , f) th Lohengrin 239 Pu(n , f) th Lohengrin 245 Cm(n , f) th Lohengrin 245 Cm(n , f) th JEF2 245 Cm(n , f) th Zp 249 Cf(n , f) th Lohengrin

A < Af /2

0.42

 0.6

0.58

 0.6

0.45 ± 0.03

0.61 ± 0.12 0.58 ± 0.20 0.65 ± 0.25

0.52

 0.6

of A  5 for a sinusoidal-type structure is visible, well-known in the asymmetric-fission region, and traced to the charge odd–even staggering. For the 245 Cm(nth, f) data from the present experiment this odd–even staggering is especially well pronounced. Table 5 presents the mean width σ¯ Z;A averaged over different mass regions for 245 Cm(n , f), 235 U(n , f), 239 Pu(n , f) and 249 Cf(n , f). In the mass region A < A /2 (A th th th th f f is the mass number of the fissioning nucleus), for 235 U(nth , f), 239 Pu(nth, f) and 252 Cf(sf), σ¯ Z;A has been calculated to be around 0.6 charge units [15,18]. It appears that, except for the 239 Pu(nth , f) system, the square root of the mean variance in the super-asymmetric region is slightly smaller than σ¯ Z;A calculated over the whole light peak. In a statistical model, the variance of a charge distribution is proportional to the intrinsic-excitation energy of a fully equilibrated system (see for instance Ref. [31]). In this hypothesis, with the exception of the 239 Pu case, the conclusion is that the intrinsic-excitation energy in super-asymmetric fission is smaller than the one in asymmetric fission. For low excitation energies, also the neutron emission numbers will be low. This latter statement was already conjectured above in connection with the observed constancy of the average E(A; Z) in super-asymmetric fission. 2 ¯ of the isotopic distribution 3.4. Mean mass A(Z) and variance σA;Z

¯ The mean mass A(Z) and root mean square of the variance σA;Z of the isotopic ¯ distribution can be obtained from the measured data (Table 4). To calculate A(Z) and σA;Z for Z > 31, the nuclear charge distributions for the masses higher than A = 77 are complemented with the values from Ref. [21]. For Z = 27, the value of σA;Z is not shown because the distribution is not known. The data from this work are presented on Fig. 7 ¯ together with the mean mass A(Z) and σA;Z calculated from data obtained in 30 MeV proton-induced fission of 238 U [33] and from thermal-neutron induced fission data for 235 U, 239 Pu and 249 Cf. Concerning the dependence of the mean mass on Z, our data are in good agreement with the systematics defined by the other actinides. For a given nuclear charge of a fission fragment, the mean mass is observed to decrease when the mass of the fissioning nucleus increases. This can be explained by the fact that for a larger mass of the fissioning nucleus, more neutrons are emitted during fission. This is a well-known trend which is linked to the higher excitation energies being set free the heavier the fissioning nuclei are. Therefore the fission fragments from 246 Cm are less neutron-rich than, e.g., those of 236 U . This

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¯ Fig. 7. Comparison of the mean mass A(Z) and width σA;Z of isotopic mass distributions for different reactions.

explanation is corroborated by 30 MeV-proton induced fission (Ref. [33]): the mean masses for Z = 28, 29 and 31 are clearly below the mean masses for the fission fragments from thermal-neutron induced fission (see Fig. 7). On the right panel of Fig. 7, the variation of σA;Z as a function of nuclear charge calculated with the present data in this region is small, as it is also for the other actinides. Furthermore all the σA;Z values lie between 1.1 and 1.4, except for 240 Pu and 250 Cf at Z = 28. In the case of 245 Cm(nth, f), the σA;Z appears slightly smaller than for the other actinides. However, not too much importance should be attached to this feature since the determination of variances is delicate; it depends on the number of nuclear charges with low yields close to background which are taken into account in the evaluation of the superasymmetric fission. 3.5. Single-fragment kinetic-energy distribution The kinetic-energy distribution (mean value and sigma) for each fission fragment mass can be calculated from our measurements on Lohengrin as explained in Refs. [35,36]. Fig. 8 shows the mean kinetic energy from Table 1, compared to the data from 235 U(nth , f) [12,35], 237 Np(2nth, f) [36], 245 Cm(nth , f) for A > 76 [21], and 249 Cf(nth , f) [14]. The value for A = 67 for 245 Cm(nth, f) is shown without error bars because only one kinetic energy was measured. As follows from this figure, and as it is also well known, the single-fragment kinetic energy for a given mass increases with the fissility of the fissioning nucleus in thermal-neutron induced fission. The values from the super-asymmetric fission of 245 Cm(nth, f) follow well the trend defined by the data in asymmetric fission for the same reaction from Ref. [21]. As seen in Fig. 8, average kinetic energies of fragments are reported for masses A < 74 only for 235 U(nth, f) and 245 Cm(nth, f), and for masses below A = 70 only the present data for 245 Cm(nth, f) are available. From the results for 246 Cm

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Fig. 8. Mean single-fragment kinetic energy as a function of the fragment mass. See text for references.

it appears that the near-constancy of the average kinetic energies for fragments throughout the light mass wing still holds for the very light fragments from super-asymmetric fission. 3.6. Proton local odd–even effect Various definitions for odd–even effects of fission fragment yields have been compared in Ref. [37]. A theoretical description of these odd–even effects has been given in Ref. [38]. The local odd–even effect of nuclear charge yields is usually calculated following a prescription which was proposed by Tracy et al. [39]. In this definition, the deviations of four consecutive isotopic yields from a smooth Gaussian curve are considered. The results for the proton local odd–even effect for 245 Cm(nth, f), 235 U(nth , f) and 249 Cf(nth , f) are presented in Fig. 9. As already mentioned for 235 U(nth, f) [12], 242m Am(nth, f) [15] and for 249 Cf(nth, f) [14], the local odd–even effect increases strongly in the region of super-asymmetric nuclear charge. The same phenomenon was observed in both, even-Z and odd-Z fissile nuclei, and in super-asymmetric fission of 228 Pa, 226 Th and 233 U nuclei using inverse kinematics [40]. In super-asymmetric fission the local odd–even effect of nuclear charge yields is larger than 20%. It reflects the strong preferential formation of fragments with even nuclear charges in this mass region. As first observed for the reaction 235 U(n , f) [12], the large odd–even effect in super-asymmetric fission indicates that the th intrinsic excitation energy at scission and hence nuclear dissipation is particularly low for these fragmentations of nuclei.

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Fig. 9. Local odd–even effects for protons following the definition by Tracy et al. [39].

4. Conclusion The super-asymmetric mass region for light fragment masses A < 80 was investigated for the 245 Cm(nth, f) reaction from mass A = 77 down to A = 67, corresponding to a decrease by three orders of magnitude in yield. As for the other actinides measured in this region, the proton shell effect in the light peak has been observed for the mass A = 70 at nuclear charge Z = 28. Similarly to the thermal fission of 235 U, 239 Pu and 242m Am, the dependence of the average kinetic energy of isotopes on mass indicates that the neutron evaporation from the very light super-asymmetric fission fragments is low, as it is for standard asymmetric fission in the vicinity of the doubly closed shell nucleus A = 132. Finally, a preferential formation of light fragments with even nuclear charges (Z = 28 and Z = 30) was found in this mass region. This effect was also observed for other fissile nuclei.

Acknowledgements We wish to thank Prof. H.O. Denschlag from the Johannes-Gutenberg Universität, Institut für Kernchemie, Mainz, Germany for having initiated this project, and Dr. Trautmann from the same institute for his collaboration in the target preparation. We are also grateful to Dr. A. Wahl for his advices concerning the interpretation of these data.

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