First observation of medium-spin excitations in the 138Cs nucleus

Abstract.Medium-spin, yrast excitations in the 138Cs nucleus, populated in the spontaneous fission of 248Cm, were observed for the first time. 138Cs was studied by means of prompt γ-ray spectroscopy using the EUROGAM2 array. The newly observed yrast cascade, built on the known 6- isomer at 80 keV, was successfully described by shell model calculations. Analogously to the 136I isotone, the 6- isomer in 138Cs has the $\ensuremath{(\pi g_{7/2} ^4 d_{5/2} \nu f_{7/2})_{6^-}}$ dominating configuration and the 7- excitation, located 175 keV above, corresponds to the $\ensuremath{(\pi g_{7/2} ^3 d_{5/2}^2 \nu f_{7/2})_{7^-}}$ as dominating configuration. Similarly as in 136I, changing the position of the d5/2 proton orbital improves the reproduction of the data. However, in 138Cs the energy of this orbital should be increased compared to its energy in 133Sb, to get the best description, in contrast to 136I and 135Sb, where it had to be decreased. The best reproduction of excitation energies in 138Cs is obtained assuming that the πd5/2 orbital in 138Cs is located about 100 keV higher than in 133Sb. These observations suggest that the lowering of the d5/2 s.p. energy in 135Sb is not a physical effect due to the appearance of a neutron skin, as proposed by other authors, but rather an artifact due to some deficiency of the input data used in the shell model calculations in the region of the doubly magic 132Sn core.

The 138 Cs nucleus has been studied before experimentally in a measurement of the IT decay of the 6 − isomer [1] and in beta decay of 138 Xe [2]. Very recently these low-spin excitations were investigated theoretically within the shell model [3]. This last study has shown that the SMPN set of two-body matrix elements (tbme's), proposed recently for the 132 Sn region [4], can reproduce rather well the 6 − isomer in 138 Cs. Interestingly, no other interaction, usually used in this mass region, can reproduce the isomeric nature of the 6 − state with a half-life of the order of minutes and even the 3 − ground state is not reproduced in some of these calculations (see refs. [3,5] for details). Similarly good description was also obtained in our study of an analogous 6 − isomer in the isotone 136 I [6] where the single-particle energy of the proton d 5/2 orbital had to be lowered by 400 keV relative to its position in 133 Sb. This puzzling effect was first observed in 135 Sb and interpreted as due to the formation of neutron skin past the N = 82 a e-mail: Teresa.Rzaca@fuw.edu.pl shell [7,8]. Using the SMPN set we confirmed the need to lower the d 5/2 orbital in 135 Sb but in ref. [6] we argued against the neutron skin hypothesis, noting that its formation should be a slow phenomenon like other changes in this region connected with the growing number of neutrons, whereas the need for a decrease of d 5/2 s.p. energy was rather abrupt. Instead, we suggested that the lowering of the πd 5/2 s.p. energy may be an artificial effect, which surprisingly well accounts for deficiencies of some of the tbme's, possibly proton-neutron interactions. To propose any improvement one would like to know how the effect varies with the proton and the neutron number. In fig. 1 we show the approximate shifts (in keV), which have to be applied to the πd 5/2 s.p. energy in various nuclei in the 132 Sn region in order to reproduce them properly. Figure 1 suggests that the effect grows with the number of valence neutrons and/or the number of πν pairs. It is thus of interest to find its magnitude in the 138 Cs nucleus. On one hand, fig. 1 Fig. 1. Values of shifts (in keV) to πd 5/2 s.p. energy, which should be applied to reproduce properly the excitation energies in the indicated nuclei. The data are taken from refs. [3,4,[6][7][8][9]. The value at 135 Sb is an average of values calculated in ref. [7] and using the SMPN set. See text for more explanations.
with SMPN interaction, which reproduced well low-spin levels in 138 Cs, were performed without any shift to the πd 5/2 orbital. We note that in ref. [3] although the isomeric nature of the 6 − state could be reproduced, its excitation energy was slightly under-predicted. The existing experimental data on 138 Cs, to be compared with the calculations, is rather limited. Therefore to get more precise answer one should first obtain more experimental information on the 138 Cs nucleus.
In this letter we report on the observation of a mediumspin cascade in 138 Cs decaying to the 6 − isomer at 80 keV. The new data were obtained from the measurement of prompt gamma radiation following spontaneous fission of 248 Cm, performed using the EUROGAM 2 array [10], equipped additionally with four Low Energy Photon (LEP) detectors. We measured high-fold coincidences between gamma rays from fission fragments. The data were sorted into 3D histograms, which were used to produce doubly gated gamma spectra (see refs. [11,12] for more details).
A useful technique to find new gamma cascades in fission fragments is based on the observation that in fission act a nucleus breaks into two fragments, which evaporate a few neutrons but not protons. Thus, in the spontaneous fission of 248 Cm, Cs nuclei are produced in pairs with Nb nuclei. In addition 3.5 neutrons are evaporated from fission products, on average. All this happens in less than a femtosecond. Subsequently, the so-called prompt gamma rays are emitted from both fragments at the same time. Therefore by gating on gamma lines of Nb isotopes one can observe gamma rays from the complementary Cs isotopes in the gated spectra.
It is expected that the most abundant complementary fission fragment to 138 Cs in the spontaneous fission of 248 Cm is the 106 Nb nucleus. Unfortunately, no prompt gamma cascades are known in 106 Nb. The heaviest Nb isotopes where such cascades are known is 105 Nb. This nucleus is produced together with 138 Cs when 5 neutrons are evaporated, which makes this process less likely, but still possible to observe. To search for prompt gamma rays in 138 Cs we thus gated on known lines from 105 Nb. A gamma spectrum, doubly gated on the 128 keV and 162 keV lines    fig. 3. Spins of the excited levels were proposed tentatively, based on the observed branching and the assumption that spins are growing with increasing excitation energy, as commonly observed in prompt gamma measurements from fission. As discussed above the newly constructed decay scheme belongs to a cesium isotope. Its pattern is characteristic of excitations in a spherical nucleus. In our earlier studies we identified excitation schemes of 141,143,145 Cs [16]. The 141 Cs and 143 Cs nuclei exhibit a collective behavior [17] with signs of octupole deformation. It is expected that heavier Cs isotopes also will be deformed. We also found an excitation scheme of 139 Cs [14], which, although spherical, shows signs of some collectivity. The new cascade is similar in character to the excitation scheme of 137 Cs [18]. We therefore propose that the new cascade belongs to its neighbour, 138 Cs. An analogous cascade was found in 136 I [19], the isotone of 138 Cs. As we have shown recently, the cascade in 136 I is based on the 6 − isomer, with the 7 − excitation of πg 7/2 νf 7/2 dominating   configuration, located 42 keV above the isomer. In 138 Cs one may expect a similar excitation pattern. The new cascade is thus built on the known T 1/2 = 2.9 min isomer with spin I π = 6 − and excitation energy of 79.9 keV [1] and the 7 − is located 175.5 keV above it.
To verify this hypothesis we performed unrestricted shell model calculations, where five protons were allowed to occupy the g 7/2 , d 5/2 , d 3/2 , s 1/2 and h 11/2 orbitals and the odd neutron was allowed on the f 7/2 , h 9/2 , f 5/2 , p 3/2 p 1/2 and i 13/2 orbitals. We used the SMPN set of two-body matrix elements [4] and the OXBASH computer code [20]. The results of the calculations are compared in fig. 4 with the experimental excitation energies, normalized to each other at the 3 − ground state.
In the calculations we varied the single-particle energy of the proton d 5/2 orbital to check its role in the neutronrich nuclei, as discussed at the beginning of this letter. The change to the πd 5/2 s.p. energy (in keV) is marked in fig. 4 as D.  The gross feature of the calculated scheme, rather independent of the D value, is a clear distinction between lowspin levels (up to spin 7 − ), dominated by the πg 7/2 νf 7/2 configuration (with essential πd 5/2 contribution) and higher-spin excitations. The calculated scheme corresponds very well to the experimental excitation pattern, where similar distinction is observed. We note that this pattern is similar to the one observed in the 136 I isotone.
Closer inspection shows that the description improves when the πd 5/2 s.p. energy increases and the optimum is reached at D ≈ 150 keV. Again, as observed in the case of 136 I, one of the 6 − levels varies rapidly its energy as a function of D (it is marked by full circles in fig. 4). This 6 − state is dominated by the πd 5/2 νf 7/2 configuration, which explains its behavior. The wave function of the 7 − state contains the odd proton in the g 7/2 orbital. We mention, though, that there is an upper limit to the πd 5/2 s.p. po What differs the 138 Cs case from other cases indicated in fig. 1 is that here the optimum reproduction requires the πd 5/2 s.p. energy to be increased relative to its position in 133 Sb. Figure 4 shows, again, that the πd 5/2 s.p. energy is a (surprisingly) convenient parameter to compensate for some unknown deficiencies of the shell model description in the 132 Sn region. However, the change to this energy, applied in the calculations, probably does not correspond to any real πd 5/2 s.p. energy change in nuclei. While one could consider the argument of refs. [7,8] about the neutron skin pushing the πd 5/2 down in energy, it would require some anti effect to push it up.
It was found that shell model calculations give too high binding energies (E B ) for the ground states in the 132 Sn region [4,21]. Decreasing the s.p. energy of the πd 5/2 orbital makes the situation even worse [6,9]. It is interesting to see that in 138 Cs, where the πd 5/2 orbital is not lowered, the calculated energies agree rather well with the experiment. This is illustrated in fig. 5 where we compare, on the "absolute" energy scale (binding energies, relative to the g.s. energy of 132 Sn), calculated and experimental energies for the three lowest levels in 138 Cs. While the distances between the levels in 138 Cs are best reproduced at D ≈ 150 keV (see fig. 4), the absolute energies for the three discussed levels, calculated at D = 150 keV are slightly higher than experimental values. This result, combined with the observations for other nuclei [6,9], indicates that the overbinding grows with the increasing neutron number.
We have argued against the "neutron skin" hypothesis above. Nevertheless, this work supports the observation that there is a new, unexplained effect in the neutron-rich nuclei of the 132 Sn region. The "map" shown in fig. 1, en-riched now by the D ≈ +100 keV value at 138 Cs, suggests that the discussed effect concerning the πd 5/2 s.p. energy depends on the number of valence neutrons past the N = 82 line. At the beginning of this letter we also mentioned about a possible dependence on the number of πν pairs. The new data on 138 Cs suggest, however, that such a dependence is less likely as can be deduced from the comparison of the πd 5/2 s.p. energy shifts in 138 Cs and 135 Sb. Consequently, the solution of the problem may require something else than correcting proton-neutron interactions in the region. The present work still does not provide the answer. New studies are required, preferably of the most neutron-rich rich nuclei, close to the Z = 50 closed shell, where, on one hand, the effect is expected to be clearly present and, on the other hand, the nuclei in question could be described in the framework of the shell model.
In summary, a medium-spin cascade was identified on top of the 6 − isomer in 138 Cs. The new cascade is well reproduced by shell model calculations using the SMPN set of two-body matrix elements proposed recently for the 132 Sn region. The best fit to the experimental data, including the ground stated and the 80 keV isomer is obtained when the position of the d 5/2 orbital is increased by 100 keV, compared to its position in 133 Sb. This result again shows an important role of πd 5/2 s.p. energy in the region of 132 Sn, but the positive sign of the energy shift is an argument against the "neutron skin" hypothesis, proposed in other works, though we confirm that the effect depends on the number of valence neutrons.