*3.5. Heavier Collective Nuclei: Triaxiality in 130Xe and 140Sm*

The 130Xe and 140Sm isotopes are examples of relatively heavy nuclei, probed with low-energy Coulomb excitation, for which extensive Shell-Model calculations have been performed [16,72]. Both isotopes were studied at ISOLDE, with the measurement for the stable 130Xe being a by-product of a radioactive beam experiment. Beam energies were 4.2 MeV/*A* and 2.8 MeV/*A*, respectively, and states up to *I<sup>π</sup>* = 6<sup>+</sup> <sup>1</sup> were observed in 130Xe, while the 2<sup>+</sup> <sup>1</sup> , 4<sup>+</sup> <sup>1</sup> and 2<sup>+</sup> <sup>2</sup> states were populated in 140Sm. The results point to the importance of the triaxial degree of freedom in the structure of low-lying levels in both nuclei.

The extracted transitional and diagonal *E*2 matrix elements indicate that 130Xe and 140Sm are collective, and their ground states are characterized by *<sup>β</sup>*<sup>2</sup> ≈ 0.15 and *<sup>γ</sup>* ≈ <sup>30</sup>◦. For 130Xe, this conclusion was drawn on the basis of the determined quadrupole invariants, while, for 140Sm, it results from the measured *Qs*(2<sup>+</sup> <sup>1</sup> ) = <sup>−</sup>0.06+0.41 <sup>−</sup>0.15 *<sup>e</sup>*b, compatible with zero, and the enhanced *B*(*E*2; 2<sup>+</sup> <sup>1</sup> <sup>→</sup> <sup>0</sup><sup>+</sup> g.s.) = 53(5) W.u. value. Shell-Model calculations for 130Xe and 140Sm were performed in a large model space consisting of the 100Sn inert core and all orbitals up to *N* = *Z* = 82. The GCN50:82 effective interaction [73] was employed for both cases, complemented by the SN100PN effective interaction [74] for 130Xe. The experimental and theoretical results showed good agreement (see Figure 5), which is remarkable considering the evident collective nature of the two nuclei and the relatively high number of allowed valence particles in the Shell-Model calculations. However, for both 130Xe and 140Sm, effective charges larger than the standard *e<sup>ν</sup>* = 0.5*e*, *e<sup>π</sup>* = 1.5*e* values were needed to reproduce the measured *B*(*E*2) values. For 130Xe, *e<sup>ν</sup>* = 0.945*e*, *e<sup>π</sup>* = 1.53*e* and *e<sup>ν</sup>* = 0.84*e*, *e<sup>π</sup>* = 1.68*e* were adopted for the GCN50:82 and SN100PN interactions, respectively, while *e<sup>ν</sup>* = 0.64*e*, *e<sup>π</sup>* = 1.65*e* were used for the GCN50:82 interaction in the case of 140Sm. The need for increasing the effective charges in this mass region with respect to the standard values is known [75,76], and it suggests that a further expansion of the model space is necessary.

Despite the good reproduction of the experimental results by state-of-the-art Shell-Model calculations, further developments are needed to properly describe the structure of *<sup>A</sup>* <sup>≈</sup> 130–140 nuclei within this theoretical approach. This is particularly relevant for 130Xe, which would be the daughter of the 130Te neutrinoless double-*<sup>β</sup>* decay. If this process is observed at ongoing experiments, such as CUORE [77] and SNO+ [78], the relevant *ββ* nuclear matrix elements will need to be calculated in order to extract the Majorana mass. Such calculations are under way, also within the Shell Model [79], with important experimental constraints coming from recent measurements of valence proton and neutron occupations in 130Te and 130Xe [80,81]. Further low-energy Coulomb-excitation studies should help to elucidate the nuclear structure at *<sup>A</sup>* ≈ 130–140. A 130Xe beam could be delivered by a stable ion beam facility with a much higher intensity than that available

in [16], and the use of a heavier target (e.g., 208Pb) would increase the excitation cross sections. For 140Sm, an experiment with a higher beam energy would be beneficial. Under favourable conditions, such experiments should be capable of extracting higher-order quadrupole invariants related to the dispersions in *β*<sup>2</sup> and *γ* for the ground state.

**Figure 5.** Comparison of low-energy parts of the experimental 130Xe and 140Sm level schemes with Shell-Model calculations using GCN50:82 and SN100PN interactions [16,72]. The states are labelled with their spin and parity *I<sup>π</sup>* and excitation energy in keV. Transitions are labelled with reduced transition probabilities expressed in Weisskopf units. Spectroscopic quadrupole moments are reported in *e*b. See text for further details about the calculations.
