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Generalized-Seniority Pattern and Thermal Properties in Even Sn Isotopes

Even tin isotopes of mass number $A = 108 \sim 124$ are calculated with realistic interactions in the generalized-seniority approximation of the nuclear shell model. For each nucleus, we compute the lowest ten thousand states ($5000$ of each parity) up to around $8$ MeV in excitation energy, by allowing as many as four broken pairs. The lowest fifty eigen energies of each parity are compared with the exact results of the large-scale shell-model calculation. The wavefunctions of the mid-shell nuclei show a clear pattern of the stepwise breakup of condensed coherent pairs with increasing excitation energy. We also compute in the canonical ensemble the thermal properties -- level density, entropy, and specific heat -- in relation to the thermal pairing phase transition.