Generalized-Seniority Pattern and Thermal Properties in Even Sn Isotopes

TL;DR

This study uses the generalized-seniority approximation to analyze the energy states and thermal properties of even tin isotopes, revealing patterns of pair breaking and phase transitions in nuclear structure.

Contribution

It introduces a detailed shell-model calculation of tin isotopes using generalized seniority, highlighting the stepwise pair breakup and thermal phase transition phenomena.

Findings

Wavefunctions show stepwise breakup of pairs with excitation energy.

Thermal properties indicate a pairing phase transition.

Comparison with exact shell-model results validates the approximation.

Abstract

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.