Generalized-seniority pattern and thermal properties in even Sn isotopes

Abstract

Even tin isotopes of mass number A = 108 ∼ 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.

Application of the variational principle to a coherent-pair condensate: The BCS case

“…These fitting parameters should be fine-tuned to generate optimum interactions for VDPC+HFB. In addition, higher-order correlations beyond VDPC can be included, for example, by the generalized-seniority truncation of the shell model [28,[36][37][38][39][40][41][42].…”

Shell Model Description of Heavy Nuclei and Its Monopole Channel

“…Our recent studies on the seniority coupling scheme may be found in Refs. [2,[11][12][13][14][15]. One can also derive the exact solution of the pairing Hamiltonian by diagolizing the matrix spanned by the seniority v = 0, spin I = 0 states which represent only a tiny part of the total wave function.…”

Generalized seniority on a deformed single-particle basis

“…In realistic applications usually the number of t [γ1γ2...γr] α1α2...αp;β1β2...βp (13) is still too large to fit into memory, and further simplification is necessary. On the spherical single-particle basis, we switch to the 'occupation number representation' [62][63][64]…”

“…The generalized seniority quantum number, emphasizing pairing, was proposed [49][50][51][52][53] in the spherical shell model and frequently used as a truncation scheme [22,[54][55][56][57][58][59][60][61]. We recently proposed an algorithm [62] that greatly reduces the computer time cost and promotes the generalized-seniority truncation to an accurate tool for semi-magic nuclei [63,64]. The concept of generalized-seniority can be straightforwardly extended to be defined on a deformed (for example Nilsson) single-particle basis.…”