Practical calculation scheme for generalized seniority

Abstract

We propose a scheme or procedure for doing practical calculations with generalized seniority. It reduces the total computing time by calculating and storing in advance a set of intermediate quantities, taking advantage of the memory capability of modern computers. The requirements and performance of the algorithm are analyzed in detail.

Generalized-seniority pattern and thermal properties in even Sn isotopes

“…The P (s = 0) amplitude vanishes by symmetry and the P (s = 4) amplitude is negligible. Although appreciable generalized-seniority mixing exits, we notice that the P (s) compositions of the 0 25. We see that the P (s) curve of a given J P is much narrower (less dispersive at a specific excitation energy) compared with the P (s) curve of a given parity P from Fig.…”

“…However, as pointed out in these works, higher S is necessary to achieve convergence, which is challenging and not done yet. Using the fast algorithm for generalized seniority we developed [25] and applied [26] recently, in this work we compute with modern realistic interactions [13] the lowest ten thousand states (5000 of each parity) of 108∼124 Sn in the S = 8 subspace. The distribution of wavefunctions in terms of generalized seniority is examined in detail.…”

Generalized seniority on a deformed single-particle basis

“…For clarity we consider only one kind of nucleons, the extension to the case of active protons and neutrons is straightforward as done in for example Ref. [62]. The pair-creation operator…”

“…This work redesigns the computing scheme to revive it. The generalized-seniority truncation of the deformed shell model runs as fast as that of the spherical shell model [62] with the new algorithm.…”

“…We derive analytical expressions of the many-pair density matrix in Sec. IV, and how this revives the spherical algorithm [62] in the case of deformed single-particle basis is explained in Sec. V. Section VI applies the method to the rare-earth nucleus 158 64 Gd 94 .…”