Generalized seniority for the shell model with realistic interactions

Abstract

The generalized seniority scheme has long been proposed as a means of dramatically reducing the dimensionality of nuclear shell model calculations, when strong pairing correlations are present. However, systematic benchmark calculations, comparing results obtained in a model space truncated according to generalized seniority with those obtained in the full shell model space, are required to assess the viability of this scheme. Here, a detailed comparison is carried out, for semimagic nuclei taken in a full major shell and with realistic interactions. The even-mass and odd-mass Ca isotopes are treated in the generalized seniority scheme, for generalized seniority v ≤ 3. Results for level energies, orbital occupations, and electromagnetic observables are compared with those obtained in the full shell model space.

Generalized seniority with realistic interactions in open-shell nuclei

“…Thus, the generalized seniority model space with one broken pair (v = 2) for any even Ca isotope taken in the pf shell has the same dimension as the shell-model space for 42 Ca -dimension 4 for J = 0, 8 for J = 2, 6 for J = 4, etc. [23]. Similarly, if both valence protons and neutrons are present, the basis size is the same as for the shell-model problem with only v p protons and v n nucleons.…”

“…To provide a baseline for comparison, it is helpful to review the analogous results for the semimagic Ca isotopes in the v = 2 space, from [23], shown at top in figure 3. It should first be noted (see appendix of [23]) that the ground state obtained in the v = 2 space is simply the v = 0 S-pair condensate, provided the α a coefficients have been chosen variationally as in section 2. Therefore, the ground-state energies obtained in v = 0 and v = 2 spaces are identical.…”

“…To review the situation for the Ca isotopes [23], the evolution of B(E2; 2 + 1 → 0 + 1 ) strengths [ figure 7(a,b)] across the shell is reproduced in the generalized seniority v = 2 space in its qualitative features (minima and maxima) and with a quantitative accuracy averaging ∼ 12% for FPD6 or ∼ 6% for GXPF1. The magnitude of Q(2 + 1 ) [ figure 7(g,h)] is markedly attenuated in the generalized seniority calculations relative to the full-space results, although the generalized seniority results demonstrate the same qualitative features as the results in the full space, notably exhibiting the same alternations in sign as a function of N .…”

Selected Aspects of the Structure of Exotic Nuclei and New Opportunities with GRETINA

“…[7][8][9]. The rather constant energy of the 2 + state suggests that such a description may be adequate.…”

Phenomenological analysis ofB(E2)transition strengths in neutron-rich carbon isotopes

“…Can we understand the overall behavior of the quadrupole collectivity by considering a seniority inspired scheme [9][10][11] 1 In what follows, we will use B(E2) for short. [7] (open diamond), [4,5] (circles), [3] (open squares), and [6] (diamond).…”