Importance-sampling diagonalization algorithm for large-scale shell model calculations onN=80isotones

Abstract

An iterative matrix diagonalization algorithm endowed with an importance sampling, recently reformulated and tested through large-scale shell model calculations on some heavy Xe isotopes, is here applied to N = 80 isotones. For these nuclei, the iterative sampling procedure is shown to converge more rapidly than in the case of Xe isotopes. The improved convergence rate enables us to produce accurate eigenvalues and eigenfunctions even in spaces of dimensions N ∼ 10 9 . It is therefore possible to offer an exhaustive description of low-energy spectroscopic properties for all N = 80 isotones from 132 Te up to 140 Nd through the calculation of spectra and transition strengths. The results are fairly consistent with the available experimental data and with other shell model calculations based on the Lanczos algorithm.

Ground-state correlations within a nonperturbative approach

“…We need to resort to a more sophisticated importance sampling [52], shown to be effective in large-scale shellmodel calculations [53,54], and check if the sampled basis is sufficiently restricted to allow the access to subspaces with a larger number of phonons. Preliminary calculations are encouraging.…”

Local suppression of collectivity in theN=80isotones at theZ=58subshell closure

“…in 140 Nd is compared to recent large-scale shell-model calculations [21] as well as to the quasiparticle phonon model in connection to the systematics of the N = 80 isotones [18,21]. In both models, the computed B(E2) strengths in the stable N = 80 isotones increase smoothly with Z.…”

“…for the protons. [1,4,[22][23][24] including the extracted value for 140 Nd are presented in comparison with the large-scale shell-model calculations [21] as well as the quasiparticle phonon model [18]. In that approach nuclear data is parameterized to explicitly emphasize the valence p-n interaction.…”

“…In order to test such a suggestion, one should compute explicitly the effective E2 operators within the linked cluster expansion theory, which is known to generate different effective charges for different subshells [26]. However, it was pointed out [19,21] that a calculation in an enlarged shell-model space, which includes core excitations, is not feasible.…”

“…The experimental level scheme for 140 Nd is shown (b) together with the calculated ones from the (a) QPM and (c) shell model[21]. The illustration concentrates on the 2 +x states.…”