Multi-shell effective interactions

Abstract

Background: Effective interactions, either derived from microscopic theories or based on fitting selected properties of nuclei in specific mass regions, are widely used inputs to shell-model studies of nuclei. The commonly used unperturbed basis functions are given by the harmonic oscillator. Until recently, most shell-model calculations have been confined to a single oscillator shell like the sd shell or the pf shell. Recent interest in nuclei away from the stability line requires, however, larger shell-model spaces. Because the derivation of microscopic effective interactions has been limited to degenerate models spaces, there are both conceptual and practical limits to present shell-model calculations that utilize such interactions. Purpose: The aim of this work is to present a novel microscopic method to calculate effective nucleon-nucleon interactions for the nuclear shell model. Its main difference from existing theories is that it can be applied not only to degenerate model spaces but also to nondegenerate model spaces. This has important consequences, in particular for intershell matrix elements of effective interactions. Methods:The formalism is presented in the form of a many-body perturbation theory based on the recently developed extended Kuo-Krenciglowa method. Our method enables us to microscopically construct effective interactions not only in one oscillator shell but also for several oscillator shells. Results: We present numerical results using effective interactions within (i) a single oscillator shell (a so-called degenerate model space) like the sd shell or the pf shell and (ii) two major shells (nondegenerate model space) like the sdf 7 p 3 shell or the pf g 9 shell. We also present energy levels of several nuclei that have two valence nucleons on top of a given closed-shell core. Conclusions: Our results show that the present method works excellently in shell-model spaces that comprise several oscillator shells, as well as in a single oscillator shell. We show, in particular, that the microscopic intershell interactions are much more attractive than has been expected by degenerate perturbation theory. The consequences for shell-model studies are discussed.

Identification of deformed intruder states in semi-magicNi70

“…The calculated potential-energy surfaces in Ref. [13] also indicate the likelihood of shape coexistence in 70 Ni.…”

“…Much of this effort has been concentrated thus far on 68 Ni itself, with substantial improvements made to the level scheme [30][31][32] and deduced decay rates [12,31], as well as with comparisons of the data with Monte-Carlo shellmodel (MCSM) calculations [33,34]. The latter have provided strong evidence for coexisting spherical, oblate, and prolate shapes in this nucleus [12,13]. The calculated potential-energy surfaces in Ref.…”

“…As with 68 Ni [12,13,31], the updated 70 Ni level scheme is compared to shell-model calculations using interactions confined strictly to neutron excitations and to MCSM calculations employing a much larger model space, revealing better agreement for the negative-parity levels and insight into the nature of the non-yrast lowspin levels. These data provide a new test of the interactions relevant for the description of more exotic neutronrich nuclei out to doubly-magic 78 Ni and beyond and hint at a deeper understanding of their underlying structure.…”

“…The structure of neutron-rich nuclei in the vicinity of 68 Ni has been the subject of considerable scrutiny in recent years, including investigations related to the magicity of 68 Ni [1][2][3][4][5][6][7][8][9][10], the existence of multiple coexisting shapes [11][12][13][14], the presence of intruder states originating from orbitals across a shell gap [15][16][17][18][19][20][21][22], and the unexpected disappearance of seniority isomers [23][24][25][26][27][28][29]. The delineation of levels up to several MeV in excitation energy in these nuclei is an important step towards providing a firmer understanding of their properties through comparisons with modern theoretical models.…”

β-Decay Measurements in the Vicinity of 78Ni with the EURICA Setup

“…In such context, nuclei at Z=28, N=50 shell gaps are particularly interesting since they are good candidates to reveal changes into the shell structure. Recent shell model calculations showed that these modifications not only affect the level sequence but also the overall shape of the nucleus [2]. Both central and non-central components (i.e.…”