To Shell Model, or Not to Shell Model, That Is the Question

Abstract

The present review takes steps from the domain of the shell model into open shell nuclei. The question posed in the title is to dramatize how far shell model approaches, i.e., many nucleons occupying independent-particle configurations and interacting through two-body forces (a configuration interaction problem) can provide a description of nuclei as one explores the structure observed where neither proton nor neutron numbers match closed shells. Features of doubly closed and singly closed shell nuclei and adjacent nuclei are sketched, together with the roles played by seniority, shape coexistence, triaxial shapes and particle–core coupling in organizing data. An illuminating step is taken here to provide a detailed study the reduced transition rates, B(E2;21+→01+), in the singly closed shell nuclei with doubly closed shell plus or minus a pair of identical nucleons, and the confrontation between such data and state-of-the-art shell model calculations: this amounts to a review of the effective charge problem. The results raise many questions and point to the need for much further work. Some guidance on criteria for sharpening the division between the domain of the shell model and that of deformation-based descriptions of nuclei are provided. The paper is closed with a sketch of a promising direction in terms of the algebraic structure embodied in the symplectic shell model.

Prolate-oblate asymmetric shape phase transition in the interacting boson model with SU (3) higher-order interactions

“…Some new ideas also emerges recently. The shell model has some deficiencies [112], the role of the single-particle energy gap has bee also stressed [113,114], and oblateprolate phase mechanism in the Te-Ba region is also studied [76]. We expect our new model can provide more insights on these new ideas.…”

Low-spin excitations in Br89 populated in β− decay of Se89Rza̧ca‐Urban1, Sieja2, Czerwiński3 et al. 2022Phys. Rev. C1000View full textAdd to dashboardCite

“…This again emphasizes the need for reliable s.p. input data which, in addition to supporting a better description of nuclei in the region, may bring us closer to answering the thought-provoking question of whether the spherical shell model, as we know it at present, is capable of properly reproducing collective effects emerging in transitional nuclei (see, e.g., the review [4] for further reading).…”