Predominance of Prolate Nuclear Deformations Emerging from Many-Body Interactions

TL;DR

This paper introduces a shell model approach using random interactions to explain why prolate nuclear shapes are more common among deformed nuclei, identifying key force components responsible.

Contribution

It presents a novel method exploring random rotationally-invariant interactions within the shell model to explain prolate shape dominance in nuclei.

Findings

Prolate deformations are prevalent in the ensemble of interactions studied.

Certain matrix elements of effective forces are linked to prolate shape emergence.

Identifies specific energy ratios and quadrupole moments associated with prolate nuclei.

Abstract

A new approach to the old problem of the predominance of prolate deformations among well deformed nuclei is proposed within the shell model framework. The parameter space is explored using the ensemble of random rotationally-invariant interactions. Subsets with rotational energy ratio $E(4^{+})/E(2^{+})$ and the rigid-rotor relation between the quadrupole moment $Q(2^{+})$ and the transition probability $B(E2;2^{+}\to 0^{+}))$ are found exhibiting prolate predominance. We identify matrix elements of the effective forces responsible for the predominance of prolate deformation.