A further look at prolate dominance in nuclear deformation

TL;DR

This paper investigates the reasons behind the dominance of prolate over oblate shapes in deformed nuclei, linking it to orbital splitting and interactions, and shows this dominance is specific to certain particle numbers.

Contribution

It provides a detailed analysis of the Nilsson diagram and orbital interactions, explaining prolate dominance as a non-generic feature of finite nuclear systems.

Findings

Prolate dominance is related to increased orbital fanning out on the prolate side.

Oblate side exhibits avoided crossings that suppress orbital fanning.

Prolate dominance is not universal and depends on particle number.

Abstract

The observed almost complete dominance of prolate over oblate deformations in the ground states of deformed even-even nuclei is related to the splitting of high $\ell$ "surface" orbits in the Nilsson diagram: on the oblate side the occurrence of numerous strongly avoided crossings which reduce the fanning out of the low $\Lambda$ orbits, while on the prolate side the same interactions increase the fanning out. It is further demonstrated that the prolate dominance is rather special for the restricted particle number of available nuclei and is not generic for finite systems with mean-field potentials resembling those in atomic nuclei.