Regularities and symmetries of subsets of collective 0+ states

TL;DR

This paper explores regular patterns and symmetries in the energies of excited 0+ states across different collective nuclear models, revealing universal formulas and group theoretical insights.

Contribution

It uncovers a universal formula describing subsets of 0+ states in geometric models and the IBA near critical points, linking regularities to underlying symmetries.

Findings

A single formula describes 0+ states in infinite well models.

Similar regularities are observed in the IBA near phase transition points.

Group theory explains the observed energy regularities.

Abstract

The energies of subsets of excited 0+ states in geometric collective models are investigated and found to exhibit intriguing regularities. In models with an infinite square well potential, it is found that a single formula, dependent on only the number of dimensions, describes a subset of 0+ states. The same behavior of a subset of 0+ states is seen in the large boson number limit of the Interacting Boson Approximation (IBA) model near the critical point of a first order phase transition, in contrast to the fact that these 0+ state energies exhibit a harmonic behavior in all three limiting symmetries of the IBA. Finally, the observed regularities in 0+ energies are analyzed in terms of the underlying group theoretical framework of the different models.