Electromagnetic transition strengths in soft deformed nuclei

TL;DR

This paper investigates electromagnetic transition strengths in nuclei across different deformation regimes, proposing a criterion for the validity of rotational formulas and an interpolation method to connect spherical and deformed limits.

Contribution

It introduces a simple criterion based on angular momentum fluctuations and an interpolation formula to accurately describe transition strengths from spherical to deformed nuclei.

Findings

The validity of rotational formulas depends on the mean square fluctuation in angular momentum.

An interpolation formula effectively describes transition strengths across all deformations.

The study compares approximate formulas with exact projection results, validating the approach.

Abstract

Spectroscopic observables such as electromagnetic transitions strengths can be related to the properties of the intrinsic mean-field wave function when the latter are strongly deformed, but the standard rotational formulas break down when the deformation decreases. Nevertheless there is a well-defined, non-zero, spherical limit that can be evaluated in terms of overlaps of mean-field intrinsic deformed wave functions. We examine the transition between the spherical limit and strongly deformed one for a range of nuclei comparing the two limiting formulas with exact projection results. We find a simple criterion for the validity of the rotational formula depending on $<\Delta \vec{J}^2>$, the mean square fluctuation in the angular momentum of the intrinsic state. We also propose an interpolation formula which describes the transition strengths over the entire range of deformations, reducing to the two simple expressions in the appropriate limits.