Simultaneous analysis of matter radii, transition probabilities, and excitation energies of Mg isotopes by angular-momentum-projected configuration-mixing calculations

TL;DR

This paper uses a beyond mean-field framework with angular-momentum projection and configuration mixing to accurately analyze matter radii, transition probabilities, and excitation energies of Mg isotopes, providing insights into nuclear deformation effects.

Contribution

It introduces a comprehensive BMF approach with infinitesimal cranking to simultaneously analyze multiple nuclear observables in Mg isotopes, highlighting the effects of deformation and symmetry restoration.

Findings

Successfully reproduces experimental data for radii, transition probabilities, and excitation energies.

Clarifies the impact of deformation and symmetry restoration on different observables.

Proposes practical BMF calculation methods for various nuclear measurements.

Abstract

We perform simultaneous analysis of (1) matter radii, (2) $B(E2; 0^+ \rightarrow 2^+ )$ transition probabilities, and (3) excitation energies, $E(2^+)$ and $E(4^+)$, for $^{24-40}$Mg by using the beyond mean-field (BMF) framework with angular-momentum-projected configuration mixing with respect to the axially symmetric $\beta_2$ deformation with infinitesimal cranking. The BMF calculations successfully reproduce all of the data for $r_{\rm m}$, $B(E2)$, and $E(2^+)$ and $E(4^+)$, indicating that it is quite useful for data analysis, particularly for low-lying states. We also discuss the absolute value of the deformation parameter $\beta_2$ deduced from measured values of $B(E2)$ and $r_{\rm m}$. This framework makes it possible to investigate the effects of $\beta_2$ deformation, the change in $\beta_2$ due to restoration of rotational symmetry, $\beta_2$ configuration mixing, and the inclusion of time-odd components by infinitesimal cranking. Under the assumption of axial deformation and parity conservation, we clarify which effect is important for each of the three measurements, and propose the kinds of BMF calculations that are practical for each of the three kinds of observables.