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

摘要

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 tothe axially symmetric $\beta_2$ deformation with infinitesimal cranking. TheBMF 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 dataanalysis, particularly for low-lying states. We also discuss the absolute valueof 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 rotationalsymmetry, $\beta_2$ configuration mixing, and the inclusion of time-oddcomponents by infinitesimal cranking. Under the assumption of axial deformationand parity conservation, we clarify which effect is important for each of thethree measurements, and propose the kinds of BMF calculations that arepractical for each of the three kinds of observables.