Low-lying state investigations of odd-A Mn isotopes around N = 28

Abstract

Based on the systematic studies for low-lying states of the odd-$A$ $\rm {}^{49-57}Mn$ isotopes, the ground-states inversion and the rotational properties of ground-state-based sequence are revealed and discussed. The energy levels of low-lying states and electromagnetic moments in odd-$A$ $^{49-57}$Mn isotopes have been well reproduced in shell-model calculations, and the above phenomena could be understood with obviously different occupation numbers in proton orbitals such as $\pi f_{7/2}$ and $\pi p_{3/2}$, which changes similarly with the obtained quadrupole deformation in covariant density functional theory~(CDFT). After considering the coupling of collective rotation and intrinsic single-particle motion, the available experimental magnetic moments in $\rm ^{53}Mn$ and adjacent nuclei can be well explained with CDFT. The present calculations suggest that the $5/2^-$ and $7/2^-$ states in $^{53}$Mn are formed by $\pi5/2^-[312]$ and $\pi7/2^-[303]$ respectively. Together with behavior of levels, this provides proofs for the level sequences of low-lying states in $\rm ^{53}Mn$ distinct from the $K^\pi=5/2^-$ rotational band in $^{49}$Cr and other odd-$A$ Mn isotopes.