Deformed ground state of ${}^{32}$Mg and breaking of pseudo-spin symmetry

Abstract

Deformed ground state of ${}^{32}$Mg is investigated using the axially deformed relativistic Hartree-Fock-Bogoliubov (D-RHFB) model with the effective Lagrangian PKA1, which provides coincident description with the experimental measurements. It is illustrated that obvious breaking of the pseudo-spin symmetry (PSS) given by PKA1, being consistent with the experimental observation in nearby isotone ${}^{40}$Ca, is crucial for describing correctly the deformed ground state by producing unique shape evolution of neutron orbit $1/2_4^{+}$ in ${}^{32}$Mg. The PSS breaking is essentially determined by characteristic in-medium balance between nuclear attractions and repulsions that is manifested as unparalleled density dependent behaviors for coupling strengths $g_{\sigma }$ and $g_{\omega }$ in dominant $\sigma$-scalar and $\omega$-vector channels.

Comments: 10 pages, 6 figures, 2 tables