Empirical proton-neutron interaction of even Ra isotopes probed by the quadrupole-octupole collective Hamiltonian based on the covariant density functional

Abstract

The empirical proton-neutron interaction $\ensuremath{\delta}{V}_{pn}$ for even-even Ra isotopes is analyzed by using the covariant density functional theory and the quadrupole-octupole collective Hamiltonian approach. It is shown that the static deformation and collective fluctuation are crucial ingredients for good reproduction of the data. Particularly, the introduction of octupole deformation ${\ensuremath{\beta}}_{3}$ dramatically changes the $\ensuremath{\delta}{V}_{pn}$ with $N=134,136,140$. The collective fluctuation smoothly corrects the $\ensuremath{\delta}{V}_{pn}$ with good trend. Taking $^{224}\mathrm{Ra}$ as an example, the detailed contributions from the static deformation and the collective fluctuation are analyzed, and the microscopic single-particle levels, the octupole driving pairs, and the enhancement of proton-neutron interaction are discussed.