The empirical proton-neutron interaction $\delta V_{pn}$ 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 ${\beta }_3$ dramatically changes the $\delta V_{pn}$ with $N=134,136,140$. The collective fluctuation smoothly corrects the $\delta V_{pn}$ 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.

• Received 24 July 2019
• Revised 25 September 2019

DOI:https://doi.org/10.1103/PhysRevC.100.054303