Coulombic effect and renormalization in nuclear pairing

Abstract

We investigate the effects of the Coulomb force on the nuclear pairing properties by performing the Gogny Hartree-Fock-Bogolyubov calculations for the $N=20$, $28$, $50$, $82$, and $126$ nuclei. The Coulomb force reduces the proton pair energy and the even-odd mass difference by about $25%$, except for nuclei at and around the proton shell or subshell closure. We then propose a renormalization scheme via a reduction factor ${\ensuremath{\gamma}}_{p}$ for the proton pairing channel. It is found that a single value ${\ensuremath{\gamma}}_{p}=0.90$ accounts well for the Coulombic effect for nuclei covering a wide range of the mass number and the neutron excess, including the nuclei around the shell or subshell closure.