Mass relations of corresponding mirror nuclei

Abstract

In this paper we report two simple relations of masses between corresponding mirror nuclei, the first of which is based on the regularity of empirical neutron-proton interactions, and the second of which is based on the regularity of the one-nucleon separation energy. We demonstrate that, for $N\ensuremath{\ge}10$, the empirical neutron-proton interaction of given nucleus with neutron number $N\ensuremath{-}1$ and proton number $Z$ (we use the convention that $N=Z$ in this paper), or abbreviated by the $(N\ensuremath{-}1,Z)$ nucleus, equals the neutron-proton interaction of its corresponding mirror nucleus, i.e., the $(N,Z\ensuremath{-}1)$ nucleus; we also demonstrate that one-proton separation energy ${S}_{p}$ and one-neutron separation energy ${S}_{n}$ of the $(N\ensuremath{-}k,Z)$ nucleus ($k=1,2,3,4$) equals one-neutron separation energy ${S}_{n}$ and one-proton separation energy ${S}_{p}$, respectively, of the $(N,Z\ensuremath{-}k)$ nucleus, after a simple correction of Coulomb energy and proton-neutron mass difference are considered. Numerical experiments show that these correlations provide us with a remarkably accurate approach to predict masses and separation energies of some proton-rich nuclei with neutron numbers from 10--46. Our predicted masses of proton-rich nuclei are tabulated as a Supplemental Material of this paper.