Neutron-Proton Pairing Interaction

Abstract

The neutron-proton pairing interaction $\ensuremath{\lambda}$ between the last odd neutron and the last odd proton in the outermost neutron and proton shells of an odd-odd nucleus has been estimated from nuclear masses in the regions just beyond $Z=20$, $N=20$, and just beyond $Z=40$, $N=50$. Behavior of $\ensuremath{\lambda}$ in these two regions and in the heavy element region $Z>82$, $N>126$, as estimated by Ghoshal and Saxena, is discussed. It is found that the behavior of $\ensuremath{\lambda}$ may be understood in terms of a simple $\mathrm{jj}$-coupling shell model. According to this model, $\ensuremath{\lambda}$ arises from the spin-independent part of the two-body force and is proportional to $(2{j}_{1}+1\ensuremath{-}2z)(2{j}_{2}+1\ensuremath{-}2n)$, where $z$ is the odd number of protons in the outermost proton shell ${j}_{1}$, and $n$ is the odd number of neutrons in the outermost neutron shell ${j}_{2}$ of the odd-odd nucleus.