Residual proton-neutron interactions and the $N_{\mathrm{p}}{N}_{\mathrm{n}}$ scheme

We investigate the correlation between integrated proton-neutron interactions obtained by using the up-to-date experimental data of binding energies and the $N_{\mathrm{p}}{N}_{\mathrm{n}}$, the product of valence proton number and valence neutron number with respect to the nearest doubly closed nucleus. We make corrections on a previously suggested formula for the integrated proton-neutron interaction. Our results demonstrate a nice, nearly linear, correlation between the integrated p-n interaction and $N_{\mathrm{p}}{N}_{\mathrm{n}}$, which provides us with a firm foundation of the applicability of the $N_{\mathrm{p}}{N}_{\mathrm{n}}$ scheme to nuclei far from the stability line.