Repulsive Core and Charge Independence

Abstract

In an earlier paper Schwinger derived expressions for the effective strengths of the neutron-proton and proton-proton interactions in the singlet $S$ state. He showed their difference is small and can be accounted for by magnetic forces if a long-tailed potential (Yukawa) is assumed but not for a short-tailed potential. In this paper an equivalent analysis is carried out for nuclear potentials which have a repulsive core. It is shown that for core radii of more than about 0.3×${10}^{-13\mathrm{}}$ cm the effect of the magnetic interaction is decreased and the difference between the $n-p$ and $p-p$ interactions is increased. Numerical values of the discrepancy are given for different core radii.