Model analysis of the relationship betweenS13scattering length and the root-mean-square radius of the deuteron

By considering a number of nonrelativistic potential models, the relationship between the ${}_{}{}^3{}_{}{}^{}\mathrm{S}_1^{}{}_{}{}^{}$ scattering length and the root-mean-square radius of the deuteron is studied. It is found that this relationship for certain classes of potentials is characterized by approximately straight line graphs similar to the one obtained by Klarsfeld et al. for a set of realistic nucleon-nucleon interactions. The implication of this study is that nonrelativistic nucleon-nucleon potentials of the types considered must include nonlocal components in order to be able to predict simultaneously the experimental triplet S-wave scattering length and the root-mean-square radius of the deuteron.