Separable potential for the neutron-proton system

Abstract

A separable potential is proposed for the $n-p$ interaction in ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ partial waves. In the singlet $S$ state the potential fits new phenomenological phases rather accurately in the laboratory kinetic energy range 0-600 MeV; it is also capable of reproducing singlet effective-range parameters in close agreement with experiment. In the coupled state ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ the potential provides a correct description of the deuteron data ($E_D$, $p_D$, $Q$, $\eta$), while at the same time it adequately fits modern phenomenological phases up to $E_{\mathrm{lab}}\gtrsim 500$ MeV in both the $S$ and the $D$ wave; triplet effective-range parameters are also in agreement with experimental data. Only the mixing parameter ${\epsilon }_1$ deviates from predictions of phase-shift analyses. In the construction of the potential care was taken that its off-shell behavior be reasonable. As an eminent property it thus exhibits an off-shell behavior similar to the one of the Paris potential. In particular the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ potential yields a deuteron $S$-state wave function, which in momentum space shows a zero like the Paris potential. Still the model is simple enough to be of good use in modern computer codes for few-body systems and other nuclear applications.