Separable potentials for the nucleon-nucleonS13−D13channel

Separable potentials of rank one to five for the nucleon-nucleon ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ channel are constructed using a method introduced by Ernst, Shakin, and Thaler. The potentials all have the same deuteron wave function as the Reid soft-core potential. In addition the phase shifts of the rank-four and -five potentials are quite close to the experimental phase shifts. A survey of previously published separable potentials of rank greater than one is made and it is concluded that most of these potentials have unacceptably poor deuteron properties. A number of errors that were made in the fitting of these potentials to the data are pointed out. A simplification of the Reid soft-core potential for the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ channel is also presented. The simplified potential consists entirely of Yukawa terms but has experimental properties that generally differ from the original Reid soft-core properties by less than the present experimental error.