Analytic separable approximation to realistic nucleon-nucleon interactions

Abstract

The EST approach is used to construct analytic, low-rank, separable approximations to the Reid soft core potentials. All previous efforts to approximate potentials by an energy-independent separable form are shown to be of the EST type. For the uncoupled channels, separable approximations of rank three which utilize spherical Bessel functions in their construction are found to reproduce phase shift in the range 0 to 400 MeV. For channels coupled by the tensor force, more complicated functions which are carefully fit to the wave functions generated by the original potential are required. A rank nine separable approximation is necessary in the 3S[1]-3D[1] channel. This rank approximation is capable of quantitatively reproducing all properties of the deuteron as well as the phases and mixing parameter up to 400 MeV. A rank seven approximation is employed in the coupled 3P[2]-3F[2] channel. A new model is proposed which incorporates the effects of the coupling of the inelastic channels on the elastic channel. Large effects of the coupling are found in the 1D[2]-3D[2] channels far below the inelastic threshold. This implies, within the context of the model, that the coupling to pion-production channels must be included in realistic models for these channels.