Separable NN potentials from inverse scattering for nuclear matter studies

Low-rank separable potentials greatly simplify perturbation-theory based many-body computations and are especially useful in finite temperature and nonequilibrium nuclear matter studies. With local potentials such calculations become very lengthy. In this paper, we present a first version of a separable potential constructed directly from available empirical nucleon-nucleon phase shifts (E_lab<1.6 GeV), and established deuteron properties, via nonrelativistic inverse scattering. In our approach, the on-shell and off-shell properties of the potential can be independently varied: the on-shell scattering data are exactly fitted by construction while physically motivated off-shell features can be systematically included. This advantage is illustrated by the application of the procedure in the ³S₁-³D₁ channel, where the deuteron wave function serves as off-shell input at the binding energy. The simplest potential thus constructed in this channel has rank 4. The deuteron wave function is nevertheless empirically undetermined at high momenta, prompting us to adopt as well as construct several model wave functions that all fit the low momentum deuteron data while allowing variations at high momenta. The effects of these off-shell variations on predicted nuclear matter properties are discussed. No off-shell information is included in the other channels, leading to potentials of rank either 1 or 2. With this simple model potential we perform standard Brueckner nuclear matter ground state calculations and compare the results with Machleidt's using Bonn OBEP. The agreement is good in the S channels and in the singlet D₂ channel. Other channels show larger discrepancies, the most significant of which coming from the ³P₁, and ³D₁ channels. These results are explained by the off-shell behavior of our model potential as compared to the Bonn OBEP. Further off-shell input, empirical and/or theoretical, will be explored in future improved versions of the model.