Studies in Nonlocal Potentials

Abstract

<p>The two-body elastic scattering data and the binding energy of the deuteron do not uniquely determine the nucleon-nucleon interaction. Many potentials, which fit these data, may give different results in many-body problems due to their different off-energy-shell behaviour. It is also expected that the nucleon-nucleon interaction would be nonlocal at short relative distances and local at comparatively larger (r ≥ 2 Fm) distances. Thus it is of interest to construct and study partly nonlocal potentials.</p> <p>We have generalized the Jost-Pais theorem for nonlocal central and noncentral potentials. A method, based on the formalism of Fuda, has been developed to construct partly nonlocal central phase equivalent potentials. These potentials, constructed in the S-state, have an attractive local part, superimposed with a short range repulsive rank-one separable potential. We study the behaviour of such partly nonlocal potentials in nuclear matter, with a view to examine if these differ significantly from corresponding phase equivalent separable potentials.</p> <p>We have also studied the dependence of the threshold cross section for the reaction p+p → π⁺+d on the nature of the deuteron wave function. Phase equivalent potentials with varying D-state probability of the deuteron have been generated using unitary transformations on the two-body Hamiltonian which includes a local or separable potential. It has been shown that the cross section depends sensitively not only on the D-state probability of the deuteron but also on the form of the wave function at short relative distances, and hence to the off-shell behaviour and the nonlocality of the interaction.</p>