Separable representation of proton-nucleus optical potentials

Abstract

Recently, a new approach for solving the three-body problem for (d,p) reactions in the Coulombdistorted basis in momentum space was proposed. Important input quantities for such calculations are the scattering matrix elements for proton (neutron) nucleus scattering. We present a generalization of the the Ernst-Shakin-Thaler scheme in which a momentum space separable representation of proton-nucleus scattering matrix elements in the Coulomb basis can be calculated. The success of this method is demonstrated by comparing S-matrix elements and cross sections for proton scattering from 12 C, 48 Ca, and 208 Pb with the corresponding coordinate space calculations.

Li6 in a three-body model with realistic Forces: Separable versus nonseparable approach

“…However, when solving the n + p + A problem for bound systems where A > 4, and given the wide range of nucleonnucleus effective interactions available, we expect one will need to inspect the properties of the two-body nucleon-nucleus t matrices carefully and revisit the issue of optimum energy and momentum support points in those cases again. Similar to [26][27][28], we find here that the structure of the two-body t matrices as a function of energy and momentum determines the minimal rank needed for an accurate description of both the two-body and three-body observables.…”

“…In this work, we explore solving momentum-space Faddeev equations using separable interactions based on the EST scheme [26][27][28], for bound three-body systems of the type n + p + A. Our goal is to benchmark this separable method against the standard approach of directly solving momentum-space Faddeev equations.…”

“…According to Eq. (27), the latter are uniquely specified by the EST support points {E l ,p l }, where E l is a fixed energy and p l a fixed momentum. We shall refer to E l as the support energy and p l the support momentum hereafter.…”

“…(27), the EST separable expansion employs solutions of the LSE as basis states. These states depend on two parameters, the two-body energy E l as well as the asymptotic momentum p l .…”

“…The pioneering work of Hlophe and collaborators [26][27][28] demonstrated that an EST-based separable interaction of rank up to 5 provides a precise description of nucleon-nucleus elastic scattering for a wide range of energies, including nuclei as heavy as 208 Pb. The development of these separable complex (and energy dependent) effective potentials opens the path to apply the method of Ref.…”