Separable representation of energy-dependent optical potentials

Abstract

Background: One important ingredient for many applications of nuclear physics to astrophysics, nuclear energy, and stockpile stewardship are cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often not feasible, indirect methods, e.g. (d,p) reactions, should be used. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques.Purpose: Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. Optical potentials representing the effective interactions in the neutron (proton) nucleus subsystem are usually non-Hermitian as well as energy-dependent. Potential matrix elements as well as transition matrix elements calculated with them must fulfill the reciprocity theorem. The purpose of this paper is to introduce a separable, energy-dependent representation of complex, energy-dependent optical potentials that fulfill reciprocity exactly.Methods:: Momentum space Lippmann-Schwinger integral equations are solved with standard techniques to obtain the form factors for the separable representation.Results: Starting from a separable, energy-independent representation of global optical potentials based on a generalization of the Ernst-Shakin-Thaler (EST) scheme, a further generalization is needed to take into account the energy dependence. Applications to n+ 48 Ca, n+ 208 Pb, and p+ 208 Pb are investigated for energies from 0 to 50 MeV with special emphasis on fulfilling reciprocity. Conclusions:We find that the energy-dependent separable representation of complex, energy-dependent phenomenological optical potentials fulfills reciprocity exactly. In addition, taking into account the explicit energy dependence slightly improves the description of the S matrix elements.

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.…”

“…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.…”

Separable representation of multichannel nucleon-nucleus optical potentials

“…The generalization to complex, energy-dependent optical potentials of Refs. [15,16] fulfills the same conditions and in addition guarantees that reciprocity is fulfilled.…”

“…In this manuscript we extend the work of Refs. [15,16] to obtain a separable representation of complex, energy-dependent multichannel optical potentials. First we derive the formulation for multichannel neutron-nucleus optical potentials in Sec.…”