SWANLOP: Scattering waves off nonlocal optical potentials in the presence of Coulomb interactions

SIDES: Nucleon–nucleus elastic scattering code for nonlocal potential

This paper examines the presence of extra nodes in the scattering wave function for a nonlocal potential. Extra nodes are known to result from the nonlocality of an effective potential which incorporates the Pauli principle. It is shown that an extra node is directly linked to the existence of a continuum bound state or a spurious state in the scattering spectrum. Thus the presence of extra nodes occurs in conjunction with zeros of the Fredholm determinants D/sup plus-or-minus/(k) and D (k) associated with the integral equations for the physical and regular scattering solutions, respectively. The behavior of the nodes due to spurious states and continuum bound states is differentiated. Two possible definitions of the phase shift for a nonlocal potential are discussed in connection with this behavior. Both are consistent with the local limit. The definition of the phase shift as the negative of the phase of the Jost function L/sup +/(k) is suggested as preferable. This definition is shown to be in accord with the nodal behavior of the wave function and its interpretation in terms of an absolute value of the phase shift. Examples of potentials with a spurious state and of potentials with a continuum bound statemore » are given. The nodal behavior of the wave function and the associated phase shift behavior are examined for each.« less

Extra nodes and the phase shift of the scattering wave function for a nonlocal potential

Jacques Raynal provided two powerful tools to the nuclear reaction community interested in scattering processes, namely the ECISxx and DWBAxx computer codes (xx standing for the version year), which are renowned for both their numerical efficiency and the numerous applications they cover. The purpose of this work is twofold. First, it extends the possibilities of calculation of microscopic optical and transition potentials compared to what is proposed in the DWBA code. Then, following previous work by Arellano [Phys Rev C 76:014616, 2007], we develop a method to deal with coupled-channel calculations with non-local ingredients. Both codes DWBA and ECIS, and numerous past discussions with their author, offered guidance to elaborate and to validate new results focusing on neutron scattering off spin-0 target. Special attention has been paid to match the numerical precision of J. Raynal’s tools. This was made possible by using a specific quadrature method for numerical integrations of functions with discontinuous derivatives.

https://link.springer.com/content/pdf/10.1140/epja/s10050-021-00585-7.pdf

B. Bagchi

Papers

Analytic solutions in configuration space representation for scattering from a class of separable nonlocal potentials