Abstract
We introduce the package SIDES (Schrödinger Integro-Differential Equation Solver) that solves the integro-differential Schrödinger equation for elastic scattering of a nonlocal optical potential in coordinate space. The code is capable of treating the Coulomb interaction without restrictions. The method is based on previous developments by Jacques Raynal in the DWBA07 code. Elastic scattering observables such as differential and integral cross sections, as well as analyzing power and spin rotation functions for both neutron and proton projectiles are evaluated, with no restriction on the type of nonlocality of the potential nor on the beam energy. The corresponding distorted wavefunctions are calculated as well. The SIDES package includes a Perey–Buck potential generator with two parametrizations. It includes as well local potential parametrizations and allows for mixing local and nonlocal contributions. Benchmarks are performed and discussed. Program summaryProgram Title: SIDESProgram Files doi:http://dx.doi.org/10.17632/cmpjgyrngr.1Licensing provisions: GNU General Public License, Version 2Programming language: FORTRAN-90Nature of problem: The description of nucleon elastic scattering off a target nucleus involves solving the Schrödinger’s wave equation for positive incident energy. The determination of scattering observables calls for accurate treatments of the continuum. The effective coupling between the projectile and the target is accounted for by an optical potential, an operator which is by nature complex, energy-dependent and nonlocal. The coupling becomes long-range in the case of charged projectiles. In a general scenario under nonlocal potentials, Schrödinger’s equation becomes an integro-differential equation.Solution method: SIDES solves the Schrödinger integro-differential equation numerically by matrix inversion using Gibbs, Numerov or a modified Numerov method with a uniform radial mesh in a box. The solution is refined by an iterative procedure until a specified precision is achieved. To obtain elastic scattering observables, the associated phase-shifts are calculated via matching of the numerical solution with its analytic asymptotic behavior.
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