Numerical determination of complex resonance energies by using a superposition of δ‐potentials

Abstract

ABSTRACT:A method using a superposition of a finite but varied number of ␦-potentials has been applied to treat the integral Schrö dinger equation with three different potentials. Positions of scattering resonances are numerically determined as complex poles of the partial-wave S-matrix. The method, in principle, makes it possible to obtain several resonances for short-range potentials like a square well (or barrier). The numerical method is elaborated to treat integral equations and is applicable to solve problems for which no differential equations can be derived.

Integral equations and complex resonance energies for analytical potentials

“…This implies that U( z) decreases as r 3 ϱ only if ͉͉ Ͻ /2, i.e., if the ray (27) is in the right half plane. At the same time, the more ͉͉ is increasing, the slower the decrease of the potential.…”

“…This method has proved a successful technique for solving homogeneous integral equations [27]. If the parameter r N is large enough, the contribution from the potential's tail U ( ) (r N ) at large r N can be neglected in Eq.…”

A general solution of the Dirac equation with superposition of δ-potentials and its application

“…Thus, using (8) and (9) we can obtain exact analytical solution of the Dirac equation with superposition of δ-potentials and numerical solution for a smooth potential.…”

“…To calculate the phase shifts (8) it is necessary to have the coordinates array a q and the coefficient array V q . In this method of solution the step between δ-functions can be different, therefore accuracy of numerical solution can be improved through increasing of density distribution of the δ-functions near sharp variation of the potential field.…”

“…In quantum theory, superposition of δ-potentials can be used, for example, approximate smooth analytical potentials [8], describe localized interactions together with a smooth potential [9], describe the nucleon-nucleon interaction [10], and describe particles in periodic structures [3,4].…”