Reskit: A toolkit to determine the poles of an S-matrix

Abstract

We present the python package reskit, developed to calculate the coefficients of an analytical continuation of the S-matrix of a physical system by means of Padé approximants and, from this fit, determine the complex poles of this S-matrix.The current implementation of the program is restricted to elastic scattering, i.e. cases in which all channels have the same energy. It has been tested using as input ab initio scattering data for electron–molecule collisions obtained for energies along the real axis. The identification and characterisation of the resonances present in the systems using reskit is described and discussed. Program summaryProgram Title:reskitProgram Files doi:http://dx.doi.org/10.17632/p47yys8wpm.1Licensing provisions: MITProgramming language: Python 2.7Nature of problem: the S-matrix of a system is usually calculated as a function of real energy (for example by varying the kinetic energy of a projectile in a scattering process). Locating its complex poles requires some type of extrapolation on the Riemann sheets relating the total energy, in the complex plane, to the momentum. The program determines the complex poles of the fitted polynomial S-matrix that identify its resonant, bound and virtual states.Solution method: the program is based on the method developed by Rakityansky and collaborators [1] in which a Padé approximant is used to fit provided S-matrix data, determined as a function of a real energy. Expressing the S-matrix in the Jost form, the generally complex poles of the S-matrix can be found by determining the stability of the roots of the determinant of the Jost matrix as S-matrix data for an increasing number of energies are used for the fit.Additional comments including restrictions and unusual features: the current implementation requires that all channels/states have the same energy and that no long-range Coulomb interaction potential is present. The first of these restrictions results in a simplified S-matrix that is defined solely as a function of the momentum in the complex plane.[1] P. Ogunbade, S. Rakityansky, S-matrix parametrization as a way of locating quantum resonances and bound states: multichannel case, in: Proceedings of the 2nd South Africa - JINR SYMPOSIUM, Models and Methods in Few- and Many-Body Systems, JINR, 2010, 52–61.