Jost matrices and the analytic structure of the multi-channel scattering matrix
Seminar “Nuclear Theory”
Date and Time: Monday, 2 March 2020, at 3:30 PM
Venue: Blokhintsev Lecture Hall (2nd floor), Bogoliubov Laboratory of Theoretical Physics
Seminar topic: «Jost matrices and the analytic structure of the multi-channel scattering matrix»
Speaker: S. A. Rakitianski (University of Pretoria, South Africa)
A new approach is proposed and developed that allows one to analyze nonrelativistic multichannel processes with binary channels. The approach is based on a direct calculation of the Jost matrices at any given point on the Riemann surface of the energy. This allows one to solve the scattering as well as the bound-state and resonance problems in a unified way. The semi-analytic representations of the Jost matrices are obtained, where all the factors responsible for the branching of the Riemann surface, are given explicitly. The Jost-matrix symmetry relations at various points of the Riemann surface are studied. Specifically, it is shown that the Coulomb forces, if present, do change the topology of the Riemann surface and lead to the absence of the so-called “mirror” resonances. It is suggested to use the semi-analytic representations of the Jost matrices for parametrizing experimental data. The developed approach is generalized for the one- and two-dimensional problems as well as for a limited class of the many-body problems that allow using the hyperspherical expansion. Within the approach a number of problems of nuclear and hypernuclear physics is also considered.
(based on the Doctoral Thesis)