Locating Resonances in a Complex Potential Field

Abstract

The main question that has been answered in this research project is: what happens to the singularities of the S-matrix when the interaction potential becomes complex? In other words, we looked at the resonance spectral points and traced their movements on the complex momentum plane, when the imaginary part of the potential is gradually increased from zero to a certain reasonable value. This question is important in many fields of research where optical potentials are used. An optical potential can effectively take into account the loss of the beam of particles into all the reaction channels that are formally ignored. Such a simplified approach is widely used in nuclear and atomic physics. In order to study the movement of the spectral points, we used a simple potential and the Jost function method that allowed us to easily locate the spectral points as complex zeros of the Jost function.