Jost function formalism with complex potential

TL;DR

This paper extends the Jost function formalism to include complex potentials, deriving new relations and demonstrating their properties through numerical calculations with complex Woods-Saxon potentials.

Contribution

The paper introduces an extension of the Jost function formalism incorporating complex potentials and derives related unitarity and optical theorem relations.

Findings

Derived the Jost function with complex potentials.

Established the optical theorem for complex potentials.

Numerical validation using complex Woods-Saxon potential.

Abstract

The Jost function formalism is extended with use of the complex potential in this paper. We derive the Jost function by taking into account the dual state which is defined by the complex conjugate the complex Hamiltonian. By using the unitarity of the S-matrix which is defined by the Jost function, the optical theorem with the complex potential is also derived. The role of the imaginary part of the complex potential for both the bound states and the scattering states is figured out. The numerical calculation is performed by using the complex Woods-Saxon potential, and some numerical results are demonstrated to confirmed the properties of extended Jost function formalism.