Jost-function approach to quantum defect theory

We present an approach to the quantum-defect theory theory using the Jost functions and Jost solutions as the main building blocks. An attractive feature of this approach is that it allows us to avoid use of the explicit form of the solutions of the radial Schrödinger equation for the Coulomb problem. We obtain a concise representation of the Jost function for the superposition of the Coulomb and short-range potentials, which distinctly separates terms analytic in k2 and terms singular at k=0. This representation can be used to design simple and efficient procedures allowing us to determine scattering phase shifts from the information about the bound states.