Generalization of the Jost function and its application to off-shell scattering

An off-shell generalization of the Jost function is developed within the framework of the differential-equation approach to the off-shell T matrix. Irregular solutions of the inhomogeneous Schrödinger-like equation that occurs in this approach are introduced, and their behavior at the origin is used to define an off-shell Jost function. The half-off-shell T matrix is expressed directly in terms of the off-shell Jost function. It is shown how the fully off-shell T matrix for a particular partial wave can be expressed simply in terms of a single integral involving the irregular solution for that partial wave. An integral equation for the irregular solution is developed, and used to derive an integral representation for the off-shell Jost function. Iteration of the integral equation leads to a series of successive approximations to the T matrix. The formalism is applied to several examples, including a boundary-condition model.