Interrelation between variational principles for scattering amplitudes and generalizedR-matrix theory

Abstract

We establish a connection between the Kohn variational principle, with (complex) outgoing-wave boundary conditions, and the Kapur-Peierls form of the R-matrix theory. We show that the complex Kohn method, unlike the usual Kohn method, does not suffer from the problem of spurious singularities. We also discuss a generalization that allows the calculation of scattering cross sections over a continuous range of energies from a single diagonalization of the Hamiltonian. Several numerical examples are presented.