The generalised scattering length and resonances in e+-H S-wave scattering

Using as a definition of resonance, a discrete complex eigenvalue of the rotated Hamiltonian H alpha obtained from H by the transformation r to re i alpha , it is shown that an infinite sequence of S-wave resonances (disregarding relativistic effects), approaching the H(n=2) threshold along a line, will exist. The location of these resonances depends asymptotically on the generalised scattering length b, which is related to the form of the solution of Schrodinger's equation at the threshold energy. With the help of the Kohn variational principle, b is calculated using Pekeris basis functions (1958), which give rise to a sparse matrix. It is found that the resonances have a small width.