Generalized Variational Bounds on the Positron-Hydrogen Reaction Matrix. II. Effective Distortions

The problem of the two-channel positron-hydrogen rearrangement collision is studied with the formalism of the generalized variational bounds. For the zero total partial wave, a reasonably complete treatment of this scattering system is presented, including a detailed discussion of the energy spectrum of the closed-channel Hamiltonian $M$. The coupling of the open channels to the closed channels gives rise to the effective interaction potentials, and these distortion terms are estimated variationally using the bound property of $M$. The orthogonality of $M$ to the open-channel space is maintained by the presence of the energy-shift operator $S$, and the role of $S$ is demonstrated in detail numerically, which produces essential cancellation of various terms. Partly owing to the crudity of the trial functions used, we have not been able to find resonance states below the first excitation threshold. Bounds on the diagonal $K$ matrix elements and eigenphase shifts are presented.