Positronium-hydrogen elastic scattering

The elastic scattering of positronium atoms by hydrogen atoms below the excitation threshold at 5.1 eV has been investigated, with the investigation limited to the spin-zero (singlet) state of the two electrons. Nonresonant S-wave phase shifts have been obtained from normalizable trial functions by extracting the center-of-mass wave function and examining its spatial behavior. An effective-range expansion is fitted to the phase shifts and the previously obtained positronium-hydride bound-state energy to yield a scattering length a approx. = 5.3a0 compared with Fraser's corrected exchange result, a=7.28a0 (a0 is the Bohr radius). The stabilization method suggests that a resonance occurs at a scattering energy of 4.5 eV, about 0.6 eV below the excitation threshold. Using the complex rotation method, evidence confirming the existence of the resonance and an estimate of its width of about 6 times 10-2 eV have been obtained