Feshbach resonances in positron-hydrogen scattering

Abstract

Seiler, Oberoi, and Callaway first located resonances in the positron-hydrogen system below the $n=2$ inelastic threshold, using the algebraic close-coupling method without including the open positronium channel. Several other calculations including both open channels have failed to find any resonances. In an attempt to clarify the situation, a calculation has been performed which is an extension of the work of Seiler, Oberoi, and Callaway. A wave function including the $1s$, $2s$, and $2p$ eigenstates of hydrogen and the $\stackrel{-}{1s}$ ground state of positronium was used in a calculation that is a simplification of the usual close-coupling technique and that resembles the optical-potential method. In this approximation it is found that the lowest resonance of Seiler, Oberoi, and Callaway is destroyed by opening the $\stackrel{-}{1s}$ channel. It is concluded that any resonances which may occur in this system must lie closer to the $n=2$ threshold than do the corresponding electron-hydrogen resonances.