A resonant state and the ground state of positronium hydride

Abstract

The lowest-lying resonance occurring in $S$-wave positronium-hydrogen scattering is reinvestigated, using the complex-rotation method. By employing a generalized Hylleraas-type wave function that includes all six interparticle coordinates, a very accurate value of the resonance position $E_r$ is obtained, along with a good value of the width. The present result for $E_r(-1.205\mathrm{}\pm 0.001 \mathrm{Ry})$ is lower than the previous result of Drachman and Houston, who omitted the interelectronic coordinate $r_{12}$ in their trial function. In addition, the lowest ground-state energy of positronium hydride is obtained by using 210 terms in the trial wave function. The effect of the $r_{12}$ coordinate and others on both the resonant energy and the binding energy of PsH is discussed.