Positronium in a LiH Crystal

Abstract

The question as to whether the existence of a bound positronium-like system in an ionic crystal is energetically possible is considered with particular reference to lithium hydride. The crystal field of LiH is simulated by a potential expressed as a sum of central field potentials centered on the ion sites. An upper bound is obtained for the ground-state energy of a system of an electron and a positron in Coulomb interaction with each other and moving in the crystal potential, and comparison is made with estimates of the energies of the positron and the electron moving independently in the crystal. The result is energetically favorable to the formation and persistence of positronium in the crystal through capture by a positron of an electron from the valence band.