Electric Field Dependence of Positronium Formation in Matter

Abstract

Positronium (Ps) can be formed whenever positrons, on slowing down in a substance, pass through an Ore gap, i.e., a range of energies, just below the ionization threshold of the substance, of width comparable to the Ps binding energy. We have studied the time evolution of the energy distribution of the positrons below the ionization threshold in an external electrostatic field, and find: (1) The field induces diffusion out of the Ore gap, which decreases Ps formation. (2) The over-all heating effect of the field on the positrons increases Ps formation. Depending on the magnitude of the relevant cross sections, (1) can outweigh (2), at small fields, and cause a significant decrease in the Ps formation. At field strengths larger than a characteristic value, (2) becomes the dominant effect. In this way measurements of the field dependence of Ps formation can give access to the cross sections for Ps formation and for positron-energy loss and scattering in matter.