Positronium formation by the passage of positrons through an electron gas

Abstract

A new approach to the problem of positronium formation in an electron gas is discussed by considering the competing processes of thermalization of the incident positron, capture of an electron by the positron and disintegration of the positronium so formed. We calculate, using the methods of quantum field theory of the electron gas: 1) the probability of finding the 1s and 2s states of positronium (plus a hole) in a positron beam passing through the electron gas, 2) the probability of disintegration of the positronium states into electrons and positrons as a result of many-body interactions and 3) the cross-section for thermalization of the incident positron. These calculations show that although the positronium formation cross-section is comparable to the rest of the competing processes for most incident-positron energies, there is, nevertheless, a very narrow band of energies where this cross-section dominates the rest. Therefore, in spite of thermalization of the incident positron and disintegration of the positronium formed in the metal, a large fraction of the incident beam will be converted to positronium when equilibrium is reached during its passage through the electron gas.