The Positronium state in quartz

TL;DR

This paper models the positronium state in quartz as a superposition of free positron and positronium lattice states, deriving conditions for formation and proposing a variational method to calculate annihilation parameters.

Contribution

It introduces a superposition model for positronium in quartz and develops a variational approach to determine formation conditions and annihilation parameters.

Findings

Positronium in quartz can be described by a superposition of free and lattice states.

Conditions for positronium formation in electron gas are derived.

A variational method for calculating the self annihilation parameter $7$ is proposed.

Abstract

The positronium state in quartz is described by a linear superposition of two states: the first describing the free positron in the crystal and the second corresponding to a positronium Bloch wavefunction in the lattice. The condition for positronium formation in the electron gas is deduced by using variational calculations of the positron binding energy to the electron system. The self annihilation parameter $\kappa$ introduced in positron lifetime experiments can be properly justified by using the mixed state. A variational method to calculate $\kappa$ is proposed.