The Positronium state in quartz

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.