Many-body calculations of positron scattering and annihilation from noble-gas atoms

We have applied many-body theory methods to study the interaction of low-energy positrons with noble-gas atoms. The positron - atom correlation potential includes explicitly the contribution from the target polarization by the positron and that from the virtual positronium (Ps) formation. It is demonstrated that the correlations and Ps formation (or tunnelling of electrons from the atom to the positron) create virtual levels in the positron - atom system. The existence of the virtual levels strongly influences the scattering and increases the positron annihilation rate by up to 400 times. The calculated elastic cross sections are in good agreement with experimental data. The inclusion of virtual Ps formation greatly improves the agreement with experimental annihilation rates with respect to calculations taking only the polarization into account. Our calculations have highlighted the difference between the calculation of positron - atom scattering and the calculation of corresponding annihilation rates. The annihilation rate is very sensitive to the behaviour of the wavefunction at small positron - electron separations. A simple approximate formula based on the Sommerfeld factor is suggested to account for the effect of electron - positron Coulomb attraction on the annihilation rates.