Quantum Monte Carlo estimators for the positron-electron annihilation rate in bound and low-energy scattering states

Variational and exact estimators for the positron-electron annihilation rate in bound states of systems containing a positron in the framework of quantum Monte Carlo methods are presented. The modification needed to compute the effective number of electrons Z(eff) when scattering states are concerned is also discussed. The algorithms are tested against four cases for which close to exact results are available, finding an overall good agreement. The systems are Ps(-), PsH, and the s-wave scattering component of e(+)H and e(+)He.