Convergence of partial-wave expansions for energies, scattering amplitudes and positron annihilation rates

We use many-body theory to find the asymptotic behaviour of second-order correlation corrections to the energies and positron annihilation rates in many-electron systems with respect to the angular momenta l of the single-particle orbitals included. The energy corrections decrease as 1/( l + ½) 4 , in agreement with the result of Schwartz, whereas the positron annihilation rate has a slower 1/( l + ½) 2 convergence rate. We illustrate these results by numerical calculations of the energies of Ne and Kr and by examining results from extensive configuration-interaction calculations of PsH binding and annihilation.