Elastic scattering of positrons on mercury: A negative-energy Dirac-Fock treatment

In a new extension of the Dirac-Fock method, calculations have been performed on the 80 electrons of mercury (in 22 nlj orbitals) plus one continuum electron of negative energy less than -${\mathit{mc}}^2$. The asymptotic form of the numerical wave function of the negative-energy electron determines the phase shifts for the elastic scattering of positrons on Hg. The self-consistent-field calculations include the usual exchange interaction between electrons. The exchange between the bound Hg electrons and the negative-energy continuum electron represents the positron-electron annihilation-creation process. Such effects are usually computed in quantum electrodynamics to some order of approximation in a perturbation expansion. We believe ours is the first Dirac-Fock calculation of this effect, but we find its influence on the elastic positron scattering to be negligible.