Single-Quantum Annihilation of Positrons by ScreenedK- andL-Shell Electrons

Abstract

Single-quantum annihilation of positrons in an atomic field is considered. Numerical calculations of the differential and total cross sections and the various polarization correlation functions are presented for the $K$ and $L$ shells of a range of elements from $Z=47\mathrm{}$ to $Z=92\mathrm{}$. The positron wave function is described by a partial-wave expansion in angular momentum eigenstates, and the interaction of the positron and bound electron with the radiation field is treated in lowest-order perturbation theory. Numerical programs are constructed for the solution of the radial part of the positron wave function and for the partial-wave phase shifts and normalization factors in ȧn arbitrary non-Coulomb central potential, and for the evaluation of the differential and total cross sections. The effects of screening are included by using the bound-state wave functions and central potentials predicted by the relativistic Hartree-Fock-Slater atomic model. Screening corrections to the Coulomb $K$-shell total cross sections are found to be sizable for large atomic numbers and low positron energy, and the ratio of $L$- to $K$-shell total cross sections is found to be significant for heavy atoms. The angular distributions for this atomic potential exhibit the sharp forward peak predicted in previous work assuming a purely Coulombic potential.