Central-field model for the γ spectrum of positrons annihilating on rare-gas atoms

Abstract

A central field model is used to study the two-photon positron annihilation spectrum for the rare gas atoms He, Ne, Ar, Kr, and Xe at energies close to thermal. Correlation effects are incorporated with a semiempirical polarization potential. The $\ensuremath{\gamma}$ spectrum is given, with values reported for individual subshells. The predicted full widths at half-maximum (FWHM) for all systems are typically $5%--20%$ larger than the experimental values reported using the positron trap at the University of California, San Diego, while, with the exception of neon, generally being $2%--10%$ smaller than the FWHMs measured at University College London. The detailed spectrum for xenon is reported and the likelihood of core annihilation's making a measurable contribution to the observed Doppler spectrum is discussed. The $\ensuremath{\gamma}$ spectra are found to be insensitive to variations in the scattering potential and whether the target is represented by a Hartree-Fock or a Dirac-Fock wave function. The model potential used in the solution of the positron-atom Schr\odinger equation provides a reasonable fit to recent total elastic cross-section measurements reported by the Australian National University and University of Trento groups.