Assumption-Independent Single-Particle Wave Functions for Positrons in Solids: Applications to Angular Distributions in Al and Si

Abstract

The single-particle positron wave function in a solid may be calculated by a new technique which is entirely free of any theoretical assumptions by virtue of its use of experimental x-ray form factors to construct the potential. The results obtained accordingly form an excellent starting point for a systematic treatment of many-body effects in electron-positron annihilation processes. The positron wave function, which has the full crystal symmetry, is used together with pseudopotential wave functions for the valence electrons to compute the angular distribution of annihilation radiation from Al and Si for several crystal orientations. Agreement with experiment is excellent. The angular distribution from Al is found to be practically isotropic, despite the angular variation of the positron wave function. The substantial anisotropy in Si is reproduced within experimental error. Use of a constant positron wave function somewhat reduces the agreement. The calculated curves are little affected, however, by appreciable changes in the pseudopotential coefficients, indicating that positron annihilation is an insensitive probe of semiconductor band structures. The validity of using pseudopotential electron wave functions in the present context is discussed. The approximation is found to be excellent for most of the angular distribution because the positron is largely excluded from the core, where pseudo-wave-functions are incorrect. Accordingly, unlike positron lifetimes, the angular distribution can be well explained by an independent-particle model, even when it displays considerable anisotropy.