Influence of lattice effects on the electron-positron interaction in metals

We describe the influence of the crystal lattice on the enhancement of the electron-positron annihilation rate in metals by the use of an alternative version of the Bloch-modified ladder (BML) theory, which we call the optimized BML approximation. This approach to the problem of positrons interacting with an inhomogeneous electron gas can be reliably applied to metals with high and medium valence electron density, especially to transition metals, but is less efficient for metals with low electron densities such as, e.g., alkali metals. It enables us to describe the role of lattice effects in an approximative but nevertheless physically reasonable way. The paper offers (i) an extensive presentation of the theory and (ii) a summary of momentum-dependent enhancement results obtained for a series of simple and d-band metals (Al, Cu, Pd, Mn, and V) both for the central momentum region and for near umklapp regions. These BML enhancement factors are compared with corresponding results of the local-density approximation and with enhancement factors extracted from two-dimensional angular correlation experiments. The main result of this paper is that we are able to demonstrate that for all metals and for all regions of the momentum space investigated, the lattice effects on the electron-positron enhancement are significant and therefore should not be neglected in theoretical work. © 1996 The American Physical Society.