Positron Annihilation

If an epithermal positron from an external radioactive source such as sodium-22 is injected into a, say, metallic sample, it is usually thermalized within a very short time (a few picoseconds) compared to its mean lifetime in such a material (typically of the order of 100 to 1000 picoseconds). As a particle in thermal equilibrium with its environment, the positron "survives" a certain time until it annihilates with one of the electrons of the sample under emission of (usually) two annihilation photons. An analysis of this annihilation radiation gives, dependent on the complexity of the experimental equipment, a one- or two-dimensional projection of the electron-positron momentum density distribution in the material investigated. One of the advantages of this method is a remarkably high momentum resolution what is especially important if momentum distributions are used to investigate the Fermi surface of metallic systems. From the theoretical point of view, the greatest objection to the positron annihilation technique is the fact that the positively charged test particle polarizes the electron gas in the solid. The resulting so-called electron-positron enhancement effect represents, since many years, one of the most challenging problems of theoretical positron physics, especially if the annihilating fermions are not simply treated as free particles but as Bloch particles. The development of a theory describing the momentum distribution of annihilating pairs of electron and positron Bloch particles in spatially inhomogeneous electron gases including this enhancement effect was and is the main topic of my theoretical work since about 1990. These efforts led to the so-called Bloch-modified ladder (BML) theory (1996), an approach which is based on a perturbation expansion of the two-particle electron-positron Green's function. A selected list of publications to the topics BML theory and calculations of electron-positron momentum densities in metals is given in the following. Further relevant papers are in preparation.

[1] H. Sormann: "Influence of lattice effects on the electron-positron interaction in metals", Phys. Rev. B 54 (1996) 2401.
[2] H. Sormann and A. Fenkart: "Lattice and relativistic effects on the electron-positron momentum density of transition metals", Materials Sci. Forum 255-257 (1997) 590.
[3] H. Sormann and M. Sob: "Sensitivity of electron and electron-positron momentum densities to various electron and positron crystal potentials", Phys. Rev. 64 (2001), 045102.
[4] H. Sormann, G. Kontrym-Sznajd, and R. N. West: "On the reliability of various enhancement theories for a description of electron-positron densities in metals", Materials Sci. Forum 363-365 (2001) 609.