Insight into the electron–positron correlations in metals through the looking glass

Abstract

A semi-empirical analysis of the positron annihilation experimental spectra indicates for a strong sensitivity of the two-particle electron–positron (e–p) enhancement factor to the l=s, p, d, f character of the initial electronic state [1,2]. The essential discrepancy between the models consists in the dependence of the relevant correlation functions on the energy of the annihilating electron. The present contribution contains a theoretical study of the e–p enhancement factors for s, p, d and f states as a function of the electron energy. The slope of the resulting characteristics is directly related to the degree of localisation of the s, p, d and f electrons in the electron density of states. This effect occurs especially for d electrons in transition metals, in favour to the approach of Ref. [1].The energy dependence of the two-particle correlation functions is also a source of controversy between various theoretical approaches. The energy dependent enhancement factors describe properly the positron interaction with delocalised s and p electrons, but this approach overestimates the high momentum components of the e–p momentum densities, dominated by the localised d and f states. On the contrary, the calculations that employ the energy averaged enhancement factors match better with experiment for localised d and f electrons, but they hardly reproduce experimental spectra for nearly-free electron populations. An attempt to visit two sides of the looking glass is made in the theory of the present work. The model combines the properties of both approaches. The resulting e–p momentum densities and enhancement factors are in good agreement with the experimental data for simple, noble and transition metals, both in the low and high momentum region.