Influence of the zero motion of a positron on positron lifetime in a metal lattice due to higher Fourier components of its Bloch function

摘要

Arponen and Pajanne suspected that the strong internal electric field of a real lattice decreases the contact density of electrons on the positron in comparison to expectations based on jellium calculations. In this work we propose an approach to this problem which indeed leads to decreasing annihilation rates of positrons in real metals. This is due to higher Fourier components of the Bloch function of the positron. With some probability the positron moves with regard to the electron gas. Owing to that the electron accumulation on this particle decreases. This improves agreement between theoretical and experimental annihilation rates in metals. However, because of the smallness of this effect the best agreement is still obtained if the Boronski-Nieminen formula is accepted for the electron-positron correlations in an electron gas. Consequences of this fact are discussed.