Thermalization Time of Positrons in Metals

Abstract

<p>The thermalization time of positrons in metals has been computed as a function of the electron density parameter r_s, in the complete metallic electron density range (2 < r_s < 5.6). Our calculations are based on the propagator technique of many body perturbation theory, to first order in the electron-positron effective force. The rate of energy loss of the positron, in our formalism, is given by the imaginary part of the self energy operator; this quantity is worked out both in the Random Phase and the Hubbard approximation. We find that, in the low momentum transfer region, which is really the only regime of importance here, the electron-positron interaction can be approximated by a screened Coulomb potential e²/r exp (-λ_TFr) where λ_TF is the Thomas-Fermi momentum given by √4π∝ p_F. Here ∝ is related to r_S, the usual density parameter, by ∝ = r_S/1.919π²</p> <p>Further, we find that, in general, the time taken by the positron to drop to an energy of .025 e.v. is not as short as is generally believed, although it can be said beyond doubt that complete thermalization has taken place before annihilation at room temperature. However, for aluminium at 100°k, the thermalization time is longer than the annihilation time. On the basis of this result, we suggest that this lack of thermalization in aluminium might be detectable in an experiment similar to that recently reported by Stewart and Shand (1966), concerning the positron effective mass in sodium, although without more extensive calculations it is not possible to say precisely how a small amount of non-thermalization would affect the angular correlation curves.</p>