Thermalization of Positrons and Positronium

Abstract

sional-multichannel method and to demonstrate that it works well, it is of some relevance to further consider the comparison between the CPA and the space-time Magnus methods. The CPA starts to break down for nonresonant inelastic processes where the energy transfered is a large fraction of the kinetic energy in one of the channels. 1 Consequently, a comparison can be made with a simple model like the following: W 119 W 00 =<*> for x< 0, W 00 = 0 and W u = 1 for x> 0, and W 01 = V (a constant) for 0 < x^ A and W 01 = 0 for x>A.The full quantum method, the CPA method, and our method (for a single interaction interval) may be solved analytically for this model. We find that at high energies the space-time Magnus method and the CPA both agree with the exact quantum results, and at low energies both methods give good results for the average transition probability. However, at low energies the spacetime Magnus method very accurately reproduces the correct oscillations in the transition probability while the CPA is badly out of phase with the correct oscillations. (In the very-low-energy limit, the single-interaction-interval space-time Magnus method begins to develop some discrepancies.)The reason that the semiclassical method provides an improvement over the CPA can readily be understood. The only approximation inherent in the semiclassical method involves the choice of a finite interval size, as the Magnus decom-For many years the annihilation of positrons in solids has been used to investigate various characteristics of electrons in matter. It has usually been assumed that at the time of annihilation the positron, or sometimes the positronium atom, was in its lowest state in thermal equilibrium with its environment, although the experiments position and the semiclassical approximation to the space-time propagator both become exact as the interval size decreases. It is the use of heavy masses and slowly varying potentials that permits the use of rather large intervals, thereby making the method useful.We are grateful to Professor John Light for many helpful discussions and suggestions"Positrons in metals and positronium in quartz have been observed to thermalize down to nearly liquid-helium temperatures before annihilation. The achievement of such low temperatures by both positrons and positronium in approximately 10" 10 sec indicates that phonon scattering plays a major role in thermalization. These results have important implications for the ability to achieve high precision in Fermi-surface studies by the positron-annihilation technique. 852

Energy-Resolved Positron Annihilation in Flight in Solid Targets

“…As energetic positrons penetrate a solid target they rapidly loose kinetic energy via electronic collisions to several eV within ϳ0.1 ps [1] and come into thermal equilibrium with the target within 10 ps [2]. The characteristic lifetime of the positron in a solid target is several 100 ps which is consistent with the observation that virtually all positrons annihilate with thermal kinetic energy.…”

Compton Scattering and Various ACAR Experiments in~Mg

“…Kubica and Stewart, studying thermalization of positrons, performed measurements with a very high instrumental resolution varying from 0.014 up to 0.034 a.u., the smaller one at low temperatures. They tted 1D ACAR data in Mg with a phenomenological enhancement for b = 0.25 and c = 0.38 [12]. Shiotani et al estimated b = 0.20 and c = 0.145 [7], almost the same as determined by us for data [6] while Nakashima et al [8] obtained b = 0.18 and c = 0.06 along Γ M and Γ K directions.…”

“…Additionally, when the ep interaction potential used in the BML theory would be replaced by its self-consistent form, the enhancement factor would be higher (up to 1.1 times, see Fig. 5 in [5]) for high values of the enhancement near the FS pointed out by Kubica and Stewart [12].…”

“…5 and 7 of Ref. [5] and results of a very precise experiment [12]. Therefore, despite appearance, results of the experiment [6] seem to be closer to the reality.…”

Methods of Extracting Electron-Positron Enhancement Factors from Experimental ACAR Data

“…On the other hand, in alkali metals the Fermi momentum is rather small and the influence of the resolution function of the equipment can disable us to study prec(p) and Nexp(pz ) in the neighborhood of 0.8pF. As a conclusion, detailed studies of Nb (pz ) require the equipment of high resolution, as the one used by Kubica and Stewart [7].…”