Minimum Energy of Positrons in Metals

Kim, S. M.; Stewart, Andrew; Ćarbotte, J. P.

doi:10.1103/physrevlett.18.385

Cited by 51 publications

(5 citation statements)

References 4 publications

(3 reference statements)

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“…Angular-correlation apparatus capable of achieving a resolution comparable with the thermal motion of positrons at liquid-helium temperature was recently built by us 6 and hence we attempted to resolve the discrepancy between the most recent theoretical predictions 5 and previous measurements. 1 In a series of carefully annealed metals of widely different valence-electron densities (K, Mg, and Al) we have observed that positrons are close to thermal equilibrium with the sample at liquid-helium temperature. Assuming that the best fit to the total smearing of the angular-correlation curve reflects just the optical resolution, positron penetration into the sample, and the Maxwell-Bo ltzmann momentum distribution of free positrons at temperature T, we find T = 25 ± 25°K in K, T=10±10°KinMg, and T = 30± 25°K in Al.…”

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confidence: 97%

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Thermalization of Positrons and Positronium

Kubica

Stewart

1975

Phys. Rev. Lett.

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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

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confidence: 97%

“…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.…”

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confidence: 99%

Thermalization of Positrons and Positronium

Kubica

Stewart

1975

Phys. Rev. Lett.

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“…measurement It should be noted that the problem of positron effective mass was considered in a number of theoretical (14 to16) and experimental(17,18) works and the positron effective mass value M*in Na and Rb was measured equal to 2 M where M i s the free positron mass. Recent detailed calculation(16) showed that in metals M*/M the previously obtained experimental values.…”

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On positron annihilation anomalies in ionic crystals

Vorob'ev¹,

Annenkov²,

Arefiev³

et al. 1973

Physica Status Solidi (b)

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“…Positron thermalization in solids at low temperatures is an interesting and challenging problem that has been studied both experimentally and theoretically every now and then over the last 40 years. [1][2][3][4][5][6][7] Besides from the point of view of positron-host interactions, the problem is important also when considering positron annihilation studies of defects in solids. In analyzing the annihilation radiation data, it is generally assumed that the positron is in thermal equilibrium ͑or very near͒ with the host very soon after implantation ͑within 10 ps͒ even at 10 K. This assumption is widely accepted to be true irrespective of the material.…”

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confidence: 99%

Positron thermalization in Si and GaAs

2001

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Positron thermalization in Si and GaAs has been studied both by experiments and simulations. The decrease in the positron mean energy due to the interactions with longitudinal-acoustic phonons was calculated down to 4 K by solving numerically the Boltzmann equation for the positron momentum distribution. We find that the differences in the strength of the positron-phonon coupling can result in considerable variations in the thermalization time. At 10 K, the time needed by the positrons to reach twice the thermal energy is 25 ps in Si, and 80 ps in GaAs. We find experimental support for the calculated thermalization behavior by studying the temperature dependence of the positron trapping rate at negative vacancy-type defects in Si and GaAs. In Si, we observe that positron lifetime data depends strongly on the sample temperature at least down to 8 K, which supports the predicted fast thermalization. In GaAs, the trapping rate below 20 K is observed to increase considerably less than expected for positrons thermalized instantly after implantation. This demonstrates experimentally that the thermalization time in GaAs is indeed much longer than in Si. We show further that the calculated positron energy-loss rates can explain quantitatively the temperature dependence of the experimental trapping rate in GaAs down to 8 K.

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Minimum Energy of Positrons in Metals

Cited by 51 publications

References 4 publications

Thermalization of Positrons and Positronium

Thermalization of Positrons and Positronium

On positron annihilation anomalies in ionic crystals

Positron thermalization in Si and GaAs

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