Thermalization of Positrons in Metals

Abstract

It is shown that a thermalization time of 3X 10~1 2 sec follows from the assumption that the interaction between a positron and a conduction electron can be approximated by an exponentially screened Coulomb potential.K NOWLEDGE of the thermalization time of a positron in a metal is pertinent to the interpretation of measurements of the angular correlation 1,2 of annihilation radiation and of the time distribution of annihilation. 3 Garwin 4 has pointed out that the estimate of 3X10~1 0 sec for thermalization in gold, made in Appendix I of reference 1, is too long because collisions between the positron and the conduction electrons are ignored; including this effect he estimated 10~1 4 sec for the thermalization time. Using a method similar to that of Sec. 5 of reference 5, we shall remove some of the crude approximations underlying Garwin's estimate and show that it is too short.The conduction electrons are treated as a freeelectron gas at the absolute zero of temperature. The Exclusion Principle is assumed not to apply to a system consisting of a positron and an electron. Transitions from an initial state consisting of a positron and an electron with wave vectors ki and k 2 , respectively, to a final state (k/,k 2 / ) occur because of the interaction -e*r~l exp(-qr). The number of transitions suffered per second by the positron is fIP®, P(t) being given as a multiple integral in Sec. 5. 8 To find the energy lost per second, we alter the integrand to include a factor representing the energy loss in a given transition, namely h 2 {2m)'~l{k^-ki 2 ).After a number of elementary integrations an expression for i?, the rate of loss of energy by the positron, can be found. We now suppress subscripts and write k and E for positron wave number and energy; also, for k/q we put x. R= (d>Tr)-l {me%~^)EF{k/q) 6 x L +-(18 J tan-^a (1) x\ 2x 2 / 5 56 F(x) = -+ Y2 3 log(l+4# 2 ) 32/20 \ 1 = -xH 1 rH I for b|«-. 35 V 9 / 2 1

Minimum Energy of Positrons in Metals

“…1 " 4 The results of these experiments have been shown to be compatible with the formation of a cavity in helium by an excess electron due to the repulsive exchange force between the excess electron and helium atoms. 5 " 8 An equilibrium cavity size is obtained by balancing the zero-point kinetic pressure of the electron by the surface and hydrostatic pressures on the cavity.…”

“…In fact, our final approximate formula is identical with that written some time ago by Lee-Whiting. 4 An essential difference, however, is that in the present result the Fermi-Thomas parameter, A, replaces the semiphenomenological screening length used by Lee-Whiting. When this change is made the resulting thermalization time increases considerably because of the strong (A 4 ) dependence on screening length.…”

Physicochemical and Radiation Modification of Titanium Alloys Structure

“…The fundamental result of this phenomenon is the positron thermalization time, during which the positron dissipates its initial energy. Its calculated value is 3 10 -12 s. [1].…”

Effect of an RF field on the positron angular correlation in a NaCl single crystal

“…physica status solidi(b) 68 Positron angular correlation arrangement;(1) ,sample, (2) source, (3) parabolic lead shield, (4) supplementary slits, (5) rf coil, (6) movable detector,(7) fixed detector, (8) angular correlation without r f field,(9) angular correlation with rf field both singles, were added pointwise for all the runs separately for the rf field on and off conditions. These curves are shown inFig.…”