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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

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