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Lifetime of positive electrons in metals Jones, Garth

Abstract

Positron lifetimes in a variety of metals have been measured using a high-stability time sorter developed in this laboratory. This instrument consists of a time-to-pulse-height converter containing high-frequency microwave diodes as the discriminating elements, and limiter circuits specially designed for high stability and count-rate insensitivity. The intrinsic electronic resolution time of the time sorter is .05 nanoseconds, with an electronic stability of ± 1 x 10⁻¹¹ seconds over the course of a day. A resolution time for the prompt gamma rays of Co⁶⁰ of 0.8 nanoseconds was readily obtained. In addition, the time sorter was characterised by a linear time calibration over the range involved in the lifetime measurements of one to ten nanoseconds. The absolute lifetime of positrons in aluminum was measured by two methods which differed primarily in the means employed for obtaining the prompt resolution curve for the instrument. The first method involved the use of Co⁶⁰ as a prompt source of coincident gamma rays. Positron lifetimes were measured by analysing the delayed coincidence resolution curve resulting from the use of a Na²² source of positrons embedded in an aluminum absorber. The delayed coincidence resolution curve was determined by measuring the time interval between detection of the 1.28 Mev gamma ray in one channel (indicating the instant of emission of the positron) and detection of the 0.51 Mev radiation in the other channel (indicating the instant of annihilation of the positron). An analysis of the first two moments of the resulting resolution curves enabled a determination of the first two moments of the probability distribution characterizing the annihilation of the positrons. The mean lifetime of this distribution was found to be (2.45 ± 0.15) x 10⁻¹⁰ seconds and the square root of the second moment about the mean was (2.50 ± 0.15) x 10⁻¹⁰ seconds. The equality of these two values suggests an exponential probability distribution for positron annihilation in aluminum, since most other probability distributions would yield significantly different values for these two characteristics of the distributions. The second method was distinguished by the use of annihilation gamma rays as the prompt source. Although it was impossible to obtain a measure of the mean lifetime of the annihilation probability distribution, because of the symmetric nature of the resulting resolution curves, analysis of the second moments (which correspond to a measure of the width of the curves) yielded a value of the square root of the second moment about the mean of (2.65 ± 0.25) x 10⁻¹⁰ seconds, in agreement with the corresponding value obtained by the first method. In addition, comparisons of the mean lifetime of positrons in a variety of metals (twenty two in number) to that in aluminum were obtained. The results of these measurements indicated a range of lifetimes from 2.0 to 2.7 (x 10⁻¹⁰ seconds) but failed to indicate any dependence of the lifetime on the conduction electron density as would be expected for a pure collisional annihilation process. Instead, the positron lifetimes were found to be shortest in those metals characterised by dense crystal structures. An interpretation of these results in terms of annihilation of the positron from a bound negative positronium ion state is presented, the annihilation being characterised by an intrinsic mean lifetime of about 3.2 x 10⁻¹⁰ seconds. In metals with crystal lattices of small dimensions, the resulting shortened lifetime is attributed to an enhanced positron annihilation rate due to "pick-off" annihilations between the positron in the positronium ion and core electrons of the surrounding metal ions. Finally, this interpretation is shown to be in qualitative agreement with the results of the annihilation radiation angular correlation measurements with the high-momentum component of these measurements being attributed to the "pick-off" annihilations with the metal ion core electrons.

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