This Letter reports an important new discovery in positron annihilation in metals, viz., that positrons are not always thermalized before annihilation and thus that the ultimate resolution of the technique is limited. The next paragraphs outline the experimental and theoretical discoveries of this phenomenon, and present the results of calculation and measurements.Observations of positron motions in metals, first reported last year, 1 ' 2 have been continued in a series of metals over a wider range of temperatures. The positron-annihilation technique measures the momentum distribution of all annihilating pairs of electrons and positrons, i.e., the convolution of the distribution of electron momentum with positron momentum. By examining the momentum distribution of annihilation photons in the region corresponding to the Fermi momentum, where the electron distribution has a sharp cutoff, information can be obtained concerning positron motion. In terms of experimental measurements, the angular correlation of annihilation photons yields the usual parabolic distributions shown in Fig. 1. It can be seen that as the temperature of the specimen is raised the smearing of the parabolic cutoff is increased. This effect was naturally taken to imply increased motion of the positron in the hotter metal. Only one parameter of the positron motion can be obtained from present experimental results. We have called this parameter the positron effective temperature, having assumed for its energy distribution the Boltzmann formula for free particles.Data have been collected for positrons annihilating in Li, Na, K, Rb, and Ca at various temperatures, and analyzed by a method similar to that described in Ref. 2. In brief, the analysis consisted of comparing the data in the "slope" presentation (i.e., the deriva-
the kaon-mass splitting are both dominated by an s-wave, -f = 0, pion-pion resonance, somewhat higher than the kaon mass to ensure m^ >m s , then the relation cos(cp w + 6) = 0 must be satisfied. For small 5 2 , this is precisely the exceptional limit we have just examined.Comparison with experiment. -Presently available experimental data permit us to determine 8 0 -6 2 approximately. Inserting into Eq.(1) the values of R = 2.9±0.6 6 and cp =0.60± 0.23, 7 we obtain the inequalityThis result is compatible with other determinations of the pion phase shifts at 500 MeV. 8 We thank V. Teplitz for his help, as well as N. Cabibbo and S. Weinberg for interesting discussions.
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