Collisional ion-pair formation in an excited alkali-metal vapor

Abstract

Thermalization of hot t\ensuremath{\mu} atoms formed in ${\mathrm{D}}_{2}$-DT-${\mathrm{T}}_{2}$ mixtures and relaxation of the triplet hyperfine state of t\ensuremath{\mu} are treated by Monte Carlo simulation. The cross sections for collisions with molecular targets are derived from cross sections for collisions with the component atoms. The statistical histograms for the time-dependent velocity distributions are fitted by sums of two Maxwellian functions, and the coefficients and temperatures are tabulated for tritium fractions of 10%, 50%, and 90% and mixture temperatures of 30, 100, and 300 K. The results provide a basis for analyzing some previously puzzling aspects of the observed cycling rate in recent muon-catalyzed-fusion experiments. In particular, thermalization is found to be very incomplete for some low-temperature targets. Also, the relative rates of kinetic thermalization and hyperfine-state relaxation depend strongly on the target tritium fraction, and hyperfine effects may be observable. The velocity distribution of t\ensuremath{\mu} atoms at times of molecular dt\ensuremath{\mu} formation is shown to depend only rather weakly on the initial velocity distribution, which is not well known.