Diffusion of muonic deuterium and hydrogen atoms

Abstract

Diffusion of muonic deuterium \ensuremath{\mu}d and muonic hydrogen \ensuremath{\mu}p atoms produced following the stopping of negative muons in ${\mathrm{D}}_{2}$ or ${\mathrm{H}}_{2}$ at 300 K was studied at pressures of 47--750 mbar (${\mathrm{H}}_{2}$) and 94--1520 mbar (${\mathrm{D}}_{2}$) in two distinct target geometries. Time intervals were recorded between entry of negative muons into the gas and arrival of each resulting \ensuremath{\mu}d or \ensuremath{\mu}p atom at one of 50 foils immersed in the gas, and spaced regularly along the muon beam axis. The results of such measurements were fitted to time distributions generated by Monte Carlo methods, using theoretical scattering predictions and empirically chosen forms for the initial energy distributions of the muonic atoms in the 1S state. Results indicate muonic atom energy distributions which (a) are different for \ensuremath{\mu}d and \ensuremath{\mu}p and (b) vary with pressure. The best-fit energy distributions have mean energies ranging from 1.5 eV for \ensuremath{\mu}d at 94 mbar to \ensuremath{\geqslant}9 eV for \ensuremath{\mu}p at 750 mbar. The data are also sensitive to scattering cross sections for \ensuremath{\mu}d and \ensuremath{\mu}p, and are consistent with current theoretical calculations for the \ensuremath{\mu}d+${\mathrm{D}}_{2}$ cross sections. In the case of \ensuremath{\mu}p+${\mathrm{H}}_{2}$ scattering, the experimental data suggest discrepancies with the theoretical predictions.