Thermalization of muonic hydrogen in hydrogen targets

The thermalization of p mu atoms in protium and d mu atoms in deuterium is considered. Monte Carlo calculations are performed for gaseous (300 K) and solid (3 K) protium and deuterium targets. Complete sets of the total and differential cross sections for the scattering of p mu on protium targets and d mu on deuterium targets are used as an input to the Monte Carlo simulations. At 300 K, muonic atom scattering from single molecules of H-2 and D-2 is considered. In the case of solid hydrogen the correlation effects from all molecules of the sample are taken into account. In particular, the Bragg and phonon scattering cross sections are calculated. The spin states and average energy of the muonic atoms are shown as functions of time. It is shown that at energies below about 0.01 eV the solid-state effects influence strongly the calculated cross sections, and therefore the deceleration processes in the solids are much slower than in the gaseous targets. It is shown that the neutron spectrum due to dd mu formation and subsequent dd fusion is significantly affected by slow d mu thermalization in solid deuterium.