Resonant dt-mu formation in condensed hydrogens

Abstract

Resonant formation of the muonic molecule dt-mu in t-mu atom collision with condensed H/D/T targets is considered. A specific resonance correlation function, which is a generalization of the Van Hove single-particle correlation function, is introduced to calculate the resonant-formation rate in such targets. This function is derived in the case of a polycrystalline harmonic solid. Also is found a general asymptotic form of the resonance correlation function for high momentum transfers, valid for any solid or dense-fluid hydrogen-isotope target. Numerical calculations of the rates are performed for solid molecular hydrogens at zero pressure, using the Debye model of an isotropic solid. It is shown that condensed-matter effects in resonant formation are strong, which explains some unexpected experimental results. In particular, the resonance profiles are affected by large zero-point vibrations of the hydrogen-isotope molecules bound in the considered crystals, even for high (1 eV) collision energies. This is important for explanation of the time-of-flight measurements of the dt-mu-formation rate, carried out at TRIUMF. The calculated mean values of the dt-mu-formation rate in solid D/T targets, for fixed target temperatures and steady-state conditions, are in good agreement with the PSI and RIKEN-RAL experiments.