Resonantdtμformation in condensed hydrogen isotopes

Abstract

Resonant formation of the muonic molecule $dt\ensuremath{\mu}$ in $t\ensuremath{\mu}$ 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, a general asymptotic form of the resonance correlation function for high momentum transfers is found, which is valid for any solid or dense-fluid hydrogen-isotope target. Numerical calculations of the rates are performed for solid hydrogen isotopes at zero pressure, using the isotropic Debye model of a 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 $(\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ collision energies. This is important for explaining the time-of-flight measurements of the $dt\ensuremath{\mu}$-formation rate, carried out at TRIUMF. The calculated mean values of the 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.