Scattering of $p\mu$ muonic atoms in solid hydrogen

We present the results of experimental and theoretical study of the scattering of low-energy $p\mu$ atoms in solid hydrogen cooled to 3 K. Strong effects resulting from the solid state interactions have been observed in the TRIUMF experiment E742 where muons were stopped in thin frozen layers of hydrogen. The resulting emission of low-energy $p\mu$ atoms from the hydrogen layer into the adjacent vacuum was much higher than that predicted by calculations which ignored the solid nature of the hydrogen. New differential scattering cross sections have been calculated for the collisions of $p\mu$ atoms on solid hydrogen to account for its quantum crystalline nature. Analysis of the experimental data performed using such cross sections shows the important role of the coherent scattering in $p\mu$ atom diffusion. For $p\mu$ energies lower than the Bragg cutoff limit $\left(\approx 2\mathrm{meV}\right)$ the elastic Bragg scattering vanishes which makes the total scattering cross section fall by several orders of magnitude, and thus the hydrogen target becomes transparent allowing the emission of cold $p\mu$ atoms to occur.