  The differential cross sections for low-energy muonic hydrogen atom
scattering from hydrogenic molecules are directly expressed by the
corresponding amplitudes for muonic atom scattering from hydrogen-isotope
nuclei. The energy and angular dependence of these three-body amplitudes is
thus taken naturally into account in scattering from molecules, without
involving any pseudopotentials. Effects of the internal motion of nuclei inside
the target molecules are included for every initial rotational-vibrational
state. These effects are very significant as the considered three-body
amplitudes often vary strongly within the energy interval $\lesssim{}0.1$ eV.
The differential cross sections, calculated using the presented method, have
been successfully used for planning and interpreting many experiments in
low-energy muon physics. Studies of $\mu^{-}$ nuclear capture in $p\mu$ and the
measurement of the Lamb shift in $p\mu$ atoms created in H$_2$ gaseous targets
are recent examples.
