Cross-sections for elastic scattering of muonic hydrogen on helium nuclei, (hμ)_{1s} + He^{++}, where h and He^{++} stands for a hydrogen and a helium isotope nucleus, respectively, were calculated in the one-level adiabatic approximation for a range of collision energies from 0 to 50 eV. Bound states and energy levels of (hμHe)^{++} molecular ions were also calculated and compared with their Born-Oppenheimer counterparts. It is shown that adiabatic corrections are responsible for proper positions of the Ramsauer-Townsend minima in (hμ)_{1s}+He^{++} elastic scattering and, at the same time, they significantly influence bound states and energy levels of (Heμh)^{++} and (Heπh)^{++} ions. Calculations were performed in the frame of the phase-function method.
Direct and inverse muon transfer between atomic orbits of muonic hydrogen isotopes is considered in the WKB approximation. The corresponding cross sections, calculated as functions of collision energy, are different above the thresholds for the inverse transfer and approach common limits depending on the principal quantum number and hydrogen isotopes. The comparison of results obtained by integration over impact parameter and by summation over angular momentum is also presented.
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