Relativistic recoil corrections of order \boldmath$m(Z\alpha {)}^6(m\mathrm{/}M)$: Hydrogen-like atom and hydrogen molecular ion

The finite operators are derived for the recoil $m{\alpha }^6(m\mathrm{/}M)$ order relativistic corrections (to spin-averaged energy levels) in hydrogen-like atoms and ions in the two- and three-body formalism beyond the adiabatic approximation. Results are presented in a form suitable for numerical evaluation.