Nonperturbative expressions are derived for the angular resolved energy transfer spectra in the quantum regime of multiphonon scattering of inert gas atoms from surfaces. Application to He atom scattering from a prototype heatbath Xe/Cu(111) shows good agreement with experiments. This enables a full quantum calculation of the total energy transfer $mu$ and therefrom the much debated recovery or equilibrium temperature $T_{r}$ characteristic of zero energy transfer in gas-surface collisions in the free molecular flow regime. Classical universal character of $mu$ and $T_{r}$ is refuted.
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