The tetradic scattering formalism is used to develop a theory for inelastic scattering of atoms from solid surfaces. The theory accounts for the correlated dynamics of the colliding atom and the solid surface, and an analytical expression is derived for the multiphonon energy transfer probability in a collinear collision. The present formulation does not rely on a separation of time scales and is thus valid for any value of the lattice correlation time tgr;crelative to the gasndash;surface interaction strengthd. In the high temperature and strong coupling limits,dtgr;cGt;1 and the inelastic cross section contains a Gaussian broadening term. In the extreme Markov limit,dtgr;cGt;1 and the cross section contains a Lorentzian broadening term. In both extremes, the lattice dynamics is weakly correlated with the collision. We discuss and analyze the behavior of the inelastic cross section under various physical limits.
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