Rotationally inelastic molecule--surface scattering in the sudden approximation

Rotational and reorientational transitions in molecular collisions with solid surfaces are investigated by a model based on a sudden approximation with respect to both the rotational and the diffraction states that play a role in the scattering. The approximation developed leads to computationally simple expressions and provides detailed insight into the physical properties of the processes involved. A detailed quantitative study is made of the rotational state distribution produced by the collision, the variation of rotational excitation probabilities with the scattering angle, and related questions. A number of factorizations, sum-rule, and scaling properties are predicted for S/sub j/m/sub j/,00;/sub j/'m'/sub j/',mn 2, the transition probability between the initial (jm/sub j/) and the final (j'm'/sub j/') rotational states for scattering into the (mn) diffraction channel. The strongest sum rules and scaling laws are obtained using additional approximations beyond the sudden decoupling. Among the latter results: (1) The j,j' dependence of S/sub j/0,00;j'm'0,mn 2 is determined entirely by the difference variable Δj=j'-j. (2) The diffractive intensity distribution summed over all final rotational states is the same as that obtained for a mass-equivalent atom (with an interaction that is the orientation-averaged molecule--surface potential). (3) The rotational state distribution, summed over all diffraction states, equals that calculated from a corresponding flat surface. (4) All rotational transition probabilities for the (m,n) diffraction spot can be obtained from the diffraction--rotational transition probabilities in the (m,0) and (n,0) diffraction spots. The above and other properties are tested numerically in the framework of the full sudden approximation for a model of H2/LiF(001) in the energy range 0.5--0.9 eV. They are found to hold to excellent accuracy