ALBERT

Notes: Transient changes in polarizability during collisions between atoms and molecules give rise to interaction-induced rototranslational Raman scattering: the scalar component of the collision-induced polarizability Δα00 accounts for isotropic scattering, while the second-rank component ΔαM2 accounts for collision-induced depolarized scattering. We have evaluated the changes in electronic polarizability due to interactions between an atom and a molecule of D∞h symmetry in fixed configurations, with nonoverlapping charge distributions. We have cast the resulting expressions into the symmetry-adapted form used in spectroscopic line shape analyses. Our results are complete to order R−6 in the atom–molecule separation R. To this order, the collision-induced change in polarizability of an atom and a D∞h molecule reflects not only dipole-induced–dipole (DID) interactions, but also molecular polarization due to the nonuniformity of the local field, polarization of the atom in the field due to higher multipoles induced in the molecule, hyperpolarization of the atom by the applied field and the quadrupolar field of the molecule, and dispersion. We have analyzed the dispersion contributions to the atom–molecule polarizability within our reaction-field model, which yields accurate integral expressions for the polarizability coefficients. For numerical work, we have also developed approximations in terms of static polarizabilities, γ hyperpolarizabilities, and dispersion energy coefficients. Estimated polarizability coefficients are tabulated for H, He, Ne, and Ar atoms interacting with H2 or N2 molecules. The mean change in polarizability Δα¯, averaged over the orientations of the molecular axis and the vector between atomic and molecular centers, is determined by second-order DID interactions and dispersion. For the lighter pairs, dispersion terms are larger than second-order DID terms in Δα¯. In both Δα00 and ΔαM2, first-order DID interactions dominate at long range; other interaction effects are smaller, but detectable. At long range, the largest deviations from the first-order DID results for Δα00 areproduced by dispersion terms for lighter species considered here and by second-order DID terms for the heavier species; in ΔαM2, the largest deviations from first-order DID results stem from the effects of field nonuniformity and higher multipole induction, for atoms interacting with N2.

Notes: A new algorithm that determines the evolution of a surface eroding under reactive-ion etching is presented. The surface motion is governed by both the Hamilton–Jacobi equation and the entropy condition for a given etch rate. The trajectories of "shocks'' and "rarefaction waves'' are then directly tracked, and thus this method may be regarded as a generalization of the method of characteristics. This allows slope discontinuities to be accurately calculated without artificial diffusion. The algorithm is compared with "geometric'' surface evolution methods, such as the line-segment method.