Hard-ellipsoid scattering

At the high level of final state resolution provided by such experiments we can discern quantal interference effects. The more prominent feature for inelastic excitation is a rotational rainbow that arises by a mechanism similar to the intense scattering of the final velocity into certain directions (Section 2.2.5). Here too, the rainbow arises from different trajectories scattered into the same final state except that the state is specified not only by the direction of v but also by the rotational state of the molecule, NO in the case of Figure 10.9. This is a stereodynamic effect because the final state is determined not only by the impact parameter but also by the angle of approach, as shown for scattering by a hard ellipsoid in Figure 10.10. 

Figure 10.10 Scattering of an atom off a hard ellipsoid for a given impact parameter and angle of approach, y. The scattering angle is Q. The recoil momentum Ap corresponds to a change Aj = R x Ap in the rotational angular momentum of the ellipsoid. The two panels correspond to two different impact parameters that lead to scattering into the same final state.

Beck and coworkers have measured energy loss spectra for K scattering from CO and N2, for scattering angles greater than 90 and energies 0.34-1.24 eV and have also observed an isotope effect in the structure. They have successfully modeled their results with classical scattering from a hard ellipsoid. ... 

The deformation behaviors have been interpreted in terms of the two basic models(11), (i) the deformed two-phase model in which the interparticle distances and the particles, initially giving rise to Debye s hard-sphere type scattering(1U), are affinely deformed under constant volumes (designated as "deformed hard-particles") and (ii) the deformed core-shell particle model in which a spherical core-shell particle is affinely deformed under constant volume into an ellipsoidal core-shell particle. 

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