Semiclassical perturbation theory of electron—polar-molecule collisions: Total excitation and scattering cross sections

Semiclassical perturbation scattering theory is applied to electron—polar-molecule scattering. Cross sections for elastic and rotationally inelastic transitions are obtained for $\Delta j=0, 1, 2, 3, 4$, in the case of a pure charge-dipole interaction potential. Results are presented in terms of functions of dimensionless parameters involving the moment of inertia $I$ and dipole moment $\mu$ of the target, and the mass, charge, and energy of the projectile. A range of these parameters sufficient to describe most situations of practical interest is explored. Significant oscillations are found in the cross sections for $\left|\Delta j\right|=0\mathrm{} \mathrm{and} 2$ as a function of dipole strength $\beta =\frac{m\mu e}{{\hslash }^2}$. For $\left|\Delta j\right|=1\mathrm{}$, the Born approximation is shown to be appropriate for $\beta \ll 1$, and invalid for $\beta \approx 1 or >1\mathrm{}$, Scaling rules are deduced which should aid in the correlation and extrapolation of quantal calculations on specific systems. With the guidance of the Born approximation, scaling principles are also suggested for differential scattering.