Theoretical treatment of collisions of Rydberg atoms with neutral atoms and molecules. Semiquantal, impulse, and multistate-orbital theories

The semiquantal treatment of ionization in $A-B\left(n\right)\mathrm{}$ collisions, based on encounters between the Rydberg electron $e$ and incident atom or molecule $A$, is derived from the full quantal impulse approximation. The useful transformation between the dynamical variables natural to these treatments is provided. Various levels of approximation are then deduced and necessary criteria for validity of application of the basic impulse expression to various types of $A-B\left(n\right)\mathrm{}$ processes—ionization, excitation, and quasielastic—in different energy regions are emphasized, including those associated with the additional assumption of "on-the-energy-shell" ($e-A$) encounters. It is pointed out for cases involving quasielastic collisions at thermal energies that models based on ($e-A$) encounters alone may not provide either a full or proper description of the underlying mechanism. A new treatment of (in) elastic transitions via ($A-B^{+}$) encounters at thermal energies and beyond is introduced and formulated. Preliminary assessment indicates that the proposed new mechanism is significant and could well be dominant in quasielastic $A-B\left(n\right)\mathrm{}$ processes.