Rydberg electron perturbation

The pressure shift cross section has two terms, one from the elastic Rydberg electron-perturber interaction and one from the ion-perturber interaction. Explicitly,... 

Here, Q is the projector on the bound subspace and P projects onto the open, continuum channels. The intramolecular coupling is written as V+ U so that, as before, U is any additional coupling brough about by external perturbations. The equation H = Hq + V+U, where Ho is the zero-order Hamiltonian of the Rydberg electron and so includes only the central part of the potential due to the core plus the motion (vibration, rotation) of the core, uncoupled to the electron. The perturbations V + U can act within the bound subspace, as the operator Q(V+l/)Q is not necessarily diagonal and is the cause of any intramolecular dynamics even in the absence of coupling to the continuum. The intramolecular terms can also couple the bound and dissociative states. 

In Fig. 11.2(b) we show the trajectory of the Rydberg electron just before and after hitting the perturber. Prior to the collision the Rydberg atom is in state a,... 

The physical significance of this expression is that the rate constant for elastic perturber-Rydberg atom collisions is the same as the rate constant for elastic perturber-electron collisions averaged over the Rydberg electron s velocity distribution, in spite of the fact that V v. 

All the collision processes we have discussed in any detail are thermal collisions. We would now like to return to a point made early in the discussion of the theory. If the collision velocity is high compared to the Rydberg electron s velocity, the Rydberg atom-perturber cross section should be equal to the sum of electron-perturber and the Rydberg ion-perturber cross section at the same velocity. A... 

This result was first derived in an elegant manner by Fermi.2 It can also be derived in a pedestrian way using the form of the interaction given by Eq. (11.17). The derivation is implicitly statistical, in that the motion of the perturber is ignored, which at first seems to imply that it should not match the results of an impact theory. However, we are only ignoring the thermal motion of the perturber relative to the electron motion. It is still true that the Rydberg electron interacts with one perturber at a time, thus the requirement of the impact regime is met. 

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