Rydberg-atom approximation

In the experiments with Rydberg atoms it is very difficult to observe radiatively assisted collisions with cross sections more than a factor of 10 smaller than the resonant collision cross sections, so the deviations from Eq. (15.29) are not apparent. However, in other contexts, such as laser assisted collisions, this limitation does not apply, and it is interesting to consider how the above description passes over into the weak field regime, in which Jm(KEmv//oj) is small. If we restrict the integration in Eq. (15.27) to the large r region of space, in which the approximations we have used are valid, we can rewrite Eq. (15.27) as... 

This provides a simple description that can be useful for different problems, for example, to study polarization effects in atoms. Because of its simplicity this model can be applied to electron-atom scattering problems in which the polarization of the electron cloud from the incoming electron can be taken into account by including angular dependence in the variational density. Another line of application is the study of Rydberg atoms beyond the frozen-core approximation. 

Figure 9.1. Energy level diagram for hydrogen molecule, H2, and separated atoms H R = 00) and He R = 0). R = the Rydberg constant = 13.6057 eV = 0.5 a.u. (atomic unit of energy). Value from ionization potential of He (Is 2p P). Value from ionization potential of H2. The experimental ionization potentials are quite precise but for systems containing more than one electron their interpretation in terms of orbital energies is an approximation.

Electronic and nuclear energy in H2. a. Values for non-interacling electrons. 6, Coulomb energy of nuclear repulsion, c, Approximate electronic energy curve for interacting electrons. Units ordinates, 1 = Rydberg constant, abscissas, 1 = radius of first Bohr orbit in hydrogen atom. 

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