Hydrogenic radial wavefunctions for successive 2p and 3p Rydberg orbitals

The interaction between two Rydberg states of the same n, which belong to two different series, j i,n and 02,n will be derived using a convenient Hund s case basis set and by expressing the interaction as part of a residual electronic 

The electronic part, (0i)7l H 02,n ) of the perturbation interaction between two discrete states cannot be compared directly with the electronic part (0i,n H 02, ) °f flie autoionization matrix element. Only the energy-normalized perturbation interaction (see Section 7.5), pi/2 ( i n H 2,n ), which has the same dimensionality as ( i,n H 2,e) can be compared to this last quantity and should have the same magnitude. 

For Rydberg states, the density of states, pn, is given by the inverse separation between two successive states  

For a Rydberg state of a given n, the quantity I from Eq. (8.4.4), assumed previously to be constant for all n members of a second Rydberg series, will now be assumed constant in the limit n — oo, which corresponds to a continuum electron with zero kinetic energy. Thus, by combining Eq. (8.4.4) and Eq. (8.4.5), 

With the assumption that I is independent of n and therefore also independent of the energy of the ejected electron, Eq. (8.4.7) is valid for any energy e. If I varies smoothly with the energy of the ejected electron, it must be replaced by 1(e) in Eq. (8.4.7). 

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Figure 8.10 Hydrogenic radial wavefunctions for successive 2p and 3p Rydberg orbitals r is the distance of the Rydberg electron from the molecular center of mass.

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