Two-electron jumps and double Rydberg states

Since doubly-excited states involve the excitation of two electrons, it is natural to consider both excited electrons on an equal footing. To take a model problem, consider the excitation scheme 

There exists, in addition, another possibility. It will not have escaped the reader that the two electrons, in the description just given, are not treated completely symmetrically. Were one to do so, it would be necessary to increase both nj and 2, so as to form a sequence of levels with n = 2 spaced differently from the normal Rydberg series, converging on the double-ionisation potential. At the limit of this series, both electrons would escape in a completely symmetric way, and so this possibility is often referred to as the double-escape problem . 

Double Rydberg states (double because both electrons are running electrons in this case) and the symmetrical double-ionisation problem were considered first by Wannier [320], and so the completely symmetric excited states with i = I2 and nj = ri2 as the double-ionisation threshold is approached are called Wannier states. These states have very interesting 

In the present chapter, we therefore confine our attention to doubly-excited series with one running electron, while the other excited electron defines the parent ion limit. 

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