Extension to the simple quantum theory

However, in a real atom with one dispersion electron (for example, in the Rydberg series of an alkali atom, as considered in chapter 2), the 

Eventually, Kramers [130] gave the correct formulation, by considering j not as the ground, but as a general excited state. In this case, two processes must be included, viz. Ek E3, which is absorption, and Et Ej, which is emission. We thus arrive at  

For transitions between bound states, the oscillator strength is a fundamental new quantity which quantum mechanics introduces in dispersion theory. We now have not only one characteristic frequency vq but a whole series of transition frequencies Vjk, and the presence, not only of absorption terms, but also of negative absorption terms due to stimulated emission. The theory of Kramers [130] was checked experimentally by Ladenberg and Kopfermann [131] for a line in the spectrum of Ne. 

In terms of the quantum-mechanical dipole matrix element Vjk 2 which determines the strength of an allowed spectral line from the wave-functions of states j and k , the oscillator strength is defined as 

---