I've spent quite a while looking into classical models for electric susceptibility, including some semi-classical extensions to the idea, based around concepts such as effective electron mass. However, I've recently moved onto looking into the susceptibility of atomic vapours, potentially near the transition levels, where it seems necessary to take a much more quantum-based line of approach, as well as the effects of broadening.
If you look up the derivation of relatively classical electric susceptibility, it's quite easy to find derivations of the theory - which makes it quite easy to see where simplifications (such as the Drude model) are made. However, when it gets onto trying to take into account quantum effects, I can only find the basic information on the prediction of the position of lines, as derived from the Schrodinger equation, and nothing to do with broadening, or the actual shape of the spectrum as a function of frequency. If I try from the other end, to look up broadening about various spectral lines, and try to work backwards from various papers, it can be quite hard to follow the trail of research, and even if I can, inevitably the paper for which I'm looking is behind a pay-wall. I'm aware that there almost certainly isn't a closed-form solution to this problem, otherwise I would have seen reference made to it already, but if I can see a derivation, that would put me in a position to at least understand which terms are left out, and/or simulate, numerically, solutions.
So, my question: Are there any sources which you would recommend, from which I'd be able to find the derivation - or at least a starting point. I am willing to pay to get past a pay-wall, but only want to do so if I really have to.