Hi John, Josh,
Certainly if a spline can do a good job of fitting the mu_0, then the current approach is more or less ok. However in systems with strong white lines mu_0 can be strongly peaked and hence very difficult to fit with a few spline points. The broadening function lamda(E) can be constrained to be small. Also, for cases with large whitelines, the location of e0 is difficult to fit - the true e0 can lie well below the edge jump.
Oh, maybe I misunderstood. Is lambda(E) in
mu_0 = mu^thy_0(E,E_0,Gamma)[1 + lambda(E)]
just a broadening term or a highly adjustable spline?? I guess the whole question is how much freedom this function has. It definitely sounds interesting to use a theoretical mu_0, especially for challenging white lines, but it's not clear how to best make this accessible to users. I'll probably have to think about this some more, but it would be nice to know the mechanics of how you're doing it, and how well you need to know the structure before you start.
In our view, mu0 does not depend very much on structure, since it's mostly determined by the local embedded atom potential. For this reason it's calculation would also be quite fast (only phase shifts and the cross-section are needed) compared to a calculation of chi(k) which requires multiple scattering paths.
Well, usually a standard for autobk only needs a decent guess of the first shell. Getting a standard does require some prior knowledge of the system and calculation time, but I don't know that it would be a lot more knowledge and time than would be needed for a mu^thy_0(E). Anyway, it would still be interesting to compare these two (autobk using calculated chi(k) v. starting with a mu^thy_0 and massaging it to match data). On the other hand, it sounds as if the mu^thy_0(E) for a few dozen (or few hundreds) challenging systems could be tabulated. That would make it very fast and very simple to use! --Matt