Minima in generalized oscillator strengths of atomic transitions and the approach to the high-energy limit

Minima in the generalized oscillator strength (GOS) and the convergence of the GOS to the first Born approximation (FBA) limit for the Ba 6s S-1 -> 6p P-1 optically allowed transition are investigated. The random-phase approximation with exchange, which takes into account correlation effects among the atomic electrons themselves, and the convergent close-coupling (CCC) approximation are used for the calculations. We find the following. (1) The GOS as a function of the momentum transfer squared K-2 is characterized by a complex structure of multiple minima, significantly different in the two approximations and approaches the high-energy FBA limit only at small K-2 values (less than about 0.5 a.u.). (2) The number of minima calculated in the CCC approximation increases with increase in energy, but does not correspond to the number obtained in the FBA, even at high energy similar to 1 keV. The CCC and FBA minima are in general not directly related. The FBA minima, except for the first, do not correspond to physical observables at these energies. (3) At high energy the interaction between the incident electron and the target remains significant, resulting in slowing down the convergence of the CCC GOS to the corresponding nonrelativistic FBA results.