Limiting slope of the generalized oscillator strength vs momentum transfer curve

Although at the limit of zero momentum transfer, the generalized oscillator strength is equal to the Born value [E. N. Lassettre, A. Skerbele, and M. A. Dillon, J. Chem. Phys. 50, 1829 (1969)], it is found that the limiting slopes (df/dK)K=0 and (df/dK2)K=0 do not obey the Born approximation. For dipole allowed transitions (df/dK)K=0 is nonzero but finite and (df/dK2)K=0 becomes infinite at all finite incident energies. Also, the non-Born correction to f0 deduced from zero angle data is just as important as the next higher multiple term in the Born approximation. Thus in the analytic fit of experimental data it is imperative to include odd power terms in K even when the Born approximation is apparently obeyed if the purpose is to deduce the limiting slope as well as the intercept. However, if only the intercept is needed and the measured f’s shows no apparent energy dependence, it is still possible to extrapolate to f0 using a series even in K. The relevance of the present result to a number of recent electron impact experiments is discussed.