An expansion of the square of the momentum transfer times the differential cross section, in powers of the momentum transfer, about the nonphysical point of zero momentum transfer, is carried out through terms of the order of the reciprocal of the square of the incident energy. The results confirm the view that the differential cross section can be regarded as a function of the square of the momentum transfer down to relatively low energies. Simple formulas are presented for calculating corrections to electron impact estimates of the intensity at zero scattering angle in order to obtain accurate optical oscillator strengths. Correction formulas are also presented for obtaining quadrupole transition probabilities from optically forbidden transitions. The case of spin forbidden but exchange allowed transitions is also considered. It is shown that certain second Born exchange corrections exist with the same dependence on the incident energy as that found for the leading term in the first Born approximation for exchange.
展开▼
