Empirical Coulomb Correction for K-Shell Ionization by Light Ions

Recent systematic comparisons of published K-shell ionization cross sections induced by protons or alpha particles show that the various data agree fairly well with each other and with the CPSSR theory by Brandt and Lapicki (1979), except at low energies. Assuming that the latter discrepancy is due to the Coulomb correction, we plot the experimental cross sections, divided by the theoretical PSSR cross sections, versus × = πdqOξ, where d is half the distance of closest approach (for a headon collision), hqo is the minimum momentum transfer for ionization, and ξ is the binding/ polarization correction. If we approximate these "empirical Coulomb corrections" by exp(-λx), we find values λ between 1.4 and 1.7 (higher target atomic numbers Z2 corresponding to larger values); Brandt's correction CK(x) = exp(-x)/(1 + x/9) would, however, require λ = 1.11. The use of exact integration limits in the calculation of the theoretical cross section reduces λ by 0.1 but does not remove the discrepancy. Kocbach's calculation for Au targets describes the heavy target data well.