Density effect in K-shell ionization by ultrarelativistic electrons

Cross sections for K-shell ionization by 70- and 230-MeV-electron impact have been measured on the elements Na, Mg, Al, and Cl. Results for the lighter elements Na and Mg are smaller than the values predicted from the Kolbenstvedt theory and the plane-wave Born-approximation calculation. The rates of increase in the cross section with the increase in projectile energy from 70 to 230 MeV are also smaller than the predicted ones, and the cross section shows saturation at high bombarding energy. Furthermore, the increase rates of the cross section for lighter elements are compared with those for heavier elements by measuring relative x-ray yields with high accuracy on targets consisting of a pair of elements: (F,Al), (Na,Cl), (Mg,Mn), (Al,Mn), (Si,Mn), (Cl,Mn), and (Ca,Mn), and the increase rate for lighter elements is smaller than that for heavier elements except for the pairs (Cl,Mn) and (Ca,Mn). A similar result was obtained on the L-shell ionization of the pair (Zn,Sn). These results reveal the density effect in inner-shell ionization, which was predicted by Dangerfield, while the magnitude of the effect is not as large as that predicted from a simple theory. The discrepancy is discussed.