High-energy cross sections for electron excitations of excited hydrogen atoms in which the principal quantum number is changed by 2

At large energies E the cross section Q for the electron excitation from the n, l state of hydrogen to the n', l' state may be written in the form QE = A log E + B . The first Born approximation is used to calculate these A 's and B 's for all transitions with n = 1, 2, 3, 4, 5 and 6 and with n'= n +2. The A 's and B 's associated with the main optically allowed transitions (i.e. l' = l +1) are largest. In calculating the A 's for the average cross section from one level to another we found that we need only consider the main optically allowed transitions, but in calculating B 's for the average cross sections we could not ignore the other transitions, besides the main optically allowed transitions, since the sum total effect of these minor transitions is almost as large as that of the main optically allowed transitions. These minor transitions increased the B 's for the average cross sections of most of the transitions considered by more than 50%.