High-energy cross sections for electron excitations of excited hydrogen atoms in which the principal quantum number is changed by 1

At large impact 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 +1. The A 's and B 's associated with the main optically allowed transitions (i.e. l' = l +1) are largest. However, for small values of l we find that in calculating the B 's we must take account of all other transitions, besides the main optically allowed transitions, for the sum total effect of these minor transitions is almost as large as that of the main optically allowed transitions. These minor transitions can be neglected in calculating the A 's for the average cross section from one energy level to another but they increase the B 's for the average cross sections by about 25%.