Electron excitation of forbidden lines occurring in gaseous nebulae

In a previous paper the Hartree-Fock method has been used to calculate electron excitation cross-sections for the ground configuration terms of OI. In the present paper the modifications required for similar calculations on positive ions are discussed, and cross-sections are calculated for electron excitation of the ground configuration terms of N II, O II, O III, Ne III and S II. These cross-sections are of fundamental importance in discussing the physical state and chemical composition of gaseous nebulae. A first approximation to the solution of the coupled integro-differential equations is obtained by neglecting energy differences (the E.R. approximation). A comparison is made between the cross-sections calculated using exact solutions of the E.R. equations and using weak coupling approximations to these solutions. It is found that, although allowance for distortion gives a considerable improvement, the weak coupling approximations cannot in general be relied upon to give accurate results. Estimates of the magnitudes of the terms omitted in the E.R. approximation are made by perturbation methods, and in all cases these terms are found to be reasonably small. Final values for the cross-sections are probably correct to within $\pm $ 40% in absolute value and rather more accurate than this in the relative values. Cross-sections estimated for a number of other ions of astrophysical interest are considered to be correct to within a factor of 2. Hartree-Fock wave functions for N II are given in an appendix.