Excitation of forbidden lines in gaseous nebulae I. Formulation and calculations for 2pq ions

Abstract

A formulation is given for electron collisions with ions in configurations s22s22pq and The main approximation is neglect of coupling to other configurations. Hartree-Fock functions are used for the ion states and the complete wave functions are expressed as sums of vector-coupled anti-symmetrized products of ion functions and orbitals for the colliding electron. Variational principles are used to obtain coupled integro-differential equations for the radial functions for the colliding electron, and to correct results obtained from approximate solutions of these equations. All algebraic reductions are carried out without the introduction of subsidiary approximations, and conservation and reciprocity theorems are therefore satisfied exactly. Expressions are tabulated for all algebraic coefficients. Numerical calculations are made in two approximations: in the exact resonance approximation, used only for />-waves, the wave functions are calculated with quadrupole interactions neglected; and in the distorted wave approximation the wave functions are calculated from static central potentials. Variational corrections are calculated and are found to be reasonably small. It is concluded that the final corrected results should agree closely with results which would be obtained from exact solutions of the coupled equations. Collision strengths are calculated for all inelastic collisions in configurations 1 to 5, for at least three different energies, and for values of the residual charge z = 1, 2, 3, 4, 5 and the limit of z-> oo. Results may be interpolated for all members of the iso-electronic sequences. Results for energies such that some channels are open and others closed are obtained by means of extrapolation techniques.