Electron Excitation Cross Section of the3S2→3P2Transition of Sodium

The cross section of the $3{}_{}{}^2{}_{}{}^{}S\to 3{}_{}{}^2{}_{}{}^{}P$ transition of sodium produced by electron impact has been calculated by performing a numerical integration of the set of three-channel differential equations. By means of this numerical procedure, it is no longer necessary to replace the nondiagonal matrix elements of the interaction potential by their asymptotic forms and to neglect the diagonal part of the interaction-potential matrix, as was done in the previous calculations. The cross sections calculated by this numerical scheme are smaller than those of the previous work, and the difference can be ascribed to the use of the true interaction potentials rather than their asymptotic forms. An outline of the general formulation of the numerical method for an $n$-channel case is given.