The calculation of resonances in electron-ion scattering using the distorted wave approximation

In the distorted wave approximation, radial functions Fi for the colliding electron are calculated using a central potential Vi(r). The Kohn variational method is then used to calculate the R matrix; this is the matrix, used in quantum defect theory, which varies slowly as a function of the energy. For closed channels the function Fi are calculated at the eigen-energies for the central-potential problem, and suitably normalized. The resonance structures are calculated using methods of quantum defect theory. Illustrative results are obtained for the 2s2 1S-2s2p3P transition in C III and in O V, and compared with results obtained from exact solutions of coupled integro-differential equations. It is concluded that, for the calculation of rate coefficients for the excitation of more highly ionized positive ions: (i) it is necessary to take resonances into account and; (ii) good results can be obtained using the distorted wave method.