R-matrix electron-impact excitation cross sections in intermediate coupling: an MQDT transformation approach

Abstract

A widely used alternative to a full Breit-Pauli R-matrix calculation of electron-impact excitation is the transformation of S- or K-matrices, calculated in pure LS coupling, to intermediate coupling. Here we present a transformation method, based on multi-channel quantum defect theory (MQDT), that eliminates the problems associated with standard transformation methods and leads to accurate level-to-level electron-impact excitation cross sections. Instead of transforming the physical S- or K-matrices, we employ MQDT to generate unphysical K-matrices in pure LS coupling; we then treat all channels as open and transform these matrices to intermediate coupling. Finally, we generate the physical K-matrices from the intermediate-coupled unphysical K-matrices. To illustrate the accuracy of this method, we compare cross sections for several transitions in determined using: (i) the standard transformation method in which the LS-coupled physical S-matrices are transformed to intermediate coupling; (ii) an MQDT transformation method, used by others, in which the unphysical LS-coupled K-matrices are transformed to pure jK coupling; (iii) our intermediate coupling frame transformation (ICFT) method and (iv) a full Breit-Pauli R-matrix calculation. It is shown that our ICFT method eliminates the problems associated with the other two transformation methods and leads to cross sections that agree very well with those determined from a full Breit-Pauli R-matrix calculation. Furthermore, the ICFT method can be applied to complex atomic systems which are intractable to a full Breit-Pauli calculation.