The QB method: Analysing resonances using R-matrix theory, applications to C+, He and Li

A procedure for analysing resonances in atomic and molecular collision theory is introduced, which exploits the analytic properties of R-matrix theory to obtain the energy derivative of the reactance (K) matrix, without assuming a pure Coulomb potential at large distances. The QB method defines matrices Q and B in terms of asymptotic solutions, the R-matrix and energy derivatives, such that dK/dE = B(-1)Q, from which eigenphase gradients of the K-matrix can be obtained. Resonance positions are defined at the points of maximum gradient; resonance widths are related to the inverse of the eigenphase gradients. Resonance properties such as identifications are discussed. The QB method is illustrated for some overlapping resonances in C+ between the 1s(2)2s2p P-3(o) and P-1(o) ionization thresholds. It is then tested for accuracy against recent experimental measurements of positions and widths for doubly excited states of He between the n = 2 and n = 3 ionization thresholds, and for positions, widths and profiles of resonances in Li above the first inner-shell threshold.