The QB method: analysing resonances using R-matrix theory. Applications to , 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 matrix, without assuming a pure Coulomb potential at large distances. The QB method defines matrices and in terms of asymptotic solutions, the R-matrix and energy derivatives, such that , from which eigenphase gradients of the -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 between the and 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.