Spectroscopy and scattering: An extended quantum defect theory for non-Rydberg resonant states

Non-Rydberg resonant states are a special type of resonant states with open-shell electronic configurations that cannot be partitioned into a quasi-two-body system of a tightly coupled ion target and a loosely coupled projectile electron as the case of Rydberg states, which is an important type of resonant processes in atomic and molecular systems. Previous treatments of non-Rydberg resonances in the context of multichannel quantum defect theory (MQDT) were to introduce these states as resonances in the smoothly varied MQDT parameters, and the main merit of the MQDT method for Rydberg states would be lost. To reconcile the efficiency and numerical accuracy for the calculation of non-Rydberg states, a nonperturbative calculation approach is proposed in this paper. In this approach, the smooth-varying short-range scattering matrices are obtained by applying the eigenchannel $R$-matrix method to the subsystem excluding the non-Rydberg states. Subsequently, the non-Rydberg states are restored using the configuration-interaction formalism. The scattering matrices with resonant structures can then be obtained directly using simple linear algebra operations. Since the ingredients of the procedure are all smooth functions of energy, only a sparse energy grid is required for the time-consuming ab initio calculations. This makes our method highly computationally efficient and can be considered as an extension of the traditional MQDT. To demonstrate the efficacy of our method, the resonant $e+{\mathrm{O}}^{+}$ collisional complex in the ${1}^{\ensuremath{-}}$ partial wave is calculated. In addition, we demonstrate that the numerical accuracy of the scattering matrices is significantly affected by the non-Rydberg states.