One-photon resonant two-photon excitation of Rydberg series close to threshold

Abstract
We study one-photon resonant two-photon excitation of autoionizing Rydberg series close to threshold. Analytical expressions for the time evolution of bound-state amplitudes are derived by adapting ideas from quantum-defect theory. We discuss in detail the two limiting cases of excitation of Rydberg wave packets and ac-Stark splitting close to the threshold.