Two-photon excitation to autoionizing states of He detected via radiative cascades to the metastable states

We present a detailed theoretical study of two-photon above-threshold excitation to the lowest dipole forbidden S-1(e) and D-1(e) autoionizing states of helium with free-electron-laser pulses. We consider the case where the formation of these transient states is detected by monitoring the yield of atoms in the metastable 1s2s states, which are reached in the radiative cascade decays of the autoionizing states. We describe the two-photon near-resonant driving with an effective Hamiltonian operator within the density matrix formalism, and we report the relevant parameters of the model, such as the field-induced shifts, the effective Rabi frequencies, and the cascade branching ratios of both the autoionizing states and the 1snl states, to which the autoionizing states decay. We compare the calculated metastable atom yield to the vacuum ultraviolet florescence yield and to the electron yield. We discuss the effects of the intensity of the source, admixture of higher harmonics in the incident beam, polarization of the incident light, and the pulse chirp on the metastable atom yield.