EUV two-photon-ionization cross sections of helium from the solution of the time-dependent Schrodinger equation, and comparison with measurements using free-electron lasers

Two recent experimental papers reported the first measurements of absolute two-photon-ionization cross sections sigma(2) of helium, for EUV wavelengths, using free-electron laser (FEL) pulses [Sato et al., J. Phys. B 44, 161001 (2011); Fushitani et al., Phys. Rev. A 88, 063422 (2013)]. The wavelengths correspond to transitions that are off resonance as well as on resonance with the 1s2p and 1s3p(1Po) Rydberg states. Inspection of their results reveals considerable discrepancies, while their comparison with theoretical results obtained earlier from time-independent calculations, one perturbative and two nonperturbative ones, cannot lead to secure conclusions as to the true values of sigma(2). We examined this prototypical problem by implementing a time-dependent approach, which utilizes the nonperturbative solution of the time-dependent Schr odinger equation. This solution was obtained in terms of the state-specific expansion approach, in an upgraded version where the coupling matrix elements are computed using the full electric operator of the multipolar Hamiltonian. The sigma(2) were obtained for pulses of 300 fs, as in the 2011 FEL experiment. Their computation was achieved by fitting the time-dependent ionization survival probability to e(-Gamma t), where Gamma is the rate of ionization. The wavelengths and intensities are those of the FEL experiments, as well as others, such as the wavelengths 52.22 and 51.56 nm, for which the 1s4p P-1(o) and 1s5p P-1(o) levels are on resonance with the initial S-1 state. Apart from the predictions for these wavelengths, the paper contains characteristic comparisons among all the results on these EUV sigma(2), experimental and theoretical. In general, the trends predicted by nonperturbative methods are confirmed by the FEL measurements. However, discrepancies exist among the absolute numbers. Furthermore, comparison among the results of the three nonperturbative approaches (present time-dependent and two earlier time-independent ones published in 1999 and 2005) indicates an overall consistency, although quantitative differences for individual cases are apparent.