Photoionization of helium atoms irradiated with intense vacuum ultraviolet free-electron laser light. Part II. Theoretical modeling of multi-photon and single-photon processes

We consider the problem of a helium atom under the radiation field of the DESY vacuum ultraviolet (VUV) free electron laser (FEL) (Phase I, $\hslash \cong 13\mathrm{eV}$). We find by solving numerically the time-dependent Schrödinger equation, that there is a large probability for resonant two-photon excitation from the ground state into a low kinetic energy state just above the first He ionization threshold. From this it is possible to go into another quasi-free state higher up, by resonant absorption of an additional photon. There is no double ionization of He. These results are in general agreement with the He photoelectron and time-of-flight (TOF) spectra recorded on March 2002, in the last week of the DESY VUV FEL Phase I operation. A detailed report on the experiments is given in a companion paper.

Figure 1

Energy levels of helium atom.

Figure 2

(Color online) Peak power density dependence of the resonant transitions.

Figure 3

(Color online) Dependence on FEL pulse duration, of the probability for resonant two-photon absorption from the ground state $\mid 1s1s⟩$ of HeI into a low kinetic energy state ∣$1s$$(Z=2)$, free ${\mathbf{k}}_{e1}$⟩ of HeII. Also, dependence on FEL pulse duration, of the probability for resonant three-photon absorption from the ground state $\mid 1s1s⟩$ of HeI into a higher kinetic energy state ∣$1s$$(Z=2)$, free ${\mathbf{k}}_{e2}$⟩, using ∣$1s$$(Z=2)$, free ${\mathbf{k}}_{e1}$ as intermediate state. Here the peak power density on the sample is 5.4>${10}^{12}\mathrm{W}∕{\mathrm{cm}}^2$. Finally, we show as a dot curve the probability for resonant one-photon absorption of third harmonic contamination in the FEL output, whose intensity is estimated as being less than 5.4>${10}^9\mathrm{W}∕{\mathrm{cm}}^2$ (0.1% of the intensity in the fundamental). This would also populate the state ∣$1s$ $(Z=2)$, free ${\mathbf{k}}_{e2}$⟩ via a direct one-photon transition from the ground state $\mid 1s1s⟩$.