Enhanced nonlinear response of Ne8+ to intense ultrafast x rays

We investigate the possible reasons for the discrepancy between the theoretical two-photon ionization cross section, similar to 10(-56) cm(4) s, of Ne8+ obtained within the perturbative nonrelativistic framework for monochromatic light [S. Novikov and A. Hopersky, J. Phys. B 34, 4857 (2001)] and the experimental value, 7 x 10(-54) cm(4) s, reported in [G. Doumy et al., Phys. Rev. Lett. 106, 083002 (2011)] at a photon energy of 1110 eV. To this end, we consider Ne8+ exposed to deterministic and chaotic ensembles of intense x-ray pulses. The time-dependent configuration interaction singles (TDCIS) method is used to quantitatively describe nonlinear ionization of Ne8+ induced by coherent intense ultrashort x-ray laser pulses. The impact of the bandwidth of a chaotic ensemble of x-ray pulses on the effective two-photon ionization cross section is studied within the lowest nonvanishing order of perturbation theory. We find that, at a bandwidth of 11 eV, the effective two-photon ionization cross section of Ne8+ at a photon energy of 1110 eV amounts to 5 x 10(-57) and 1.6 x 10(-55) cm(4) s for a deterministic ensemble and a chaotic ensemble, respectively. We show that the enhancement obtained for a chaotic ensemble of pulses originates from the presence of the one-photon 1s(2)-1s4p resonance located at 1127 eV. Using the TDCIS approach, we also show that, for currently available radiation intensities, two-photon ionization of a 1s electron in neutral neon remains less probable than one-photon ionization of a valence electron.