Enhanced nonlinear response of Ne$^{8+}$ to intense ultrafast x rays

TL;DR

This study explores why experimental two-photon ionization cross sections of Ne$^{8+}$ are much higher than theoretical predictions by analyzing the effects of pulse bandwidth and resonance conditions using the TDCIS method.

Contribution

The paper demonstrates how pulse bandwidth and resonance effects significantly enhance the effective two-photon ionization cross section of Ne$^{8+}$, bridging the gap between theory and experiment.

Findings

Chaotic pulses increase the effective cross section by over an order of magnitude.

Resonance at 1127 eV plays a key role in the enhancement.

Two-photon ionization remains less probable than one-photon ionization at current intensities.

Abstract

We investigate the possible reasons for the discrepancy between the theoretical two-photon ionization cross section, $\sim 10^{-56}$ $\text{cm}^4 \text{s}$, of Ne$^{8+}$ obtained within the perturbative nonrelativistic framework for monochromatic light [J. Phys. B {\bf 34}, 4857 (2001)] and the experimental value, $7 \times 10^{-54}$ $\text{cm}^4 \text{s}$, reported in [Phys. Rev. Lett. {\bf 106}, 083002 (2011)] at a photon energy of 1110 eV. To this end, we consider Ne$^{8+}$ 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 Ne$^{8+}$ 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 Ne$^{8+}$ at a photon energy of 1110 eV amounts to $5 \times 10^{-57}$ and $1.6 \times 10^{-55}$ $\text{cm}^4 \text{s}$ 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 1$s^2$--1$s4p$ resonance located at 1127 eV. Using the TDCIS approach, we also show that, for currently available radiation intensities, two-photon ionization of a 1$s$ electron in neutral neon remains less probable than one-photon ionization of a valence electron.