Nonlinear Atomic Response to Intense Ultrashort X Rays

The nonlinear absorption mechanisms of neon atoms to intense, femtosecond kilovolt x rays are investigated. The production of ${\mathrm{Ne}}^{9+}$ is observed at x-ray frequencies below the ${\mathrm{Ne}}^{8+}$, $1s^2$ absorption edge and demonstrates a clear quadratic dependence on fluence. Theoretical analysis shows that the production is a combination of the two-photon ionization of ${\mathrm{Ne}}^{8+}$ ground state and a high-order sequential process involving single-photon production and ionization of transient excited states on a time scale faster than the Auger decay. We find that the nonlinear direct two-photon ionization cross section is orders of magnitude higher than expected from previous calculations.

Figure 1

Illustration of ${\mathrm{Ne}}^{9+}$ production. (a) Direct process through one-photon ($1\gamma$) or two-photon ($2\gamma$) ionization of ${\mathrm{Ne}}^{8+}$, depending on the photon energy. (b) Indirect process first ionizes ${\mathrm{Ne}}^{6+}$ into ${\mathrm{Ne}}^{7+*}$ excited state. Before Auger decay occurs, which would otherwise direct through (a), a valence electron is photoionized to produce ${\mathrm{Ne}}^{8+*}$ that can also be subsequently ionized into ${\mathrm{Ne}}^{9+}$.

Figure 2

Charge state distributions produced by (a) 1225 eV (1.45 mJ) and (b) 1110 eV (1.27 mJ) beams. Black: experiment (the detection efficiency for the different charge states is adjusted using the procedure of Ref. 8). White: model used in Ref. 7. Gray: improved model accounting for shakeoff processes. The striped bar in (b) incorporates the adjusted ${\sigma }^{(2)}$ needed to reproduce the ${\mathrm{Ne}}^{9+}$ production below threshold.

Figure 3

Normalized ${\mathrm{Ne}}^{9+}/{\mathrm{Ne}}^{8+}$ ratio as a function of pulse energy for 1110 eV (filled circles) and 1225 eV (open squares). Fits yield a quadratic response at 1110 eV (solid line) and linear behavior at 1225 eV (dashed).

Figure 4

The measured absolute ${\mathrm{Ne}}^{9+}/{\mathrm{Ne}}^{8+}$ ratio (symbols) as a function of x-ray pulse energy is compared with the modified model (solid line), incorporating shakeoff and direct two-photon ionization of ${\mathrm{Ne}}^{8+}$ using ${\sigma }^{(2)}$ from Ref. 14, (a) above and (b) below the ${\mathrm{Ne}}^{8+}$ one-photon threshold. In (b), the dotted line isolates the direct two-photon contribution, derived by subtracting results with and without ${\sigma }^{(2)}$ from Ref. 14. The dashed line is a result of the enhanced ${\sigma }^{(2)}$ value (see text).