Nonsequential two-photon absorption from the $K$ shell in solid zirconium

We report the observation of nonsequential two-photon absorption from the $K$ shell of solid Zr (atomic number $Z=40)$ using intense x-ray pulses from the Spring-8 Angstrom Compact Free-Electron Laser (SACLA). We determine the generalized nonlinear two-photon absorption cross section at the two-photon threshold in the range of 3.9–57 $\times {10}^{-60}{\text{cm}}^4\text{s}$ bounded by the estimated uncertainty in the absolute intensity. The lower limit is consistent with the prediction of 3.1 $\times {10}^{-60}{\text{cm}}^4\text{s}$ from the nonresonant $Z^{-6}$ scaling for hydrogenic ions in the nonrelativistic, dipole limit.

Figure 1

(a) Schematic for nonsequential two-photon $K\text{-shell}$ absorption in metallic Zr. When the incident photon energy exceeds half the single-photon K-absorption threshold ($\sim 18$ keV), a $1s$ vacancy can be created through the simultaneous absorption of two (or more) photons. This vacancy is primarily filled by radiative decay from the $2p$ state in the form of $K_{\alpha }$ fluorescence. (b) A powerful XFEL beam near 9 keV is focused to a submicron spot on a $25-\mu \text{m}$ thin Zr foil. The fluorescent signal is collected at 90 deg in the polarization plane using a 140-K pixel single-photon-sensitive detector. A $50-\mu \text{m}$ Zr filter is inserted in front of the detector to reduce the background from scattered photons. (c) A representative detector histogram accumulated over 3000 shots, where peaks (0), (1), and (2) correspond to pixels registering zero photons, single photons near the fundamental ($\sim 9$ keV), and single photons near the K-fluorescence peak ($\sim 16$ keV), respectively, for an incident pulse energy of $\sim 10 \mu \mathrm{J}$. The background from the pileup from two 9-keV photons in a single pixel has been suppressed as described in the text. (d) Dependence of peak (2) as the sample is scanned through the focal plane.

Figure 2

X-ray intensity dependence of the K fluorescence when incident photon energy is above (9.1 keV) and below (8.9 keV) the TPA threshold. Above-threshold data is represented by circles. Below-threshold data is represented by asterisks. This data is obtained by integrating peak (2) of the histogram as shown in Fig. 1. Above-threshold data depends quadratically on the intensity (solid line). Below-threshold measurements show a weaker nonlinearity compared to above threshold. Measurements were averaged over 3000 shots, and the statistical error due to photon counting is smaller than the size of the symbol.

Figure 3

Photon energy threshold for two-photon absorption in Zr $K$ shell. In (a) a section of histograms are shown for x-ray photon energy just below and just above the TPA threshold of 9 keV. Histograms were averaged over 3000 shots. The higher-energy peak (counts $>15.5$ keV) is seen at and above the threshold. A $100-\mu \mathrm{m}$ Zr filter was used in this measurement. (b) The integrated count within the high-energy peak as a function of photon energy. The photon energy is changed in 50-eV steps. The total count at 9 keV is about 3 times higher than the noise level, shown by the dashed line below the threshold.

Figure 4

Comparison of $K\text{-shell}$ TPA cross section from solid Zr to the Zernik $Z^{-6}$ scaling along with experimental results in other elements with different $Z$. The solid line represents the Zernik scaling for the nonresonant, nonrelativistic, and dipole limit at threshold for the H-like ions, referencing to the calculated cross section in H atom 1.27 $\times {10}^{-50}{\text{cm}}^4\text{s}$ [21, 22]. The data for He is for 41.8 eV, above the single-photon threshold, taken from [23]. The value for ${\text{Ne}}^{8+}$ is taken from Ref. [12]. The measurement for Ge is taken from Ref. [9].