$K$-edge x-ray-absorption spectroscopy of laser-generated ${\text{Kr}}^{+}$ and ${\text{Kr}}^{2+}$

Tunable, polarized, microfocused x-ray pulses were used to record x-ray absorption spectra across the $K$ edges of ${\text{Kr}}^{+}$ and ${\text{Kr}}^{2+}$ produced by laser ionization of Kr. Prominent $1s\to 4p$ and $5p$ excitations are observed below the $1s$ ionization thresholds in accord with calculated transition energies and probabilities. Due to alignment of $4p$ hole states in the laser-ionization process, the ${\text{Kr}}^{+}$ $1s\to 4p$ cross section varies with respect to the angle between the laser and x-ray polarization vectors. This effect is used to determine the ${\text{Kr}}^{+}$ $4p_{3∕2}$ and $4p_{1∕2}$ quantum state populations, and these are compared with results of an adiabatic strong-field ionization theory that includes spin-orbit coupling.

Figure 1

(Color online) The geometry used to record x-ray absorption spectra of laser-generated ${\text{Kr}}^{+}$ and ${\text{Kr}}^{2+}$. The $z$ axis is taken along the collinear propagation directions of the laser and x-ray beams. The laser produces ions within a focal volume centered at the origin. X-ray pulses arrive $\le 1\text{ns}$ after the laser pulses. X rays absorbed by ions or neutrals produce $K$ vacancies that relax by emitting x-ray fluorescence. The emitted x rays are detected over small solid angles around the $x$ axis. The x-ray beam is linearly polarized along the $x$ axis. The laser beam is circularly polarized or linearly polarized with polarization parallel or perpendicular to the x-ray polarization.

Figure 2

$K$ x-ray fluorescence spectrum of Kr recorded with a silicon-drift detector following absorption of 14.360 keV x rays. Relative absorption spectra across the $K$ edges of Kr, ${\text{Kr}}^{+}$, and ${\text{Kr}}^{2+}$ were determined from the $2p\to 1s$ count rates.

Figure 3

Cross correlation scan obtained by measuring x-ray fluorescence counts excited at the ${\text{Kr}}^{+}$ $1s\to 4p$ resonance vs. time delay between laser and x-ray pulses. The fitted curve is a Gauss error function with $98\pm 5\text{ps}$ FWHM.

Figure 4

$K$-edge photoabsorption spectra of Kr, ${\text{Kr}}^{+}$, and ${\text{Kr}}^{2+}$ determined from x-ray fluorescence counting rates. Top: laser-off spectrum of Kr (circles with connecting line) along with $1s\to np$ $\left(n\ge 5\right)$ and continuum components suggested by the fitted spectrum in Ref. [27]. Bottom: laser-on spectrum (circles) with fits to ${\text{Kr}}^{+}$ (dashed curve) and ${\text{Kr}}^{2+}$ (dotted curve) components. The solid curve is the sum of the two fitted components. The ions were generated by circularly polarized laser light, and the residual Kr component has been subtracted.

Figure 5

Ratios of x-ray fluorescence counts measured with laser on to laser off vs absorbed x-ray energy. Data are plotted for laser polarization parallel (circles connected with solid curve) and perpendicular (squares connected with dashed curve) to the x-ray polarization. Peaks are observed at the ${\text{Kr}}^{+}$ $1s\to 4p$ and $5p$ resonances.

Figure 6

$K$-edge photoabsorption spectra of ions produced with different laser polarizations. The circles are the measured x-ray fluorescence counting rates with the neutral Kr contributions removed. The dotted curves are fits to the ${\text{Kr}}^{+}$ components, the dashed curves are fits to the ${\text{Kr}}^{2+}$ components, and the solid curves are the total fits. (a) Ions generated by linearly polarized laser light with polarization parallel to that of the x-ray beam. (b) Ions generated by linearly polarized laser light with polarization perpendicular to that of the x-ray beam. (c) Ions generated by circularly polarized laser light.

Figure 7

(Color online) The $1s\to 4p$ transitions determined from x-ray fluorescence counting rates (circles) for ions generated with linearly polarized laser light with polarization parallel (top) and perpendicular (bottom) to the x-ray polarization. The data are the same as shown in panels (a) and (b) of Fig. 6. The major fitted components are ${\text{Kr}}^{+}$ $1s\to 4p_{1∕2}$ (red curves), ${\text{Kr}}^{+}$ $1s\to 4p_{3∕2}$ (blue curves), and ${\text{Kr}}^{2+}$ (green curves). The tails of the higher Rydberg excitations (dashed curves) and continuum (dotted curves) of ${\text{Kr}}^{+}$ are also plotted. The solid black curves are the total fits.