K-edge x-ray-absorption spectroscopy of laser-generated Kr⁺ and Kr²⁺

Tunable, polarized, microfocused x-ray pulses were used to record x-ray absorption spectra across the K edges of Kr⁺ and Kr²⁺ produced by laser ionization of Kr. Prominent 1s→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 Kr⁺ 1s→4p cross section varies with respect to the angle between the laser and x-ray polarization vectors. This effect is used to determine the 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.