For incident x-ray energies below the core level ionization threshold, one-photon absorption (OPA) leads to off-resonant x-ray excitations that are mediated by a virtual intermediate electronic state. In the linear regime of x-ray interaction, this intermediate state may decay radiatively and the maximum energy of the emitted photon is given by the initial and final atomic state as well as the energy of the incident photon. In the nonlinear excitation regime, however, this intermediate state may be depleted by a second x-ray absorption process as described in the sequential two-photon absorption (TPA) mechanism. Since the same intermediate state is involved in the OPA and TPA processes, the cross-section values for OPA and TPA are interconnected. We report on the determination of cross-section values for off-resonant excitation conditions, and show how the data can be used for estimating the TPA cross section in the sequential absorption mechanism. The determined off-resonant cross sections for cobalt exhibit a Lorentz-like energy-dependent behavior allowing for an energy-dependent description of the OPA and TPA cross sections with semiempirical models. The dependence of TPA cross sections on atomic number is discussed and different scaling laws are investigated. The effect of the lifetimes of a virtual intermediate state is also studied in relation to the incidence x-ray energy.

X-ray absorption spectroscopy (XAS) and X-ray emission spectroscopy (XES) are analytical techniques enabling precise analysis of the electronic structure and local atomic environment in chemical compounds and materials. Their application spans materials science, chemistry, biology, and environmental sciences, supporting studies on catalytic mechanisms, redox processes, and metal speciation. A key advantage of both techniques is element selectivity, allowing the analysis of specific elements without matrix interference. Their high sensitivity to chemical state and coordination enables determination of oxidation states, electronic configuration, and local geometry. These methods are applicable to solids, liquids, and gases without special sample preparation. Modern XAS and XES studies are typically performed using synchrotron radiation, which provides an intense, monochromatic X-ray source and allows advanced in situ and operando experiments. Sub-techniques such as XANES (X-ray absorption near-edge structure), EXAFS (Extended X-ray Absorption Fine Structure), and RIXS (resonant inelastic X-ray scattering) offer enhanced insights into oxidation states, local structure, and electronic excitations. Despite their broad scientific use, applications in pharmaceutical research remain limited. Nevertheless, recent studies highlight their potential in analyzing crystalline active pharmaceutical ingredients (APIs), drug–biomolecule interactions, and differences in drug activity. This review introduces the fundamental aspects of XAS and XES, with an emphasis on practical considerations for pharmaceutical applications, including experimental design and basic spectral interpretation.

We report on studies of state-populations during the two-photon absorption process using intense X-ray pulses. The calculations were performed in a time-dependent manner using a simple three-level model expressed by coupled rate equations. We show that the proposed approach describes well the measured rates of X-rays excited in the one-photon and two-photon absorption processes, and allows detailed investigation of the state population dynamics during the course of the incident X-ray pulse. Finally, we demonstrate that the nonlinear interaction of X-ray pulses with atoms leads to a time-narrowing of state populations. This narrowing-effect is attributed to a quadratic incidence X-ray intensity dependence characteristic for nonlinear interactions of photons with matter.