Fig. 2: The concept of transient resonances.

In a, the simulated Coulomb potential is plotted versus the distance from the charged core for a neutral Xe atom (gray dashed line) and in b for a core excited Xe+^* (gray solid line). The corresponding 3d (blue) and 4f orbitals (orange) are displayed for a neutral Xe atom ((a), dashed lines) and 3d^* and 4f^* excited Xe ion with a core-hole ((b), solid lines). First, the core-hole excitation shifts the binding energy of the remaining 3d^* electrons from hν₁ (black) to greater \(h{\nu }_{2}^{*}\) (red) due to a modified Coulomb potential. Second, the core-hole excitation also rearranges the orbitals to 3d^* (blue) and 4f^* (orange) plotted on top of the Coulomb potential. Due to the core-hole induced charge imbalance the 4f^* orbital is pulled closer to the atom’s center by almost two orders of magnitude creating a strongly increased overlap with the 3d^* wave function and hence an increased transition dipole strength for the 3d^* → 4f^* transition. This has dramatic consequences for the scattering cross-section in the vicinity of the Xe 3d absorption edge. In c, the scattering cross section σ_scat for the neutral Xe (dashed black line) and \({\sigma }_{scat}^{*}\) for the excited Xe+^* (red solid line) is plotted vs the incoming X-ray photon energy. The excited atom Xe+^* scatters two orders more strongly than neutral Xe at the shifted resonance position \(h{\nu }_{2}^{*}\) and almost two orders more compared to the neutral Xe resonance maximum hν₁. Energies, cross-sections, and radial wave functions displayed here were calculated using Hartree-Fock-Slater simulations (see Supplementary Note 1). The gray lines represent a schematic drawing of the Coulomb potential. The shape of the wave functions is a result of the Hartree–Fock simulations and its integral is normalized to one.