Electronic core levels in molecules are highly localized around one atomic site. However, in single-photon ionization of symmetric molecules, the question of core-hole localization versus delocalization over two equivalent atoms has long been debated as the answer lies at the heart of quantum mechanics. Here, using a joint experimental and theoretical study of core-ionized carbon disulfide (CS₂), we demonstrate that it is possible to experimentally select distinct molecular-fragmentation pathways in which the core hole can be considered as either localized on one sulfur atom or delocalized between two indistinguishable sulfur atoms. This feat is accomplished by measuring photoelectron angular distributions within the frame of the molecule, directly probing entanglement or disentanglement of quantum pathways as a function of how the molecule dissociates.

Creation of deep core holes with very short ($\tau \le 1\mathrm{fs}$) lifetimes triggers a chain of relaxation events leading to extensive nuclear dynamics on a few-femtosecond time scale. Here we demonstrate a general multistep ultrafast dissociation on an example of HCl following Cl $1s\to {\sigma }^{*}$ excitation. Intermediate states with one or multiple holes in the shallower core electron shells are generated in the course of the decay cascades. The repulsive character and large gradients of the potential energy surfaces of these intermediates enable ultrafast fragmentation after the absorption of a hard x-ray photon.

Cross sections and angular distribution parameters for the single-photon ionization of all electron orbitals of Li₂₋₈ are systematically computed in a broad interval of the photoelectron kinetic energies for the energetically most stable geometry of each cluster. Calculations of the partial photoelectron continuum waves in clusters are carried out by the single center method within the Hartree-Fock approximation. We study photoionization cross sections per one electron and analyze in some details general trends in the photoionization of inner and outer shells with respect to the size and geometry of a cluster. The present differential cross sections computed for Li₂ are in a good agreement with the available theoretical data, whereas those computed for Li₃₋₈ clusters can be considered as theoretical predictions.

The absolute cross sections for the competing decay channels fluorescence, dissociation, and ionization of photoexcited long-lived superexcited H2 molecular levels have been measured from the ionization threshold of H2 up to the H(1s)+H(n=3) dissociation limit. The total and partial natural widths of these levels have been determined. Good agreement is found with first principles calculations carried out by multichannel quantum defect theory. The calculations reproduce the balance between the competing decay processes as well as its substantial level-to-level evolution.

A combination of resonant inelastic x-ray scattering and resonant Auger spectroscopy provides complementary information on the dynamic response of resonantly excited molecules. This is exemplified for ${\mathrm{CH}}_3\mathrm{I}$, for which we reconstruct the potential energy surface of the dissociative I $3d^{-2}$ double-core-hole state and determine its lifetime. The proposed method holds a strong potential for monitoring the hard x-ray induced electron and nuclear dynamic response of core-excited molecules containing heavy elements, where ab initio calculations of potential energy surfaces and lifetimes remain challenging.

The $2p$ photoionization and subsequent $L_{2,3}{M}_{2,3}{M}_{2,3}$ Auger decay spectra from free $4s_{1∕2}\to 4p_{1∕2}$ laser-excited potassium atoms are studied both experimentally and theoretically. The shake-up-structure of the $2p$ photoelectron spectrum of K is resolved. A direct experimental way for resolving the satellite structure due to conjugate shake-up transitions accompanying the hole creation in the $L_{2,3}{M}_{2,3}{M}_{2,3}$ Auger spectrum of nonexcited atoms is presented. Theoretical ab initio computations based on the multiconfiguration Dirac-Fock approach were performed to interpret the experimental findings.