Symmetry-dependent vibrational excitation in N $1s$ photoionization of $N2$⁠: Experiment and theory

We have measured the vibrational structures of the N $1s$ photoelectron mainline and satellites of the gaseous $N2$ molecule with the resolution better than $75meV$⁠. The gerade and ungerade symmetries of the core-ionized (mainline) states are resolved energetically, and symmetry-dependent angular distributions for the satellite emission allow us to resolve the $Σ$ and $Π$ symmetries of the shake-up (satellite) states. Symmetry-adapted cluster-expansion configuration-interaction calculations of the potential energy curves for the mainline and satellite states along with a Franck-Condon analysis well reproduce the observed vibrational excitation of the bands, illustrating that the theoretical calculations well predict the symmetry-dependent geometry relaxation effects. The energies of both mainline states and satellite states, as well as the splitting between the mainline gerade and ungerade states, are also well reproduced by the calculation: the splitting between the satellite gerade and ungerade states is calculated to be smaller than the experimental detection limit.