Inner-shell ionization of rotating linear molecules in the presence of spin-dependent interactions: Entanglement between a photoelectron and an auger electron

Abstract
This paper reports results of a theoretical study of angle- and spin-resolved photo-Auger electron coincident spectroscopy in the form of entanglement between these two particles emitted from a linear molecule. First, we develop an expression for a density matrix needed for studying spin-entanglement between a photoelectron and an Auger electron. In order to properly represent the molecular symmetries, nuclear rotation, and the spin-dependent interactions (SDIs), we have used symmetry adapted wavefunctions in Hund's coupling scheme (a) for all the species participating in this two-step process. This expression shows that spin-entanglement in a photo-Auger electron pair in the presence of SDIs very strongly depends upon, among other things, polarization of the ionizing radia- tion, directions of motion and of spin polarization of two ejected electrons, and the dynamics of photoionization and of Auger decay. We have applied this expression, as an example, to a generic linear molecule in its J₀, M₀ = 0 state. This model calculation clearly brings out the salient features of the spin-entanglement of a photo-Auger electron pair in the presence of the SDIs.