Dynamics of Correlations and Entanglement Generation in Electron-Molecule Inelastic Scattering

Abstract: The dynamics and processes involved in particle-molecule scattering, including nuclear dynamics, are described and analyzed using various quantum information quantities throughout the different stages of the scattering. The main process studied and characterized with the information quantities is the interatomic coulombic electronic capture (ICEC), an inelastic process that can lead to dissociation of the target molecule. The analysis focuses on a one-dimensional transversely confined $\text{NeHe}$ molecule model used to simulate the scattering between an electron $\text{e}^-$(particle) and a $\text{NeHe}^+$ ion (molecule). The time-independent Schr\"odinger equation (TISE) is solved using the Finite Element Method (FEM) with a self-developed Julia package \hyperlink{https://github.com/mendzmartin/FEMTISE.jl}{FEMTISE} to compute potential energy curves (PECs) and the parameters of the interactions between particles. The time-dependent Schr\"odinger equation (TDSE) is solved using the Multi-configuration time-dependent Hartree (MCTDH) algorithm. The time dependent electronic and nuclear probability densities are calculated for different electron incoming energies, evidencing elastic and inelastic processes that can be correlated to changes in von Neumann entropy, von Neumann mutual information and Shannon mutual information. The expectation value of the position of the particles, as well as their standard deviations, are analyzed along the whole dynamics and related to the entanglement during the collision and after the process is over, thus highlighting the dynamics of entanglement generation. It is shown that the correlations generated in the collision are partially retained only when the inelastic process is active.