Signatures of magnetic field effects in non-sequential double ionization manifesting as back-scattering for molecules versus forward-scattering for atoms

For two-electron diatomic molecules, we investigate magnetic field effects in non-sequential double ionization where recollisions prevail. We do so by formulating a three-dimensional semi-classical model that fully accounts for the Coulomb singularities and for magnetic field effects during time propagation. Using this model, we identify a prominent signature of non-dipole effects. Namely, we demonstrate that the recolliding electron back-scatters along the direction of light propagation. Hence, this electron escapes opposite to the direction of change in momentum due to the magnetic field. This is in striking contrast to strongly-driven atoms where the recolliding electron forward-scatters along the direction of light propagation. We attribute these distinct signatures to the different gate that the magnetic field creates jointly with a soft recollision in molecules compared to a hard recollision in atoms. These two different gates give rise, shortly before recollision, to different momenta and positions of the recolliding electron along the direction of light propagation. As a result, we show that the Coulomb forces from the nuclei act to back-scatter the recolliding electron in molecules and forward-scatter it in atoms along the direction of light propagation.