Projectile Localization Effects in Electron Vortex Beam Ionization Collisions*

In traditional charged particle scattering theory, the incident projectile is considered to be delocalized in the transverse plane with an infinitely large coherence.  However, in the last decade, it has been shown that a finite projectile coherence length can significantly alter the collision cross sections and must be considered when comparing theoretical results with experimental data.  To date, the effect of coherence on collision cross sections has been studied for heavy ion projectiles, such as protons and carbon nuclei.  In these cases, the coherence length was controlled by changing the projectile deBroglie wavelength through its energy, which is directly related to transverse coherence length.  For heavy ions, the deBroglie wavelength is quite small and small coherence lengths can be achieved.  For non-relativistic plane wave electron projectiles, the deBroglie wavelength is much larger and achieving a small coherence length is not feasible.  However, electron vortex projectiles, such as Laguerre-Gauss electrons, offer an opportunity to study projectile coherence in electron-impact collisions.  We report here theoretical triple differential cross sections for electron-impact ionization of helium using Laguerre-Gauss projectiles.  We show that a localized projectile causes the binary peak to shift to larger ejected electron angles and enhances the recoil peak.  As the projectile becomes less localized the cross sections more closely resemble their delocalized counterparts.  We also show that the atomic target’s transverse position within the projectile beam can significantly alter the magnitude of the cross section.