Nonclassical trajectories in head-on collisions

Rutherford scattering is usually described by treating the projectile either classically or as quantum mechanical plane waves. Here we treat them as wave packets and study their head-on collisions with the stationary target nuclei. We simulate the quantum dynamics of this one-dimensional system and study deviations of the average quantum solution from the classical one. These deviations are traced back to the convexity properties of Coulomb potential. Finally, we sketch how these theoretical findings could be tested in experiments looking for the onset of nuclear reactions.

On Laser-Modified Rutherford Scattering

We present a theoretical analysis of a charged-particle scattering by a Coulomb potential in the presence of laser radiation. The effect of a laser field is studied using our recently developed nonperturbative parabolic quasi-Sturmian approach for solving the system of coupled Lippmann–Schwinger–Floquet equations in the Kramers–Henneberger frame. We calculate the ratio of multiphoton differential cross sections to the Rutherford cross section in the case of a laser-assisted electron-proton scattering process. Our results are compared with predictions of the Bunkin–Fedorov, Kroll–Watson, and Coulomb–Volkov analytical approximations: marked discrepancies are found for different net numbers of exchanged photons and different orientations of the laser-field polarization vector. Our findings clearly demonstrate deficiencies of those well-known approximations for describing laser-modified Rutherford scattering processes.