Classical and quantum scattering by a Coulomb potential

TL;DR

This paper compares classical and quantum scattering by a Coulomb potential at relativistic energies, highlighting where they agree and differ, and discusses how quantum effects and particle properties influence scattering outcomes.

Contribution

It elucidates the relationship between classical and quantum scattering cross sections at relativistic energies, emphasizing the role of corrections and particle properties.

Findings

Classical and quantum cross sections agree in the leading term at high energies.

Discrepancies arise from higher-order corrections and particle properties.

Relativistic quantum particles can pass through the field without interaction.

Abstract

For relativistic energies the small angle classical cross section for scattering on a Coulomb potential agrees with the first Born approximation for quantum cross section for scalar particle only in the leading term. The disagreement in other terms can be avoided if the sum of all corrections to the first Born approximation for large enough Coulomb charge contain the classical terms which are independent of that charge. A small part of the difference in classical and quantum cross sections may be attributed to the fact that the relativistic quantum particle can rush through the field without interaction. We expect that smaller impact parameters and spin facilitate this affect.