High-energy Coulomb scattering of spatially extended particles

TL;DR

This paper investigates high-energy Coulomb elastic scattering of charged particles, distinguishing three modes based on momentum transfer, and compares potential and QFT approaches, highlighting their differences and applicability.

Contribution

It provides a detailed analysis of Coulomb scattering modes and compares potential and QFT approaches, revealing the limitations of the potential method at high energies.

Findings

Potential approach is unsuitable for proton scattering at LHC energies.

Optical approximation effectively describes heavy nuclei Coulomb scattering.

Significant differences between potential and QFT approaches for protons at high energies.

Abstract

We analyze pure Coulomb high-energy elastic scattering of charged particles (hadrons or nuclei), discarding their strong interactions. We distinguish three scattering modes, determined by the magnitude of the momentum transfer, in which particles behave as point-like, structureless extended, and structured composite objects. The results are compared in the potential and QFT approaches of the eikonal model. In the case of proton Coulomb scattering at the LHC the difference between these two approaches is significant. This indicates the unsuitability of the potential approach. However, in the case of Coulomb scattering of heavy nuclei, the leading one is the optical approximation, which formally reproduces the prescription of the potential approach.