On the reaction $ep \to ep \gamma$

TL;DR

This study analyzes the $ep o ep \gamma$ reaction at small electron scattering angles and large photon angles, showing the cross section's sensitivity to proton polarizability and providing compact formulas for the differential cross section.

Contribution

It introduces a direct evaluation method in the diagonal spin basis and derives compact, covariant expressions for the reaction's differential cross section considering proton form factors and recoil effects.

Findings

Bethe-Heitler and interference contributions are less than 10% of the cross section.

The reaction cross section is sensitive to proton polarizability.

Derived compact and covariant formulas for the differential cross section.

Abstract

We have studied the reaction $ep \to ep \gamma$ in the kinematics corresponding to electron scattering at small angles and photon scattering at large angles, where proton bremsstrahlung dominates. The analysis is based on the direct evaluation method of the matrix elements in the so-called diagonal spin basis. The results of numerical calculations for electron beam energy $E_{e}=200 MeV$ in the above kinematics show that the relative contribution of the Bethe-Heitler and interference terms to the reaction cross section is less than 10 %, and the cross section for the reaction $ep \to ep \gamma$ is quite sensitive to the proton polarizability. Owing to the factorization of the squared electric and magnetic form factors of the proton, a compact expression has been obtained for the differential cross section of the Bethe-Heitler emission of a linearly polarized photon by an electron, taking into account the proton recoil and form factors. A covariant expression has been obtained for the lepton tensor in which contributions of states with transverse and longitudinal polarizations of the virtual photon are separated.