Majorana and the theoretical problem of photon-electron scattering

TL;DR

This paper reviews Majorana's contributions to photon-electron scattering, deriving a generalized dispersion formula, explaining the Klein-Nishina result, and extending the theory to bound electrons and magnetic fields, highlighting its historical and modern significance.

Contribution

It presents a detailed analysis of Majorana's work, including a generalized dispersion formula and new insights into bound electron scattering and magnetic field effects.

Findings

Derived a quantum generalization of the Kramers-Heisenberg formula.

Provided a quantitative description of Compton line broadening for bound electrons.

Extended the theory to include magnetic field effects in scattering.

Abstract

Relevant contributions by Majorana regarding Compton scattering off free or bound electrons are considered in detail, where a (full quantum) generalization of the Kramers-Heisenberg dispersion formula is derived. The role of intermediate electronic states is appropriately pointed out in recovering the standard Klein-Nishina formula (for free electron scattering) by making recourse to a limpid physical scheme alternative to the (then unknown) Feynman diagram approach. For bound electron scattering, a quantitative description of the broadening of the Compton line was obtained for the first time by introducing a finite mean life for the excited state of the electron system. Finally, a generalization aimed to describe Compton scattering assisted by a non-vanishing applied magnetic field is as well considered, revealing its relevance for present day research.