Numerical test of polarization sum rules for the triply differential bremsstrahlung cross section in electron-nucleus encounters

TL;DR

This paper derives a polarization sum rule for electron bremsstrahlung and numerically tests its validity across different nuclei and energies, revealing violations for high nuclear charge that indicate calculation inaccuracies.

Contribution

It introduces a new sum rule for bremsstrahlung polarization correlations and evaluates its validity using Dirac partial-wave theory across various conditions.

Findings

Sum rule holds for low nuclear charge and energies.

Violations increase with higher nuclear charge.

Violations indicate potential inaccuracies in bremsstrahlung calculations.

Abstract

Inspired by the work of Pratt and coworkers on a sum rule for the polarization correlations in electron bremsstrahlung when the outgoing electron is not observed, we derive the corresponding sum rule for the elementary process of bremsstrahlung. This sum rule is valid for arbitrary electron wavefunctions provided the electron is emitted in the reaction plane. The numerical evaluation of this sum rule within the Dirac partial-wave theory for bare inert spin-zero nuclei and collision energies in the range of 1-10 MeV reveals violations for high nuclear charge. Such violations serve as a measure of the inaccuracies in the bremsstrahlung calculations.