Compton Scattering and Photo-absorption Sum Rules on Nuclei

TL;DR

This paper revisits photo-absorption sum rules for Compton scattering on protons and nuclei, proposing a new sum rule based on constituent quarks and analyzing experimental data to compare with traditional terms.

Contribution

It introduces a novel constituent quark model sum rule for nuclear targets and analyzes the $ ext{α}=0$ pole contribution using modern data.

Findings

The constituent quark sum rule relates resonance strength to quark scattering amplitudes.

The $ ext{α}=0$ pole contribution significantly differs from the Thomson term.

Modern data shows the $ ext{α}=0$ pole is not consistent with earlier low-energy approximations.

Abstract

We revisit the photo-absorption sum rule for real Compton scattering from the proton and from nuclear targets. In analogy with the Thomas-Reiche-Kuhn sum rule appropriate at low energies, we propose a new "constituent quark model" sum rule that relates the integrated strength of hadronic resonances to the scattering amplitude on constituent quarks. We study the constituent quark model sum rule for several nuclear targets. In addition we extract the $\alpha=0$ pole contribution for both proton and nuclei. Using the modern high energy proton data we find that the $\alpha=0$ pole contribution differs significantly from the Thomson term, in contrast with the original findings by Damashek and Gilman.