Elastic Compton Scattering from 3He and the Role of the Delta

TL;DR

This paper presents detailed theoretical predictions for elastic Compton scattering from helium-3 using chiral effective field theory with explicit Delta degrees of freedom, aiming to extract neutron polarizabilities.

Contribution

The study provides a complete N3LO calculation including the Delta resonance and analyzes sensitivities of observables to neutron polarizabilities, correcting previous lower-order results.

Findings

Including the Delta enhances asymmetries sensitive to neutron spin polarizabilities.

The cross section for helium-3 is 2-3 times larger than deuterium.

Certain observables show increased sensitivity to neutron polarizabilities with the Delta included.

Abstract

We report observables for elastic Compton scattering from $^3$He in Chiral Effective Field Theory with an explicit $\Delta(1232)$ degree of freedom ($\chi$EFT) for energies between 50 and 120 MeV. The $\gamma\,{}^3$He amplitude is complete at N3LO, $\mathcal{O}(e^2\delta^3)$, and in general converges well order by order. It includes the dominant pion-loop and two-body currents, as well as the Delta excitation in the single-nucleon amplitude. Since the cross section is two to three times that for deuterium and the spin of polarised $^3$He is predominantly carried by its constituent neutron, elastic Compton scattering promises information on both the scalar and spin polarisabilities of the neutron. We study in detail the sensitivities of 4 observables to the neutron polarisabilities: the cross section, the beam asymmetry and two double asymmetries resulting from circularly polarised photons and a longitudinally or transversely polarised target. Including the Delta enhances those asymmetries from which neutron spin polarisabilities could be extracted. We also correct previous, erroneous results at N2LO, i.e.~without an explicit Delta, and compare to the same observables on proton, neutron and deuterium targets. An interactive Mathematica notebook of our results is available from hgrie@gwu.edu.