Compton Scattering on $^3$He at HI$\gamma$S and Neutron Polarizabilities

Abstract

The nucleon electric and magnetic polarizabilities ($\alpha_{E1}$ and $\beta_{M1}$) are quantities characterizing the response of the nucleon to an external electromagnetic field, and can be probed using Compton scattering processes. In recent decades, proton polarizabilities have been extracted from Compton scattering on hydrogen targets, and neutron polarizabilities have been derived from Compton scattering on deuterium. These extractions are based on dispersion relations and chiral effective field theory ($\chi$EFT). However, $\alpha_{E1}$ and $\beta_{M1}$ of the neutron remain less precisely determined due to experimental challenges. Concurrently, recent theoretical progress in lattice QCD shows great promise in predicting nucleon polarizabilities, further motivating complementary experimental studies.Measurements of elastic Compton scattering at weighted-mean incident photon beam energies of 61.5 and 97.1~MeV were conducted using a liquid $^3 \rm He$ target and a nearly 100\% circularly polarized $\gamma$-ray beam at the High Intensity $\gamma$-Ray Source (HI$\gamma$S) facility.These are the world’s first measurements of Compton scattering on a $^3 \rm He$ target with the primary goal of investigating static electromagnetic polarizabilities of the neutron. Scattered photons were detected by seven NaI(Tl) core detectors positioned at laboratory angles of $40^\circ$, $55^\circ$, $90^\circ$, $115^\circ$, and $150^\circ$. Compared to experiments using deuterium, $^4 \rm He$, and $^6 \rm Li$ targets, the cross section for elastic Compton scattering on $^3 \rm He$ arises from a different combination of the nucleon contributions (two protons and one neutron), offering an alternative way to extract the neutron polarizabilities and rigorously test the $\chi$EFT formalism.This dissertation focuses on extracting differential cross sections from the 97.1~MeV dataset, which provides sensitivity to the neutron polarizabilities. The measured differential cross sections will be used to extract $\alpha_{E1}$ and $\beta_{M1}$ of the neutron via $\chi$EFT calculations, with or without the constraint of the Baldin sum rule. This single dataset is projected to improve the precision of the extracted neutron polarizabilities by about 30\% compared to the previous most precise determination from a single measurement of elastic Compton scattering on the deuteron, and by about 10\% compared to the latest Particle Data Group recommended values, which rely on a compilation of multiple previous experiments.