Measurement of the $^3$He Spin Structure Functions and Their Moments at Low Q$^2$

Abstract

We report measurements of spin-dependent electron scattering from a polarized $^3$He target, $\vec{^3\textrm{He}}(\vec{e},e')X$, performed at the Thomas Jefferson National Accelerator Facility (Jefferson Lab). The $^3$He spin-dependent virtual-photoabsorption cross sections $σ_{TT}$ and $σ_{LT}$, or equivalently the spin structure functions $g_1$ and $g_2$, and their moments were extracted for $0.032 \leq Q^2 \leq 0.23$~GeV$^2$, with coverage from the two-body breakup threshold through the nucleon-resonance region. The moment $I_1(Q^2)$ reaches a plateau below $Q^2 \simeq 0.1$~GeV$^2$, consistent with the Gerasimov--Drell--Hearn (GDH) expectation, while the moment $I_{TT}(Q^2)$, still dominated by the finite-virtuality breakup response, peaks at $Q^2 \simeq 0.1$~GeV$^2$ and turns toward the expected GDH value. Together, the two moments constitute the first observation of a nucleus approaching its GDH sum-rule value at the real-photon point. The moments $I_2(Q^2)$ and $I_{LT}(Q^2)$ yield, respectively, the lowest-$Q^2$ nuclear test of the Burkhardt--Cottingham sum rule and the first nuclear test of the Schwinger sum rule. Besides testing fundamental sum rules, these data provide stringent benchmarks for ab initio calculations of the spin structure of light nuclei.