Measurement of the $^3$He Spin-Structure Functions and of Neutron (3He) Spin-Dependent Sum Rules at $0.035\le Q^2 \le 0.24$ GeV$^2$

Abstract The spin-structure functions g 1 and g 2 , and the spin-dependent partial cross-section σ TT have been extracted from the polarized cross-sections differences, Δ σ ∥ ( ν , Q 2 ) and Δ σ ⊥ ( ν , Q 2 ) measured for the He 3 → ( e → , e ′ ) X reaction, in the E97-110 experiment at Jefferson Lab. Polarized electrons with energies from 1.147 to 4.404 GeV were scattered at angles of 6 ∘ and 9 ∘ from a longitudinally or transversely polarized 3He target. The data cover the kinematic regions of the quasi-elastic, resonance production and beyond. From the extracted spin-structure functions, the first moments Γ 1 ‾ ( Q 2 ) , Γ 2 ( Q 2 ) and I TT ( Q 2 ) are evaluated with high precision for the neutron in the Q 2 range from 0.035 to 0.24 GeV 2 . The comparison of the data and the chiral effective field theory predictions reveals the importance of proper treatment of the Δ degree of freedom for spin observables.