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

The spin-structure functions $g_1$ and $g_2$, and the spin-dependent partial cross-section $σ_\mathrm{TT}$ have been extracted from the polarized cross-sections differences, $Δσ_{\parallel}\hspace{-0.06cm}\left(ν,Q^{2}\right)$ and $Δσ_{\perp}\hspace{-0.06cm}\left(ν,Q^{2}\right)$ measured for the $\vec{^\textrm{3}\textrm{He}}(\vec{\textrm{e}},\textrm{e}')\textrm{X}$ 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$^{\circ}$ and 9$^{\circ}$ from a longitudinally or transversely polarized $^{3}$He target. The data cover the kinematic regions of the quasi-elastic, resonance production and beyond. From the extracted spin-structure functions, the first moments $\overline{Γ_1}\hspace{-0.06cm}\left(Q^{2}\right)$, $Γ_2\hspace{-0.06cm}\left(Q^{2}\right)$ and $I_{\mathrm{TT}}\hspace{-0.06cm}\left(Q^{2}\right)$ 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.