A Preliminary Measurement of the Longitudinal Spin Asymmetry $A_1^{n}$

To date, measurements of the nucleon-virtual photon longitudinal spin asymmetry $A_1$ for both the proton and neutron have shown that the extracted helicity dependent-to-independent ratio of the down-quark parton distribution functions in the proton, $\Delta d/d$, tends towards -1/3 at large $x$, in disagreement with the perturbative QCD prediction that $\Delta d/d$ should approach unity. As part of Jefferson Lab experiment E06-014 performed in Hall A, double-spin asymmetries were measured when scattering a longitudinally polarized electron beam of energies 4.73 and 5.89 GeV from a longitudinally and transversely polarized $^3$He target in the deep inelastic scattering region, allowing for the extraction of the neutron asymmetry $A_1^n$. We will discuss the analysis of our data and present preliminary results for the nuclear asymmetry $A_1^{^3\textrm{He}}$ and $A_1^{n}$ in the kinematic range of $0.2 < x < 0.65$ and $2 < Q^2 < 5$ GeV$^2$ for the scattered electrons. Our measurement of $A_1^{n}$ will provide a test of previous results with a higher statistical precision and continuous coverage of the $x$ range above.