Systematics of Nuclear Effects in Polarized $^3$He Structure Functions and Asymmetries

We present a detailed analysis of nuclear effects in inclusive electron scattering from polarized $^3$He nuclei, including for polarization asymmetries and structure function moments, in both the nucleon resonance and deep-inelastic scattering regions. We compare the results of calculations within the weak binding approximation (WBA) at finite $Q^2$ with several commonly used ansaetze for simplifying the nuclear corrections, and assess their impact on extractions of the free neutron structure. In addition, we make predictions for the $Q^2$ dependence of quasielastic (QE) scattering from polarized $^3$He, data on which can be used to constrain the nucleon smearing functions in $^3$He. As a check of the formalism, we compare the WBA calculations in the QE region with the world's data on QE electron-deuteron cross sections.