Spin-dependent Study Using Spectator Tagging Deuteron from Polarized $^3$He

A polarized $^3$He target has proven a successful effective polarized neutron target for spin-dependent studies from electron scattering experiments. The structure function $g_{1}^{n}(x, Q^2)$ can be extracted from purely Deep Inelastic Scattering (DIS) inclusive measurements. We are now considering another interesting measurement in which the spectator deuteron is also detected. This measurement provides an access to the $g_{1}^{p}(x, Q^2)$ structure function from the strongly bound proton in the $^3$He nucleus. By comparing with the structure function for the free proton, we can search for possible medium modifications of the DIS spin structure, the so-called {\it spin-dependent EMC effect}. In this talk, we will present the feasibility study of such measurement using the CLAS12 spectrometer at JLab as well as at the EIC.