Convolution Approach

In the deep inelastic region an effective neutron spin structure function can be extracted to first order from that of $^3$He if only S, S' and D states of the $^3$He wave function are included:

$$\tilde{g_1^n} = \frac{1}{\rho_n}(g_1^{^3\rm {He}}-2\rho_p g_1^p)$$ (26)

$$\tilde{A_1^n} = \frac{W_1^{^3\rm {He}}}{W_1^n}\frac{1}{\rho_n}(A_1^{^3\rm {He}} -2\frac{W_1^p}{W_1^{^3\rm {He}}}\rho_p A_1^p) \nonumber$$

where $\tilde{g_1^n}$, $g_1^p$ and $g_1^{^3\rm {He}}$ are the spin structure functions of an effective free neutron, a free proton and $^3$He, respectively. $\rho_n=(87\pm 2)$% and $\rho_p=(-2.7\pm 0.3)$% are the effective nucleon polarizations of the neutron and proton in $^3$He due to the S, S' and D states of the wave function.