where y$_{q}$ ( y$_{χ}$ ) is the Yukawa coupling for the quark (DM) and m$_{h}$ is the Higgs mass. The per nucleon cross section is then Estimates based on recent lattice simulations seem to favor smaller values for the nuclear matrix elements [34]. If these lattice results are correct, the dominant contribution to the SI scattering cross section would be due to the heavy quark content of the nucleon (since f ( N ) TG → 1 in the limit of small f ( N ) q ) and the coefficient in Eq. (10) would be replaced by 2 × 10 − 8 pb. In cases where c$_{d}$ ≫ c$_{u}$ , which can occur in models with multiple Higgs bosons such as the MSSM, then uncertainties in the f ( N ) Tq can lead to as much as an order of magnitude variation in σ$_{SI}$ ( χ N → χ N ) [35]. The operator responsible for SD DM-nucleus interactions is Taking the expectation value of this operator between two nucleon states allows us to find the effective SD interaction of the DM with a nucleon ( N = p (proton) or n (neutron)), where s ( N ) µ is the spin of the nucleon and the Δ q ( N ) are extracted from polarized deep elastic scattering. The coefficient of the effective DM-nucleon interaction, 2 a$_{N}$ (¯ χ γ $^{µ}$γ 5 χ )( ¯ N s ( N ) µ N ), is given by The elastic scattering cross section quoted by the experiments is between the DM and a nucleon which is given by where m$_{r}$ is the reduced mass between the DM and a nucleon. Again we follow DarkSUSY and use the following values for the SD calculations, Δ ( p ) u = 0 . 77 Δ ( p ) d = − 0 . 40 Δ ( p ) s = − 0 . 12 Δ ( n ) u = − 0 . 40 Δ ( n ) d = 0 . 77 Δ ( p ) s = − 0 . 12 . (15) σ$_{SD}$ ( χ N → χ N ) = 6 π m 2 r a 2 $_{N}$, (14) a$_{N}$ = ∑ q = u,d,s d$_{q}$ Δ q ( N $^{)}$. (13) 〈 N | ¯ q γ$_{µ}$γ 5 q | N 〉 = 2 s ( N ) µ Δ q ( N $^{)}$, (12) O SD q = d$_{q}$ (¯ χ γ $^{µ}$γ 5 χ )(¯ q γ$_{µ}$γ 5 q ) . (11) B. Spin Dependent σ$_{SI}$ ( χ N → χ N ) ≈ 5 × 10 − 8 pb ( y$_{χ}$ 0 . 1$^{)}$$^{2}$$^{(}$ 115 GeV m$_{h}$ ) 4 (SI typical) . (10) 7