FIG. 3: The elastic scattering of N with a nucleus through the magnetic moment of N . 4 where M is the mass of the nucleus with atomic weight A , E$_{rec}$ is the nuclear recoil energy, Q$_{em}$ = Ze is the nuclear charge, and F$_{2}$ = 1 $_{2}$F st 2 = 1 2 ( µ µ$_{N}$ m$_{(}$$_{Z,A}$$_{)}$ m$_{p}$ − Z ) for spin 1 2 case, where F st 2 is the conventional notation. Our F$_{2}$ is a fac- tor 1 2 of the conventional definition, F st 2 . The first two terms (‘ Z terms’) in the right hand side of Eq. (7) result from the electromagnetic interaction between the tensor operator of N ( Nσ$_{µν}$N ) in Eq. (2) and the vector current of a spin 1 2 target nucleus ( ψγ$_{µ}$ψ ). On the other hand, the last three terms (‘ F$_{2}$ terms’) come from the interac- tion between the tensor operators of N and the nucleus. As seen in Eq. (2), the tensor operator of a given nucleus defines the spin of the nucleus ( ψσ$_{µν}$ψ ). For the case of a higher spin target nucleus, ‘ γ$_{µ}$ ’ and ‘ σ$_{µν}$ ’ in the vector and tensor operators of the nucleus should be replaced by larger dimensional representations of the Dirac gamma matrix and the Lorentz generator, respectively (see e.g. Ref. [14]). Using Appendix, we can deduce that F$_{2}$ = 1 $_{2}$F st 2 = 1 2 ( µ µ$_{N}$ m$_{(}$$_{Z,A}$$_{)}$ m$_{p}$ √ s$_{N}$ +1 3 s$_{N}$ − Z ) from Eq. (7) with a higher spin generalization. In the non-relativistic limit ( E$_{rec}$ ≪ { M, m$_{N}$ } and v ≪ 1), the differential cross section is given by The direct-detection rate (per unit detector mass) in a detector with nucleus is given by Here, we assume that the WIMP of mass m$_{N}$ accounts for the local DM density ρ$_{N}$ and have a local velocity distribution f ( ⃗v ) with the normalization ∫ d $^{3}$⃗vf ( ⃗v ) = 1. Using a simple Maxwell-Boltzmann velocity distribution and ρ$_{N}$ ≃ 0 . 3 GeV / cm $^{3}$, in Fig. 4 we plot the expected direct-detection rates of an almost-Dirac DM N (solid line) and the LSP χ (dash line) in the MSSM for the spin- independent(SI) interactions which always dominates for nuclei with A ≥ 30 in surveys of the SUSY parameter spaces [15]. The SI cross section is given by Λ$_{∓}$( s, m 2 $_{N}$, M $^{2}$) = ( m 2 N + M 2 − s ) 2 ∓ 4 m 2 $_{N}$M 2 , (8) dR dE$_{rec}$ = ρ$_{N}$ m$_{N}$M ∫ | ⃗v | >v$_{min}$ d $^{3}$⃗vf ( ⃗v ) dσ dE$_{rec}$ . (10) dσ dE$_{rec}$ = 2 M πv $_{2}$( Zf$_{p}$ + ( A − Z ) f$_{n}$ ) $^{2}$F $^{2}$( E$_{rec}$ ) , (11) where f$_{p}$ ≃ f$_{n}$ ≃ 10 − $^{8}$GeV − 2 are the SI cou- plings of WIMPs to protons and neutrons, respec- tively, the SI form factor F ( E$_{rec}$ ) = 3 e − κ $^{2}$s$^{2}$/ $^{2}$(sin( κr ) − κr cos( κr )) / ( κr ) $^{3}$, with s = 1 fm, r = √$_{R}$ 2 − 5 s $^{2}$, R = 1 . 2 A 1 / 3 fm, and κ = √$_{2}$$_{m}$$_{n}$$_{E}$$_{rec}$$_{.}$ In Fig. 4, we present the differential event detection rate for m$_{N}$ = 70 GeV, Eq. (10), as a solid line above the CDMS II threshold of about 10 keV. The neutralino DM case with m$_{χ}$ = 70 GeV is shown as a dashed line. To show the recoil energy dependence, we choose an arbitrary normalization such that both of these lines match at 10 keV. The target is Ge with Z = 32 and A = 73. Its anomalous magnetic moment is F$_{2}$ = − 36 . 32 as shown in Table I. The 1 /E$_{rec}$ dependence in the first term of Eq. (7) generically leads the dR $^{MDM}$/dE$_{rec}$ to diverge in low E$_{rec}$ limit. However, dσ dE$_{rec}$ = 4 πα 2 $_{em}$f 2 m 2 $_{N}$E$_{rec}$ [ Z $^{2}$(1 − E$_{rec}$ 2 Mv 2 − E$_{rec}$ m$_{N}$v $_{2}$) + ( µ µ$_{N}$ ) 2 s$_{N}$ + 1 3 s$_{N}$ ME$_{rec}$ m 2 $_{p}$v 2 ] . (9) dσ dE$_{rec}$ = 2 πα 2 $_{em}$f 2 Mm 2 N | ⃗p | 2 [ Z 2 { Λ$_{−}$( s, m 2 $_{N}$, M $^{2}$) 2 ME$_{rec}$ + (2 m 2 N + M 2 − s ) } + 2 ZF$_{2}$ (4 m 2 N − ME$_{rec}$ ) + F 2 { Λ$_{+}$( s, m 2 $_{N}$, M $^{2}$) M 2 − 2 sE$_{rec}$ M + E 2 rec } ] , (7) γ N N f ( Ze, µ anom ) •