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capture condition Eq. (22) is a large value. When the mass of DM is comparable to or larger than that of a nucleus, such as Fe or Al, the left hand side of Eq. (22) is suppressed by m$_{χ}$ so it is difficult to satisfy the capture condition. If the DM is much lighter than the nuclei, the condition Eq. (22) is still not easy to satisfy. Moreover it is difficult to satisfy the inelastic scattering condition Eq. (4) simultaneously. So the most promising situation is that DM and nuclei have similar masses and δ must not be large. 

The terrestrial iDM capture and annihilation do 

not reach equilibrium in ordinary DM scenario $^{5}$. Following from Eq. (2), the DM annihilation rate is 

where t$_{⊕}$ is the age of Earth, C$_{⊕}$ is the capture rate of the DMs in the Earth. The equilibrium time, effective annihilation rate is defined as t$_{eq}$ ≡ 

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