Scattering Cross-Sections and Depth Resolution in ERD

The chance that one particle from the beam ejects a recoil of element Z2, M2) in such a way that it starts moving in the direction of the detector is proportional to the areal density (atom cm ) of this element and the detector solid angle of the detector. Treating the interaction as purely Rutherford scattering (since the energy available in the center of mass is at least five times below the Coulomb barrier) the elastic scattering cross-section is given by Rutherford differential cross-section for ERD i.e., 

The 1 /Eo dependence of the scattering cross-section shows that the yield of recoils, and hence the sensitivity of the technique, increases with depth due to the decreasing energy Eq of the incident projectiles. 

In the surface approximation and assuming constant energy loss, the depth resolution 5x can be written as 

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