It can be deduced from the previous equation the maximum scattering angle, θ’max, as equation 2 describes: (2) Using these parameters, absorber foils do not need to be incorporated into the instrument design. When using heavy ion beams and the parameters above, the geometry can be estimated as to allow for incident particle collision and scattering at an angle deflected away from the detector. This will prevent degradation of the detector from the more intense beam energies. The differential elastic recoil cross-section σERD is given by: (3) where Z1 and Z2 are the atomic numbers of projectile and sample atoms, respectively. For m2/m1 <<1 and with approximation m=2Z; Z being the atomic number of Z1 and Z2. In equation (3) two essential consequences can be seen, first the sensitivity is roughly the same for all elements and second it has a Z14 dependence on the projector of the ion. This allows for the use of low energy beam currents in HI-ERDA preventing sample degradation and excessive heating of the specimen. When using heavy ion beams, care must be taken for beam-induced damage in sample such as sputtering or amorphization. If only nuclear interaction is taken into account, it has been shown that the ratio of recoiling to displaced atoms is independent of Z1 and only weakly dependent on the projectile mass of the incident ion. With heavy ion bombardment, it has been shown that the sputter yield by the ion beam on the sample increases for nonmetallic samples and enhanced radiation damage in superconductors. In any case, the acceptance angle of the detector system should be as large as possible to minimize the radiation damage. However, it may reduce the depth profiling and elemental analysis due to the ion beam not being able to penetrate the sample. The figure on the right summarizes the principles of ERDA and how a spectrum is obtained. This demand of a large acceptance angle, however, is in conflict with the requirement of optimum depth resolution dependency on the detection geometry. In the surface approximation and assuming constant energy loss the depth resolution δx can be written: (4) where Srel is the relative energy loss factor defined by: (5) here, α and β are the incidence angles of the beam and exit angle of the recoiling ion respectively, connected to the scattering angle ϕ by ϕ=α+β. It should be noticed here that the depth resolution