Equation 7 gives a mathematical model of the collision event when the heavier ions in the beam strike the specimen. "Ks" is termed the "kinematical factor" for the scattered particle (Eq. 8) with a scattering angle of "θ", and the recoiled particle (Eq. 9) with a recoil angle of "Φ". The variable "r" is the ratio of mass of the incident nuclei to that of the mass of the target nuclei, (Eq. 10). To achieve this recoil of particles, the specimen needs to be very thin and the geometries need to be precisely optimized to obtain accurate recoil detection. Since ERD beam intensity can damage the specimen and there has been growing interest to invest in the development of low energy beams for reducing the damage of the specimen.