is : This Figure is plane representation of a Recoiled ion path on the target surface, when both incoming and outgoing paths are in perpendicular to target surface In this simple case a collisional plane is perpendicular to the target surface, the scattering angle of the impinging ion is θ = π-θ1-θ2 & the recoil angle is φ = π-θ1-θ3. Target angle with the collisional plane is taken as α, and path is augmented by a factor of 1/cos α. For the purpose of converting outgoing particle in to collision depth, geometrical factors are chosen. For recoil R(φ, α)is defined as sin L3 = R(φ, α)L1 For forward scattering of the projectile R(φ,α)by:L2 = R(θ,α)L1 R(θ,α) = cos θ1cosα/Sin θ√(cos2α-cos2θ1)-cosθ1cosθ The Figure below is the Geometrical configuration of recoil spectrometry. Paths of scattered particles are considered to be L1 for incident beam, L2 is for scattered particle, and L3 is for recoiled atoms. Energy Depth Relationship The energy E0(x) of the incident particle at a depth (x) to its initial energy E0 where scattering occurs is given by the following Equations. (Tirira. J., 1996) similarly Energy expression for scattered particle is: and for recoil atom is: The energy loss per unit path is usually defined as stopping power and it is represented by : Specifically, stopping power S(E) is known as a function of the energy E of an ion. Starting point for energy loss calculations is illustrated by the expression: By applying above equation and energy conservation Illustrates expressions in 3 cases where E01(x)= KE0(x)and E02(x)=K'E0(x) S(E)and S_r(E) are stopping powers for projectile and recoil in the Target material Finally stopping cross section is defined by ɛ(E)= S(E)/N ɛ is stopping cross section factor. To obtain energy path scale We need to evaluate energy variation δE2 of the outgoing beam of energy E2 from the target surface for an increment δx of collisional depth, here E0 remains fixed. Evidently this causes changes in path lengths L1 and L3 a variation of path around the collision point x is related to the corresponding variation in energy before scattering : δL1 = δE0(x)/S[E0(x)----- Equation 5 Moreover, particles with slight energy differences after scattering from a depth x undergo slight energy losses on their outgoing path. Then change δ L3 of the path length L3 can be written as δL3 = δ(K’E0(x)]/ Sr[K’E0(x)) + δ(E2)/SrE2) -----Equation 6 δ L1 is the path