Assume that a free electron is at rest. At a distance r from it, another electron is travelling along the z direction. If θ represents the angle between r and z, v represents the velocity of the incident electron and the instant of impact is t = 0, − vt = r cosθ. (4.1) Defining the impact parameter b by b = r sinθ, (4.2) it is possible to see that b is the distance from the trajectory of the incident electron to the target: b2 + v2t2 = r2. (4.3) F indicates the force of repulsion between the two electrons, where Fz = e 2cosθ/r2 (4.4) and Fx = e2sinθ/r2, (4.5) and pz and pxare the components of the momentum transferred to the target electron. As cotθ = −vt/b, (4.6) differentiating with respect to θ, we can obtain dt/dθ=b/vsin2θ. (4.7) Therefore, 1/r2dt/dθ=1/bv. (4.8)
Free Path Impact Parameter Dielectric Function Inelastic Scattering Optical Data
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