Consider a collision between two particles of mass m and m₁, in which the particle of mass m₁ is initially at rest. Denote the scattering angle in the center of mass coordinate system by χ and in the laboratory coordinate system (as seen by an observer at rest) by χL.

(a) Show that

(b) Show that the relationship between the differential scattering cross section in the laboratory system σ_L(χ_L) and in the center of mass coordinate system σ(χ) is given by

Note that when m₁ = ∞ we have χ_L = χ and σ_L(χ_L) = σ(χ).

(c) Verify that when m = m₁ we obtain χ_L = χ/2 and σ_L(χ_L) 4 cos (χ/2) σ(x).

Transcribed Image Text:

tan XL sin X cos x + (m/m₁)