Question 3.5: Suppose that a neutron scattering collision is completely is......
Suppose that a neutron scattering collision is completely isotropic when observed in the COM coordinate system. If a neutron scatters off of a Carbon-12 nucleus in this system, what scattering angle would we observe in the LAB coordinate system if the scattering angle in the COM system is 90°? What would be the average cosine of the scattering angle?
The scattering angles in the COM and the LAB coordinate systems are related by the equation cos θ = (1 + A cos θ_1)/ \sqrt{(A^2 + 2Acosθ_1 + 1)}. Since θ_1 = 90° in the COM system, cosθ= 1/\sqrt{A^2 +1} in the LAB coordinate system. For a Carbon-12 nucleus, the value of A is 12, so cosθ = 1/\sqrt{12^2 + 1} = 0.083 and θ = 85.24°. The average cosine of the scattering angle will be <cos θ> = 0.67/A = 0.0558.