22.101 Applied Nuclear Physics
(Fall 2004)
Problem Set No. 8
Due: Nov. 24, 2004
Problem 1
(a) Show that the conservation of kinetic energy and linear momentum during an
elastic collision requires that in the CMCS the speed of each particle is the same
before and after the collision.
(b) Does the relative speed of particle 1 with respect to particle 2 change during an
elastic collision, (1) in the CMCS and (2) in LCS?
Problem 2
Consider the problem of neutron elastic scattering in the notation as used in class.
(a) Find an expression for E4 involving E1 and angle γ (the angle between the recoil
direction of M4 and the x-axis). Is there a one-to-one relation between E4 and γ ?
(b) Eliminate γ in favor of θ c in your result in (a), then use the fact that the
scattering is isotropic in CMCS to find the distribution P(E4), the probability per
unit energy that the recoil nucleus will have energy E4.
(c) How would you obtain P(E4) directly from the result for F (
E '→ E) derived in
class? How general is your relation between P and F?
Problem 3
Verify the relation between the angular differential cross sections for neutron elastic
scattering in LCS and CMCS, σ (θ ) and σ (θ c ) , as discussed in class. Use this relation to
discuss the behavior of µ and µ c , where µ = cos θ ?