Griffiths Introduction to Elementary Particles · Problem 6.15

Quantum Electrodynamics — David J. Griffiths

Physics — QFT · abc-theory-scattering

Problem

(a) Determine the lowest-order amplitude for

A + B \to A + B

. [Note: There are two diagrams.] (b) Find the differential cross section for this process in the

CM

frame, assuming

m_A = m_B = m

m_C = 0

. Express your answer in terms of the incident energy,

E

, and the scattering angle,

\theta

. (c) Find

d\sigma/d\Omega

for this process in the lab frame, assuming

B

is much heavier than

A

, and remains stationary.

A

is incident with energy

E

. [Hint: See Problem (6.8). Assume

m_B \gg m_A

m_C

, and

E/c^2

.] (d) In case (c), find the total cross section,

\sigma