A Modern Approach to Quantum Mechanics · Problem 13.9

Photons and Atoms — John S. Townsend

Physics — Quantum Mechanics · partial-wave-low-energy-differential-cross-section

Problem

A particle is scattered by a spherically symmetric potential at sufficiently low energy that the phase shifts

\delta_l = 0

for

l > 1

(that is, only

\delta_0

and

\delta_1

are nonzero). Show that the differential cross section has the form

\frac{d\sigma}{d\Omega} = A + B\cos\theta + C\cos^2\theta

and determine

A

B

, and

C

in terms of the phase shifts. Determine the total cross section

\sigma

in terms of

A

B

, and

C