Principles of Quantum Mechanics · Problem 19.13

Scattering Theory — R. Shankar

Physics — Quantum Mechanics · resonance-scattering

Problem

Near a resonance, the

l

-th partial wave cross section has the Breit-Wigner form:

\sigma_l = \frac{4\pi}{k^2}(2l+1)\frac{(\Gamma/2)^2}{(E - E_0)^2 + (\Gamma/2)^2}

(a) What is the maximum value of

\sigma_l

at resonance? (b) Show that

\Gamma

is the full width at half maximum of the resonance peak. (c) Relate

\Gamma

to the lifetime

\tau

of the resonant state.