The radiative-capture reaction has a measured thermal cross section at

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Nuclear reactions · Nuclear reactions

The Nucleus Resolved, Ch Reaction mechanisms: resonances, the compound nucleus, direct reactions and the optical model

Problem

The radiative-capture reaction

^{197}\mathrm{Au}(n,\gamma)^{198}\mathrm{Au}

has a measured thermal cross section

\sigma_0 = 98.7\,\mathrm{b}

E_0 = 0.0253\,\mathrm{eV}

, and follows the

1/v

law from meV energies up to just below its first resonance at

4.9\,\mathrm{eV}

. ((a)) Find the capture cross section at

E = 0.010\,\mathrm{eV}

. ((b)) Find the capture cross section at

E = 0.10\,\mathrm{eV}

. ((c)) Explain, starting from the Breit-Wigner formula far below a resonance, why

\sigma\sqrt{E}

is constant in this region.