A natural-uranium fuel rod of diameter and density sits in a graphite lattice

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Nuclear reactions · Fission, fusion and nuclear energy

The Nucleus Resolved, Ch Neutrons: the reagent with no barrier

Problem

A natural-uranium

\mathrm{UO_2}

fuel rod of diameter

d = 2.0\,\mathrm{cm}

and density

\rho = 10.5\,\mathrm{g\,cm^{-3}}

sits in a graphite lattice. Hellstrand's measured correlation for

\mathrm{UO_2}

rods gives the effective resonance integral

I_{\rm eff} = 4.45 + 26.6\sqrt{S/M}\ \mathrm{b},\qquad S/M = \frac{4}{\rho d}\ \mathrm{cm^2\,g^{-1}}.

For this lattice the moderator-to-fuel ratio is such that

N_{\rm U}/(\xi\Sigma_s) = 1.45\times10^{-3}\,\mathrm{b^{-1}}

, treated as uniform over the resonance region. ((a)) Find

I_{\rm eff}

for this rod. ((b)) Find the resonance escape probability

p = \exp[-N_{\rm U}I_{\rm eff}/(\xi\Sigma_s)]