A natural-uranium metal-rod lattice is moderated by heavy water

PHYSICS · Subjective · Fermi University Physics · Nuclear Physics · Nuclear reactions · Fission, fusion and nuclear energy

Energy from Physics, Ch The critical reactor: neutron diffusion, buckling and the size of a core

Problem

A natural-uranium metal-rod lattice is moderated by heavy water, for which the moderating power per fuel atom is

\xi\Sigma_s/N_F = 220\,\mathrm{b}

. The quoted correlation for the effective resonance integral of natural-uranium metal rods (density

\rho = 19.1\,\mathrm{g\,cm^{-3}}

) is

I_{\rm eff} \approx 2.95 + 25.8\sqrt{S/M}\ \mathrm{(barns)},

where

S/M = 2/(\rho r)

is the surface-to-mass ratio, in

\mathrm{cm^2\,g^{-1}}

, of a rod of radius

r

in centimetres. Estimate the resonance escape probability

p

of the lattice for rods of radius

r = 1.2\,\mathrm{cm}

, using the narrow-resonance form

p = \exp\!\left[-\dfrac{N_FI_{\rm eff}}{\xi\Sigma_s}\right]