Natural uranium is mixed uniformly (not lumped into rods) with graphite at carbon…

PHYSICS · Multi-part · 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

Natural uranium is mixed uniformly (not lumped into rods) with graphite at

150

carbon atoms per uranium atom. For this lattice

\eta = 1.34

and

f = 0.94

. A colleague argues: "Metal fuel rods in graphite achieve a resonance escape probability of

p \approx 0.94

because self-shielding suppresses resonance absorption. Using this value,

k_\infty = \eta p f = 1.34 \times 0.94 \times 0.94 = 1.18

, so this homogeneous mixture is critical,

k_\infty > 1

." ((a)) Find the error in this argument. ((b)) Each carbon atom scatters about

4.7\,\mathrm b

and has

\xi = 0.158

. Find

\Sigma_s/N_F

and

\xi\Sigma_s/N_F

, use the dilute correlation

I \approx 3.9(\Sigma_s/N_F)^{0.415}\,\mathrm b

to find

I

, then compute the correct

p

and

k_\infty

, and state whether the mixture is critical.