A steady source injects fission neutrons into an infinite

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 steady source injects fission neutrons into an infinite, non-absorbing moderator at a steady rate

S

. In the

1/E

slowing-down region the flux per unit lethargy is

E\phi(E) = S/(\xi\Sigma_s)

, where

S

is the number of neutrons crossing each energy per unit volume per second and

\xi\Sigma_s

is fixed by the moderator. ((a)) For a source strength

S = 5.0\times10^{5}\,\mathrm{cm^{-3}\,s^{-1}}

, compute the flux per unit lethargy in graphite, for which

\xi\Sigma_s = 0.0620\,\mathrm{cm^{-1}}

, and in heavy water, for which

\xi\Sigma_s = 0.177\,\mathrm{cm^{-1}}

. ((b)) A

^{238}\mathrm{U}

resonance at

E_r = 6.67\,\mathrm{eV}

has natural width

\Gamma = 24.5\,\mathrm{meV}

. Using

\Gamma_D = 2\sqrt{E_rk_BT/A}

with

A=238

, compute the Doppler width at

T=300\,\mathrm{K}

and at

T=900\,\mathrm{K}

, and give the ratio of the two widths. ((c)) State, without further calculation, whether raising the fuel temperature from

300\,\mathrm{K}

900\,\mathrm{K}

increases or decreases the resonance escape probability

p

for lumped

\mathrm{UO_2}

fuel, and explain why the same statement would not hold for infinitely dilute

^{238}\mathrm{U}