A steady fission source of strength operates inside a large tank of light water

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

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

Problem

A steady fission source of strength

S = 2.0\times10^{5}\,\mathrm{cm^{-3}\,s^{-1}}

operates inside a large tank of light water, treated as an infinite, non-absorbing moderator with

\xi\Sigma_s = 1.35\,\mathrm{cm^{-1}}

(uniform, no spatial dependence). ((a)) Starting from a balance of the slowing-down density in the lethargy variable

u = \ln(E_0/E)

, derive the flux spectrum

\phi(E)

in the region below the source energy, and evaluate it at

E = 5.0\,\mathrm{eV}

. ((b)) Deep in the same tank the slowed neutrons thermalise into a Maxwellian population at temperature

T

. A thin gold foil, whose neutron-capture cross section follows the

1/v

law with

\sigma_0 = 98.8\,\mathrm{b}

v_0 = 2200\,\mathrm{m\,s^{-1}}

, is immersed in a thermal neutron density

n = 1.0\times10^{13}\,\mathrm{cm^{-3}}

. Starting from the rate integral

\int \sigma(v)\,v\,n(v)\,\mathrm{d}v

, derive the capture rate per gold atom and show that its value does not depend on whether the water is at

T=293.6\,\mathrm{K}

T=600\,\mathrm{K}

. Give the numerical value.