A steady fission-like neutron source of strength sits inside a large block of beryllium

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-like neutron source of strength

S = 8.0\times10^{4}\,\mathrm{cm^{-3}\,s^{-1}}

sits inside a large block of beryllium, treated as an infinite, non-absorbing, uniform moderator with

\xi\Sigma_s = 0.154\,\mathrm{cm^{-1}}

. ((a)) From a lethargy balance, derive the flux spectrum

\phi(E)

below the source energy and evaluate it at

E = 2.0\,\mathrm{eV}

. ((b)) A tritium-breeding tile containing lithium-6, whose

(n,\alpha)

cross section follows the

1/v

law with

\sigma_0 = 940\,\mathrm{b}

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

, sits where the neutrons have thermalised into a Maxwellian at temperature

T

. Using the flux-weighted average

\bar\sigma(T) = (\sqrt\pi/2)(T_0/T)^{1/2}\sigma_0

(with

T_0 = 293.6\,\mathrm{K}

) and the mean speed

\bar v(T) = (2/\sqrt\pi)v_0(T/T_0)^{1/2}

, derive algebraically that the product

\bar v(T)\bar\sigma(T)

equals

v_0\sigma_0

for every

T

, and hence that the tritium-production rate per lithium-6 atom,

n\bar v(T)\bar\sigma(T)

, is temperature-independent. Evaluate

\bar v

and

\bar\sigma

T = 600\,\mathrm{K}

and check the product against

v_0\sigma_0