A steady neutron source emitting neutrons at is embedded in an infinite 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 neutron source emitting neutrons at E0=2.0 MeVE_0 = 2.0\,\mathrm{MeV} is embedded in an infinite block of beryllium, for which the mean logarithmic energy decrement is ξ=0.209\xi = 0.209. ((a)) How many elastic collisions, on average, does a neutron need to slow from 2.0 MeV2.0\,\mathrm{MeV} to thermal energy (0.0253 eV0.0253\,\mathrm{eV}), using N=ln⁡(E0/Eth)/ξN = \ln(E_0/E_{\rm th})/\xi? ((b)) The source strength is S=3.0×106 cm−3 s−1S = 3.0\times10^{6}\,\mathrm{cm^{-3}\,s^{-1}} and beryllium's macroscopic scattering cross section is Σs=0.737 cm−1\Sigma_s = 0.737\,\mathrm{cm^{-1}}. Compute the flux per unit lethargy S/(ξΣs)S/(\xi\Sigma_s) in the 1/E1/E region. If the beryllium is replaced by graphite, for which ξΣs=0.0620 cm−1\xi\Sigma_s = 0.0620\,\mathrm{cm^{-1}}, with the same source strength, compute the new flux per unit lethargy and the factor by which it has changed. ((c)) The Doppler width of a resonance is ΓD=2ErkBT/A\Gamma_D = 2\sqrt{E_rk_BT/A}. If both the resonance energy ErE_r and the absolute temperature TT are doubled while the mass number AA is unchanged, by what factor does ΓD\Gamma_D change? If instead AA is quadrupled while ErE_r and TT are unchanged, by what factor does ΓD\Gamma_D change?

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