# 4.6.1: Essential Cross Sections


The key for understanding the physical foundations of the operation of a nuclear reactor is the energy dependence of relevant cross sections of U-235 and $$U-238$$. The plots are shown in Fig. $$\PageIndex{1}$$.

In the process of U-235 fission, high energy neutrons are created - with average energy of about $$1.6 \mathrm{MeV}$$. For such energies, the U-238 cross section for fission is somewhat lower (about 50\%) than that of U-235 (see the red and the green curves on the right-side part of Fig. $$\PageIndex{1}$$). Yet, there are 140 atoms of U-238 per one atom of U-235, so the neutron has a very small chance, one-out-of-seventy to hit another U-235 nucleus and thus to support the chain reaction - and if it hits a U-238 nucleus, it may trigger a fission, but - as was stated before - the U-238 fission does not release any neutrons, so that it does not support the chain reaction.

The situation drastically changes in the region of very low energies, of $$0.1 \mathrm{eV}$$ and less. Here, the fission cross section for U-238 is of the order of micro-barns only. The dominant is the cross section for "radiative capture of neutron", i.e., the U-238 nucleus emits a gamma photon and changes into U-239 . But now the cross section for U-235 fission is about 3 timeshigher, so that the $$0.7 \%$$ of U-235 nuclei have a five-to-one chance over the $$99.3 \%$$ of U-238 to capture the neutron. So, the chain reaction may be saved - if the fission neutron could be removed from the uranium fuel, forced to give away its high energy - or lowering it about ten million times (from $$1 \mathrm{MeV}$$ down to $$0.1 \mathrm{eV}$$ ) - and only then returned to the fuel.

__________________________________________________

$${ }^{1} \mathrm{U}-239$$ after half-life of only $$2.35$$ minutes changes via a $$\beta$$ decay to Neptune, and after another $$\beta$$ decay with half-life of $$2.4$$ days changes to Plutonium-239, with half-life over 20,000 years - not a nice element, as it is the essential component in the A-bombs and $$\mathrm{H}$$ bombs.

4.6.1: Essential Cross Sections is shared under a CC BY 1.3 license and was authored, remixed, and/or curated by Tom Giebultowicz.