When neutrons are scattered by light nuclei there is a significant transfer of energy between the nucleus and the neutron, this being the moderation process. Consequently, when neutrons which are already ther — malised are scattered by light nuclei whose energy is higher than that of the neutrons, the kinetic energy ot the neutron is increased; the neutron energy spec­trum is ‘hardened’. Heavy nuclei (e. g., U-238) can aUo harden the spectrum but with a greatly reduced eiticiency. The effect arises from moderator and can temperature changes in magnox reactors. In addition, !n AGRs, iuel temperature changes contribute to spec­trum hardening as a result of collisions with the oxy — v’en atoms of the oxide fuel.

The absorption cross-section of many materials varies as the inverse of the neutron velocity (1/v). Since, for a given (constant) cross-section, the probability of interaction increases linearly with velo­city, the absorption probability is constant with neutron velocity. Graphite and steel are typical 1/v absorbers and their behaviour is unaffected by tem­perature. Certain materials, however, show significant deviation from this general rule; in the reactor context U-235, Pu-239 and Xe-135 are important non-1 v absorbers. Departures from 1/v behaviour are usually due to the presence of resonances.

U-235

The absorption cross-section for U-235 falls off faster than 1 /v. Any hardening of the thermal spectrum causes a reduction in the reaction rate relative to the overall absorptions in the lattice giving a negative contribution to the temperature coefficient.

Pu-239

The absorption cross-section of Pu-239 shows a broad resonance at 0.29 ev. This is higher than the mean energy of the thermal neutrons in a gas cooled re­actor in normal conditions. Any hardening of the neutron spectrum gives an increased number of ab­sorptions relative to U-235. Pu-239 has a larger value of i} (the number of neutrons per absorption) than U-235, giving a positive contribution to the tempera­ture coefficient.

Xe-135

This is a parasitic absorber in nuclear reactors and has a strong absorption resonance at 0.08 ev — hardening the neutron spectrum pushes neutrons out of the resonance giving a positive temperature effect.

Radial fine structure

The flux in a fuel pin is depressed due to absorption. If the neutron spectrum hardens, neutron scattering increases (constant cross-section) whereas absorption remains constant (1/v cross-section) thus tending to flatten the flux. This gives relatively less absorption in the moderator and more reactions in the fuel, i. e., a positive feedback effect.