Multigroup diffusion calculations can normally be expected to predict the reactivity of a system within about 0.5% and the distribution of power within about 4% throughout most of the core and within 6% close to control rods or the edge of the core. The errors are due partly to uncertainties in the basic cross-section data and partly to the approximations inherent in diffusion theory. The latter explain the larger errors near interfaces between different regions.

It is possible to check calculations by means of measurements in a reactor. In the past such experimental checks were very valuable but they have become less important as the reliability of calculation methods has been confirmed.

The most useful experimental techniques are to measure reaction rates or reactivity changes due to perturbations. Fission rates can be measured with fission chambers, and for example a 238U chamber that is responsive to the flux at high energies can be combined with a 235U chamber sensitive to the flux in the keV range to assess the accuracy of a computation over the whole energy range of interest. Neutron spectra can be measured by proportional counters or time-of-flight methods. Perturbation measurements can be made by inserting small samples of various materials into the core and noting how the control rods have to be adjusted to maintain a critical balance. The control rods can be calibrated dynamically by observing the rate at which the power diverges when they are moved slightly from the critical position.

These measurements can in principle be made on power reactors but it is often inconvenient to do so partly because it is difficult to obtain access to the core, partly because the temperature and neutron flux in the core may be too high for the measuring instruments, and partly because performing reactor physics experiments conflicts with use of the reactor for the purpose for which it was built. It is very difficult to make a perturbation measurement at anything other than very low power, for example.

For this reason most, but not all, experimental checks on reactor physics calculations have come from zero power reactors. The most productive have been demountable facilities in which a reactor of almost any required composition could be assembled from samples of the various material — structure, fuel, and even sodium coolant — present in a power reactor. Test reactors of this type operated at a power of typically a few watts so that no cooling was needed. The use of zero-power experimental reactors is described in more detail by Broomfield et al. (1969).

Figure 1.6 shows calculated and measured neutron energy spectra for a zero-energy experimental assembly (Broomfield et al., 1969). The assembly was similar in composition and size to a power reactor except that it contained carbon instead of oxygen and sodium. The spectrum

was measured by a time-of-flight method, and is compared with the result of a 46-group fundamental mode calculation. The depression in the flux caused by the iron resonance at 30 keV can be seen clearly. If there had been sodium in the assembly there would have been another depression due to the important sodium resonance at 3 keV. The quantity plotted on a logarithmic scale in Figure 1.6 is the flux per unit lethargy, ф(и). “Lethargy” Uis defined by U = — logE, where E is the neutron energy. If ф(Е)dE is the flux of neutrons with energy in the range E ^ E + dE then ф(и) = 2.303Еф(Е).