For high energy neutrons, absorption cross-sections are typically low and vary slowly. The neutron transport problem is then simple to solve. However, in the resonance region, in particular in heavy elements such as tungsten, the problem is more complex. The cross-sections tend to have a great deal of structure; their variations are substantial, sudden and irregular. In the energy range 1-100 eV the tungsten isotope absorption cross-sections have giant resonances. The resonances are resolved when they have been measured, generally up to a given energy, above which, but before the continuum, only statistical parameters are know to allow their reconstruction in a pointwise energy format. In energy ranges with no resonances, the neutron flux tends to follow smoothly the "slowing down", scattering and absorption laws, but at the resonance edge, the total cross-section increases sharply and induces a decrease in the flux roughly of inverse proportion. The neutron flux then has two components: a smooth slowing-down function and a fine structure that presents sharp dips at the resonance edges. These dips lead to a substantially reduced absorption reaction rate. This effect is called self-shielding and its magnitude is extremely dependent upon the geometry (heterogeneity), the isotopes involved (overlapping of different isotope resonances may be a factor) and the surrounding materials (moderator, coolant).

Such behaviour, to be properly represented in a computational model, requires a continuous energy treatment of the cross-section or a groupwise with probability table treatment. Monte Carlo neutron transport codes are capable of such modelling and present the advantage of working in three dimensions. An effective cross-section may be derived locally, from the Monte Carlo pointwise results, that accounts accurately for these effects. In activation calculations, where the multigroup cross-sections are uniformly processed on the basis of infinitely dilute material, the effective cross-section needs to be used for all channels and isotopes that have significant resonances. To ignore this corrective procedure leads to an overestimation of the reaction rate and any response function derived from it.

Tungsten is a candidate material for the plasma facing components (PFC) of the divertor and baffle of the ITER device. Three-dimensional neutronic modelling of the ITER divertor has been performed using the Monte Carlo code TRIPOLI. The divertor cassette was divided into nodes, chosen according to the nuclear properties and materials of the components with an heterogeneous representation of the PFC. FISPACT-FENDL/A-2.0 inventory calculations, with effective cross-section replacement for all tungsten absorption channels, modelled the activation responses. It is shown that a factor of up to 3 overestimation of the tungsten decay heat has been predicted previously when using homogeneous modelling and no effective cross-section correction.

*This work was jointly funded by the UK Department of Trade and Industry and Euratom