The Neutron Flux Perturbation Due to an Absorbing Foil; A Comparison of Theories and Experiments

Skyrme has given a theoretical treatment of the perturbation of the neutron flux in a diffusing medium by an absorbing foil. His theory is re-examined, with particular reference to the modification proposed by Ritchie and Eldridge, and the “edge correction” is evaluated. The accuracy of this modified Skyrme theory is tested by comparison with Dalton and Osborn’s computer calculations for monokinetic neutrons; the agreement is generally better than 1%. This theory is then extended to a Maxwellian neutron spectrum, for which computer calculations are not available, with the result

A is the activity per unit mass of a foil of thickness τ (in units of the absorption mean free path), Ao that of a zero thickness foil, , where t and R are the thickness and radius of the foil. The bars denote averages over the Maxwellian spectrum. The flux-depression parameter g is of the order of R/λ_tr, but its exact value depends on the velocity dependence of the transport mean free path, and on the thermalization properties of the medium. This formula is used to obtain, from the available measurements of the dependence of A on foil thickness, “experimental” values of g. For both graphite and hydrogenous media they are smaller than expected.