The reactivity effect of Xe

In an elementary account of the effect of the 135Xe isotope, one wishes to relate the macroscopic cross-section to the reactivity effect. In an early treatment, still commonly followed in teaching, Glasstone and Edlund (1952) treat the reactivity effect via the four-factor formula and the effective multiplication factor. This implies a lumping of the spatial effects and also a treatment of the energy effects inherent in the four-factor formula for the infinite multiplication factor. An alternative treatment would take a one-group diffusion model and assess the reactivity effect accordingly. This approach leads to a different result. The purpose of this note is to clarify the difference and see that it depends in part on the energy weighting but also on a small but unnecessary approximation made in the conventional treatment. (author)