Higher Order Perturbation Method in Reactor Calculations

A higher order perturbation formula for calculating changes in the reactivity up to a desired order in concise form is given; the formula uses the iterative technique well known in quantum mechanics and in the neutron life-cycle method. This procedure is possible only when the adjoint flux in the unperturbed system is used as the weighting function. The higher order perturbation formula contains the interaction between the perturbation inserted and its surrounding medium, but it consists only of the integration over the perturbed region. Numerical calculations up to the third-order perturbation show that the first-order perturbation technique gives a low value for the reactivity worths of fission, absorption, and scattering materials; further, the n’th-order perturbation is proportional to the n’th power of the concentration of an inserted perturbation.