Calculation of the delayed neutron effectiveness factor using ratios of k-eigenvalues

In this work, we derive from the transport equation the effectiveness factor used in the βeff calculation and show that, to a first approximation, it is equal to the ratio of two k-eigenvalues: one obtained using the total neutron spectrum, and the other obtained using only the delayed neutron spectrum. This method, which we shall refer to as the k-ratio method, has been tested using several different types of reactor systems. In this report we present the results for the simplest of these systems — the Godiva-I assembly at the Los Alamos Critical Experiments Facility (LACEF). Although the method is not exact, it does yield results that are remarkably close to the traditional adjoint-weighting method.