The neutron detection efficiency is a parameter required in the measurement of reactivity by the modified source technique. The direct solution of the detection efficiency at a perturbed state is costly. To solve for this, a particular variational functional, the Lewins' type variational functional, is presented. The functional is a ratio of two other functionals, each dealing with a reaction rate. The evaluation of this particular functional was done by treating the numerator and the denominator functionals separately. This leads to three flux equations, one for forward flux, and two for adjoint fluxes. The advantages of this formulation over, and the equivalence of this formulation to, the conventional functional presented in the literature are described in detail. The flexibility of the proposed functional is demonstrated by using it to estimate the detection efficiency with four different methods: variational interpolation, conventional variational, variational extrapolation, and multi- reference-state variational. Results are presented for one-dimensional and two- dimensional problems. All results are compared with direct calculations. In all cases, the results show that the variational interpolational method and the multi- reference-state variational method are efficient and practically acceptable.

A method for obtaining solutions to the time-independent Boltzmann neutron transport equation on triangular grids with nonorthogonal boundaries and anisotropic scattering is developed. A functional is obtained from the canonical form of the multigroup transport equation. The angular variable is then removed by expanding the functional in spherical harmonics, retaining only the first two moments and limiting the anisotropic scattering to be linear. The finite element method is then implemented by using quadratic Lagrange-type interpolating polynomials to span the spatial domain. The resultant set of coupled linear equations is then solved iteratively. The applicability of convergence acceleration techniques developed for the finite difference method is tested and implemented where appropriate. Finally, a number of numerical experiments are performed to evaluate the performance of the proposed method. The results are compared to results obtained by various established methods. In all cases, agreement is excellent. 16 figures, 7 tables. (auth)