A Perturbation Method Which Utilizes the Variational Principles Associated with the Neutron Diffusion Equation

This paper presents an operator-type perturbation method which may be used to solve perturbation problems associated with the neutron diffusion equation. The method is related to the hybrid Schrodinger-Heisenberg operator methods used in quantum mechanics. The operators are derived from the variational principles associated with the neutron diffusion equation; therefore, the method includes the advantages of the variational method. Two applications in one-dimensional, one-group diffusion theory are illustrated. The first example illustrates how a plane source of neutrons can be treated as a perturbation. The solution to this problem is exact. In the second example, the solution to a simplified time-independent problem involving fission-product poisoning is presented. The solution to this example is in open form as expected. It is found by way of comparison that this operator method gives a better result in this particular example than the more familiar method of approximating the perturbed solution by an expansion in terms of eigenfunctions of the unperturbed solution.