Research reactor control rods are composed of materials which strongly absorb thermal neutrons. In such materials the low-energy neutron flux varies rapidly as a function of position, which causes steep flux gradients near the absorber surface. Under these conditions Fick's law of diffusion is invalid, and so, without special methods, diffusion theory cannot be used to calculate control rod worths in thermal research reactors. Higher order methods, such as Monte Carlo techniques, are commonly used for this purpose. However, reasonably accurate control rod worths can be computed within the framework of diffusion theory by characterizing the absorber material by means of a group-dependent set of effective diffusion parameters (D_eff and S_a-eff) or by specifying group-dependent neutron current-to-flux ratios (i.e. internal boundary conditions) on the absorber surface.

The purpose of this paper is to show how effective diffusion parameters and internal boundary conditions can be calculated. Using these techniques, control rod worths are computed and compared with results of detailed Monte Carlo calculations and with measured values.