Stationary and time-dependent transport of neutrons of one speed has been studied in spheres with totally absorbing cores. For stationary, critical reactors the number of secondaries per collision has been calculated numerically for various inner and outer radii. In the time-dependent case, the decay constant has been calculated for spherical shells of different inner radii and thicknesses. For a fixed ratio between shell thickness and inner radius, the curve of the decay constant versus shell thickness crosses the Corngold limit in the same way as the curve for a homogeneous sphere. When the ratio goes to zero the curve approaches that for an infinite slab. The behaviour is discussed in view of a new result from collision theory, viz. that the following condition must be fulfilled for a body at the point where the decay constant curve crosses the Corngold limit: the average exit distance of the neutrons is equal to the mean free path for scattering.