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Using the method of weighted residuals, a detailed numerical study is made of the neutronics of spherical cold neutron sources composed of liquid hydrogen and liquid deuterium in reactor moderators of light water, heavy water and graphite. Particular attention is paid to the physical effects at the cold source boundary. The computations allow a number of conclusions to be made on the best designs of spherical cold source configurations. It is found that for small spherical sources there is little difference in neutron gain using either normal-hydrogen or para-hydrogen, and that the largest gains are obtainable from large deuterium-filled sources.

A numerical investigation is made of neutron rethermalization effects in light water near physical temperature discontinuities and discontinuities in 1/ν-poisoning. It is shown that calculations of effective neutron temperatures in unpoisoned water systems possessing only temperature discontinuities are insensitive to the details of the scattering model assumed, and that rethermalization occurs within 1 cm of the temperature interface. However, with or without the presence of physical temperature discontinuities but with one region poisoned, effective temperature differences of up to 70 K exist between predictions using the Nelkin model and the Haywood frequency distribution for the water molecule. In this case, rethermalization occurs up to 2 cm into the poisoned region.

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A detailed analysis is made of the spatial variation of the effective thermal neutron temperature near temperature discontinuities in large volumes of graphite and light water. For graphite comparisons are made with recent measurements by Day. It is seen that it is important that proper consideration be made for the gradient of the epithermal flux. For water a number of predictions are made for both poisoned and unpoisoned systems and some doubt is cast on the feasibility of such measurements for determining the accuracy of different scattering kernels for light water. It is demonstrated, for both graphite and light water, that additional information can be obtained by extracting neutron beams at angles other than perpendicular to the axis of the system.