Calculational Methods of Control Rod Worth for High Conversion Light Water Reactor

By making use of the isotope approximation; neglecting squares of relative mass differences among the isotopes, the authors derived analytically approximations to ordinary diffusion coefficients in a 3- and 4- component isotope mixture. Moreover, approximations to multi-component diffusion coefficients were given on the analogy of those to the 3- and 4-component coefficients, and these approximations were verified to satisfy constrains on the exact ordinary diffusion coefficients.

For 4-component mixture of uranium hexafluoride isotopes, ²³⁴UF_6- ²³⁵UF_6- ²³⁶UF_6- ²³⁸UF₆, composition dependences of the approximation were equal to those of the exact diffusion coefficients. In addition, relative errors between the exact and the approximations were less than 0.2% for 5-component mixture of krypton 80–82-83-84-86 isotopes.