The nuclear parameters of a reactor lattice may be determined by critical experiments on that lattice, by theoretical calculations in which only cross sections are used as input, or by methods which combine theory and experiment. Of those methods which combine theory and experiment, the Single Element Method, abbreviated SEM, is shown to have great usefulness. As used here, the method combines experiments on the smallest meaningful unit of fuel - a single fuel element - with a theory which relates the behavior of a lattice of such elements to the experimentally determined behavior of the single element. This particular division of the problem into theory and experiment is useful for at least three reasons. First, several parameters which characterize a reactor lattice - the thermal utilization and resonance escape probability, for example - often depend strongly and in a complicated manner on the properties of individual fuel elements, but only depend weakly or in a simple manner on interactions between the fuel elements. In the Single Element Method, the largest contribution to these parameters is determined by measurements on a single fuel element, and only a relatively small correction to account for the presence of the rest of the fuel elements need be estimated theoretically. Second, the determination of lattice parameters in this way represents a desirable saving of time, money, effort, and material over their determination in critical or exponential experiments. Third, it is shown that the method provides an excellent way of correlating the results of experimental measurements, since it shows what pertinent variables must be used to express the quantity of interest in a linear or nearly linear fashion. Values obtained by the SEM for the thermal utilization of lattices of uranium rods in heavy water are accurate to about 0.3 percent (by comparison with THERMOS). Values of P28, 28, and C* are obtained by the SEM for the same lattices to an accuracy of between five and ten percent (by comparison with experiment). The same method yields values of 28 with are equally accurate in lattices moderated by light water. In addition, the theoretical development of the SEM predicts that P28, 28, C*, and 625 should vary nearly linearly with the inverse of the unit cell volume (for a fixed size of fuel element). This explains the experimentally observed behavior and provides an important tool for the rational correlation of experimental results.

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This is the final report in an experimental and theoretical program to develop and apply single- and few-element methods for the determination of reactor lattice parameters. The period covered by the report is January 1, 1968 through September 30, 1970. In addition to summarizing results for the entire contract period, this report also serves as the final annual report; thus, work completed in the period of October 1, 1969 through September 30, 1970 is dealt with in more detail than the earlier work. Methods were developed to measure the heterogeneous parameters 17, [Gamma] [eta] and [Alpha] for single fuel elements immersed in moderator in an exponential tank using foil activation measurements external to the fuel. These methods were applied to clustered fuel rods in D 20 moderator and single fuel rods in H 20 moderator, and the results were extended to and compared with data on complete multi-element lattices reported by other laboratories. Advanced gamma spectrometric methods using Ge(Li) detectors were applied to the analysis of both prompt and fission product decay gammas for the nondestructive analysis of the fuel used in this work. The latter includes both simulated burned fuel containing plutonium and actual burned fuel irradiated to 20,000 MWD/T in the Dresden BWR.