Solutions of the neutron transport equation with a one-term degenerate scattering kernel for a polycrystalline plane slab with finite thickness are derived with use made of the eigenfunction expansion method. The effect brought upon the energy spectrum of reflected and of transmitted neutrons by changes in temperature are examined by numerical calculations. No discontinuous change occurs in the spectra upon passage the critical temperature, below which the discrete eigenvalue vanishes, despite the abrupt change undergone at this point by the analytical solution. The spectra of the reflected and the transmitted neutrons differ entirely from each other, particularly below the Bragg energy. The discrepancy between these spectra increases with lower-ing temperature and widening slab thickness. A sharp peak occurring in the energy spectrum for transmitted neutrons is found to grow significantly with decreasing temperature.

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Irreversible circulation of fluctuation, α, is introduced as a new variable for the analysis of reactor noise in the normal case, which further develops our previous for-mulation based on the system size expansion method. It is shown that α-considered in conjunction with the variance σ-provides useful information about reactor noise, apart from the data we usually obtain on power spectral density. The relations holding between α and the conventionally used variables are given for the case of steady state. The present formalism is applied to a non-linear system with three degrees of freedom (total neutron number, fuel energy and coolant energy), to examine numerically the behavior of the fluctuations. The stability is illustrated as a phase diagram in a reactor-parameter space. It is shown that the so-called soft- and hard-mode instabilities can be distinguished by observing α. It is also demonstrated that appropriate processing of such quantities as α and σ will provide advance information on instabilities in power reactors.

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In the thermal design of a fast reactor, it should be most effective to reduce hot spot factors to the lowest possible level compatible with safety considerations, in order to minimize the design margin for the temperature prevailing in the core. Hot spot factors account for probabilistic and statistic deviations from nominal value of fuel element temperatures, due to uncertainties in the data adopted for estimating various factors including the physical properties. Such temperature deviations necessitate the provision of correspondingly large design margins for temperatures in order to keep within per-missible limits the probability of exceeding the allowable temperatures.
Evaluation of the desired accuracy for hot spot factors is performed by a method of optimization, which permits determination of the degree of accuracy that should minimize the design margins, to give realistic results with consideration given not only to sensi-tivity coefficients but also to the present-day uncertainty levels in the data adopted in the calculations. A concept of "degree of difficulty" is introduced for the purpose of determining the hot spot factors to be given higher priority for reduction.
Application of this method to the core of a prototype fast reactor leads to the con-clusion that the hot spot factors to be given the highest priority are those relevant to the power distribution, the flow distribution, the fuel enrichment, the fuel-cladding gap conductance and the fuel thermal conductivity.

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An analytical method based on a stagewise discrete model is developed to calculate the effect of deviations in stage cut on the performance of a uranium enriching cascade. Both deterministic and stochastic effects are dealt with in terms of derivatives of flow rates with respect to stage cuts. The derivatives are calculated with no restrictions applied to the shape of the cascade or to the characteristics of the separators. This circumstance permits application of this method to an actual cascade of almost any type, composed of separators with different characteristics.
A tapered cascade is analyzed by the present model in first order approximation, and the results are compared with those given by other authors.

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An evaluation is made of the fuel cycle costs for molten-salt reactors (MSR's), developed at Oak Ridge National Laboratory. Eight combinations of conditions affecting fuel cycle costs are compared, covering ²³³U-Th, ²³⁵U-Th and ²³⁹Pu-Th fuels, with and without on-site continuous fuel reprocessing. The resulting fuel cycle costs range from 0.61 to 1.18 mill/kWh. A discussion is also given on the practicability of these fuel cycles.
The calculations indicate that somewhat lower fuel cycle costs can be expected from reactor operation in converter mode on ²³⁵U make-up with fuel reprocessed in batches every 10 years to avoid fission product precipitation, than from operation as ²²³U-Th breeder with continuous reprocessing.

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Using an AISI 304 stainless steel loop, the effect of exposure to flowing heated sodium was examined on materials considered suitable for LMFBR steam generators. The test specimens were exposed for 1, 000 hr at temperatures ranging of 550°425°C, descending in the direction of sodium flow. The oxygen concentration in the sodium was about 8 ppm. The materials tested were ferritic 2 1/41Cr-1Mo, 2 1/4 Cr-1Mo-Nb, high Cr-1Mo and austenitic AISI 316 stainless steel. The loss of weight through exposure to liquid sodium was found to depend upon the heat-treatment history in the case of the 2 1/4 Cr-1Mo steels. The principal cause of this loss of weight was confirmed to be decarburization, and dif-ferences in the heat-treatment history may possibly influence the decomposition behavior of carbides. Increasing the chromium content in Cr-1Mo steel specimens tended to modify the behavior of the specimen in the direction of increasing carbon concentration near the specimen surface during exposure to liquid sodium, altering the effect of exposure from decarburization to carburization at a chromium content somewhere between 3 and 5%. Thermal aging of annealed 2 1/4 Cr-1Mo steel was found to reduce its tensile strength at 500°C to a marked degree.

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