Conventional formulas of the neutron cross sections based on the statistical model are modified so as to keep equality between the total cross section and the sum of the partial cross sections by taking into account the effects of the cascade process ac-companied by the emission of γ-rays from the compound nuclear states, and of other processes which compete with the neutron scattering and capture. The modifications are applied to the cross-section formulas with width-fluctuation correction and resonance-resonance interference, according to the statistical distribution law of the level widths and spacings, respectively. Examples of calculations are shown for ²³⁸U, ¹⁰⁹Ag, ¹⁰³Rh and ⁹⁰Sr. Discussions are given concerning the contributions of the cascade process, the competing processes, the width-fluctuation and resonance-interference effects.

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An experimental study was carried out on steady-state boiling of sodium flowing in the annular channel formed around an electrically heated simulation of a fuel pin. In the present experiment, the inlet temperature and flow rate were held constant, and the heat flux was gradually increased up to the inception of boiling. Thereafter, the heat flux was further increased step by step until the surface temperature of the heater pin marked a sharp rise, indicating the occurrence of dry-out. Records were obtained of the changes brought by the increasing heat flux to boiling phenomena, with particular reference to the behavior of the two-phase flow pattern and to the charac-teristics of boiling noise, as well as of the frequency of bubble formation.
It was made clear that there exists a region in which steady-state boiling will be established, and under these conditions the two-phase flow pattern changes sequentially from bubbly flow to slug flow and then to annular flow. This behavior of sodium boiling in a narrow channel is quite similar to the case of water.
With rising heat flux, the level of noise intensity associated with boiling first in-creased sharply to attain a maximum point, then decreased somewhat and remained constant thereafter until dry-out.
The frequency of bubble formation depended on the size of the bubble. The product of bubble frequency and equivalent diameter was found to be constant.

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A theory is presented on the omega-d modes which are eigenfunctions of a particular type of neutron diffusion operator. First, a general discussion is given on the implicit eigenvalue problem, reality, boundedness and distribution of the eigenvalues, order of magnitude and closure of the eigenfunctions. It is shown that the regular and adjoint eigenvalue problems reduce to an identical implicit eigenvalue problem. No one has in the past explicitly shown that the eigenvalue is real. The large variation in the order of magnitude of the eigenfunctions gives rise to a large variation in the mode coupling. This implies existence of weakly coupled modes that can be ignored. Next, these pro-perties are verified for a symmetric reflected slab reactor by numerical calculations. The results disprove the conjecture advanced by others that the neutron fluxes associated with a particular cluster of seven modes are approximately same. Finally, an equation is derived for the mode amplitudes which takes into account temperature feedback and external disturbance. Discussions are also given on the choice of appropriate modes for describing various kinds of dynamical processes.

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A comparison is made between the longitudinal wave in an electron plasma and the one-velocity neutron transport, using the Neumann series solution of the linearized Boltzmann equation. As a result, the transport of the disturbance in an electron plasma and the neutron transport are both expressed by the superposition of essential modes, which describe the streaming processes of electrons and neutrons.
The spatio-time distribution of the essential mode in a neutron field is always positive, while, that in an electron plasma is negative. This difference explains why the asymptotic mode of neutrons exhibits the diffusion-like behavior and that of electrons plasma oscillation.

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The formation of PuC_1-x and Pu₂C₃ by heating a powdered mixture of PuO₂ and graphite was studied in the temperature range of 1, 000°1, 350°C under reduced pres-sure. The reactions were pursued thermogravimetry, X-ray and chemical analyses.
The reaction rates for the formation of PuC_1-x and Pu₂C₃ obey the surface reaction law, the apparent activation energies of carburization being 102 and 105 kcal/mol, respectively. In the reaction between PuO₂ and graphite, Pu₂C₃ is formed directly, and PuC_1-x is formed in turn therefrom. When the carbides are heated continuously above 1, 450°C, appreciable weight loss takes place, which could be attributed to evaporation of Pu from the carbides.

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Steady state real cascades are analyzed. The method adopted is based on two difference equation representing the conservation of the total flow and the desired material flow, respectively. Introducing what is termed the "desired material flow cut" as a stage parameter corresponding to the "total flow cut" or "cut", the flow relations of the desired material flow are reduced to the same form as that of the total flow rate. The flow rate is not subject to any restrictive assumption except the conservation of mass flow, so that the method can be applied to almost any type of real cascade with side flows and losses. Adoption of a suitable iterative calculation will permit this treatment to deal with cascades constituted of separators with large values of separa-tion factor without resorting to approximation, because the "desired material flow cut" of each stage is described exactly by the separation factors of each stage.
The difference equations are solved analytically, for which the determinants B(i, j) and D(i, j) are introduced, which are the functions of stage parameters from the i-th to the j-th stage. With these determinants, explicit relations are obtained between the flow rate of each stage and the stage parameters of the whole cascade. The determi-nants are calculated by the recurrence formula.

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