Space dependent 0°angular thermal neutron spectra were measured by time-of-flight method at several positions in a spectrum source, which is a single natural uranium plate sandwiched between two layers of pure water. Theoretical analysis was performed by means of multigroup discrete S₈ method, using Haywood's model for the scattering of thermal neutrons. Fairly good agreement was observed between experiment and theory. The experiment proved that ;
(1) The Haywoods model is valid for describing the thermal neutron spectra in het-erogeneous multiplying media like the present spectrum source, under the condition that anisotropies present in the densities of either neutron scattering or the slowing-down of source neutrons to the thermal neutrons is taken into consideration. The discrepancy between the measured and calculated spectra is very small, and the error induced therefrom in the neutron absorption of U²³⁵ is below 3%.
(2) The spatial distribution of the source neutrons requires to be taken into consider-ation, particularly in the case of thermal neutron spectra in the light water region surrounding the natural uranium plate.

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The current response matrix method based on isotropic (P₀) neutron angular distri-bution has been improved by effectively including a linearly anisotropic (P₁) angular distribution. The proposed method does not take into account the P₁ component directly, but it includes the effect of this component through consideration of the relation between the P₀ and P₁ components. The accuracy of the proposed method has been verified by comparing with exact calculation the diffusion length obtained by the present method in a uniform and infinite system: The diffusion length can be evaluated within 1% error. The present method has been further applied to one-dimensional fast reactor systems: The power distribution can be evaluated within 1%, and the neutron multiplication factor within 0.1%ΔK/K, in reference to S₁₆, calculations. This accuracy is comparable to that of a response matrix method in which the Legendre expansion about the angle is per-formed with components taken up to P₁. The proposed method adopts the same number of unknown components of neutron current as in the current response matrix method (order P₀). The computing time is thus of comparable order between these two methods, which is much shorter than for the response matrix method using the P₁ angular distri-bution. The proposed method can hence be considered useful for one-dimensional transport problems, and should also have good prospects of proving equally effective for multi-dimensional problems.

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A general theory of obtaining the higher order perturbation terms up to any desired order was given previously by the present author. However, the perturbation series is not always convergent in all problems of practical interest, and it is generally not so easy to obtain the convergence criteria for the perturbation method in a strict mathe-matical sense. When Kato's theorem developed for linear operators in Hilbert space is applied to the problem of convergence, it can then be treated rigorously in one-group diffusion approximation. The resulting convergence criterion takes a simple form con-taining only the basic parameters of the reactor system. The perturbation series is convergent if the conditions 1>{2|ρ⁽¹⁾_f|/d+3|ρ⁽¹⁾_fs|} and 1>2|ρ⁽¹⁾_c/d are satisfied for fission-able and absorbing materials respectively. When only the capture cross section is changed, the higher order perturbation series with the first n terms has the error εn ?? (2/d)ⁿ|ρ⁽¹⁾_c|ⁿ⁺¹/(1-2 |ρ⁽¹⁾_c |/d). In the formulae, d is the level distance of an eigenvalue in the unper-turbed system, and ρ⁽¹⁾_f and ρ⁽¹⁾_c are the first order reactivity worths when fissionable and absorbing materials are inserted into the system, respectively. And, ρ⁽¹⁾_fS is the first order reactivity worth when the value of the fission source term is changed. The numerical calculations for prototype and 1, 000 MWe fast reactors are presented to show practical applicability of the higher order perturbation method.

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A conversational procedure for the design of multi-layer shields has been developed and applied to parametric survey and weight minimization studies. The performance of various shielding designs is evaluated with the matrix method, after which the matrices are calculated by Sn technique. Numerical examples of water and iron laminated slab shields reveal not only the effects resulting from the combination of different shielding materials but also the usefulness of the interactive procedure for solving design problems. In another sample problem of weight minimization, an improvement of 1% has been obtained after a score of trials, despite the fact that the initial design had been care-fully optimized by parametric study.

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The stability of a power reactor with multiple transport lags and nonlinear charac-teristics embodied in the controller is analyzed by parameter plane method. The analysis covers two reactor models: (a) A rather simple model, symbolically representing the features of a nonlinear controller, one transport lag and the reactor with temperature feedback, and (b) A more realistic model depicting a practical chemical fine-control reactor system characterized by multiple transport lags and mixing effect associated with the chemical fluid, the nonlinear characteristics of chemical injection valves, and the spatial distribution of poison inside the reactor, as well as the reactor temperature feedback. These analyses yield much useful information about the stability of both systems, such as the conditions of reactor stability and of the occurrence of limit cycles, as well as the aspects of discontinuous change of the limit cycle frequency. Use of this parameter plane method will greatly simplify evaluation of the stability of even a fairly complex reactor control system that depends not only on the system parameters but also on the nonlinear controller characteristics and initial input signal amplitude.

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The vacuum freeze distillation method was successfully applied to the preparation of radiochemically pure water samples used for determining the tritium concentration in highly radioactive liquid waste produced in nuclear fuel reprocessing.
This method yielded a decontamination factor exceeding 10⁵ for radioruthenium and other long-lived fission products. The isotope effect on the tritium concentration was corrected by applying an enrichment factor determined from experiment.
A small portion of the high level liquid waste solution was taken from the Repro-cessing Plant of the Japan Atomic Energy Research Institute, neutralized with 2 N sodium hydroxide, and subjected to the vacuum freeze distillation. The distillate was subsequently analyzed for tritium by liquid scintillation counting. The tritium concen-tration in the waste solution was found to be approximately 0.13 μCi/m/, which corre-sponded to about 70% of the total tritium contained in the original spent fuel rods.

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An analytical method for determining Gd impurity in high purity Eu₂O₃ is proposed, which makes use of neutron activation and cation-exchange separation to examine its suitability as target material for the production of ^{152m, 152, 154}Eu.
Long-term irradiation of an Eu sample resulted in ¹⁵³Gd activity amounting to 1.8 times that of the same nuclide produced from an equal quantity of Gd by (n, γ) reaction. This experimental value is quite consistent with that obtained by calculation under the assumption that the ¹⁵³Gd results from nuclear reaction on ¹⁵¹Eu induced by secondary neutrons.
For the accurate determination of Gd, Gd impurity was separated from the Eu sample prior to neutron irradiation in order to reduce the self-shielding effect in the Eu sample. Separation by cation-exchange with α-hydroxyisobutyrate (0.33M, pH 3.77) made it possible to reduce the content of Eu in the Gd fraction below 7 × 10^-3%. This sufficed to assure that the ¹⁵⁹Gd content in ^152mEu was smaller than 1 × 10^-3%. For the determination of Gd content below 10⁴ ppm, however, should necessitate further purification of the irradi-ated Gd fraction.

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The recovery behavior of defects in irradiated titanium has been studied. The changes in electrical resistivity and microhardness of the samples irradiated to a fast neutron fluence of 1.3 × 10²⁰ n/cm² were measured after annealing at various temperatures. The activation energy for the recovery was found to be 0.97 eV, which was somewhat smaller than that reported for the self-diffusion of titanium (1.241.27 eV). Transmis-sion electron microscopy was applied out to determine the relation between the recovery process and changes in the microscopic structure. It was revealed that the recovery of hardness coincides with the disappearance of black spots observed in electron micrographs of irradiated titanium samples.

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