Solutions of multi-dimensional neutron diffusion equations in Cartesian coordinates are obtained in the form of regionwise multi-dimensional Fourier series. Equations for two- and three-dimensional problems are derived. A critical and a source problem in two dimensions, and a one-regional source problem in three dimensions are numerically studied.
Two kinds of Fourier series are numerically examined from the viewpoint of rapidity of convergence of the series.
To obtain the value of the flux more accurately, a method is presented which contributes to improvement of the flux profile.

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A method has been developed for predicting the interaction effect on control-rod worth and applied to a fast reactor system. The method is based on the exact perturbation theory to which several assumptions have been applied. These assumptions- numerically confirmed to be valid-all relate to separability of the effects on flux change brought by different factors of perturbation. The method permits prediction of the worth of a combination of any number of control rods solely from information obtained on single-rod worth calculations. Adoption of this method reduces from 2^NN to N+1 the number of calculations necessary for N rods of interest. Comparison with results obtained by the conventional direct k-difference method has revealed that the present method predicts the worth of a combination of control rods to within a few percent-1.3% at most in seven numerical examples studied, covering both symmetric and a symmetric rod configurations and with the interaction effect ranging about -10+15%.

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The influence of differences in resin-matrix structure on the ion-exchange adsorption of trace amounts of Ag(I), Co(II) and Cr(III) was studied by using both macroreticular and gel-type resins.
The results indicate that the rate-determining step of the exchange mechanism of these ions is film diffusion under conditions of finite volume and at an ionic strength of 1×10^-4. The diffusion coefficient decreases with increasing size of the hydrated ions- in the order D_Ag> D_Co>D_Cr. It may be said that the faster rate of exchange in the macroreticular resin is due to the larger surface area and pore size of this resin.
Also, in a column system-as opposed to batch operation, it is assumed that the rate-determining step of the exchange reaction is film diffusion. With both resins, the kinetic coefficient β decreases in the order : β_Ag>β_Co>βCr. For the same linear velocity, a higher β-value is obtained with the macroreticular than with the gel-type resin. Consequently, a higher separating efficiency may be expected from the macroreticular resin for concentrating and separating trace amounts of cations from aqueous solution.

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The carbothermic reaction of UN with graphite in the form of loose powder mixture has been studied in vacua with the aid of a high-temperature thermobalance in the temperature range of 1, 270-1, 675°C. The gravimetric measurements were conducted continuously to determine the effect of varying reaction temperature and differences in sample particle size.
The kinetics of the reaction was found to follow the diffusion-controlled kinetic equation for mixed powder, and activation energies of 76.1, 55.1 and 72.7 kcal/mol were obtained for samples of (1) -400 mesh UN and -400 mesh natural graphite mixture, (2) -150 +270 mesh UN and -150 +270 mesh natural graphite mixture, and (3) -150 +270 mesh UN and -150 +270 mesh artificial graphite mixture, respectively. X-ray diffraction studies revealed the reaction products of the coarse sample to be composed of two different kinds of UC_xN_1-x solid solutions, one having a x value of 00.2, and the other 0.80.9. From the above observations, the diffusion of C and/or N atoms through the outer carbon rich UC_xN_1-x layer may be considered to be the rate determining step.

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The isotopes of transplutonium elements were produced by irradiation of 62 mg of ²⁴¹AmO₂ in JMTR during the period July 1971 through July 1972. The transplutonium elements were separated from plutonium, fission products and cladding materials by a combination of precipitation and ion exchange. Americium, curium, berkelium and californium were mutually isolated by ordinary procedure. The isotopic ratios of americium and curium were determined by mass spectrometry, and berkelium and californium by radiochemical method. In addition to the nuclides detected in the previous work, ²⁴⁶Cm, ²⁴⁹Bk and ²⁴⁹Cf were also identified.

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Experiments were undertaken on the incorporation in plastics-polyethylene inparticular-of radioactive spent ion exchange resins produced in nuclear power plants. The resulting polyethylene products burdened with radioactive resin were tested to ascertain the properties considered important for radioactive waste management. The items chosen for testing were mechanical strength, leachability of radionuclide and radiation resistance. Polyethylene products burdened with 50w/o of resin were found to possess an impact strength of 10 kg•cm/cm and a compressive strength of 300 kg/cm², which values do not indicate any appreciable decrease in mechanical strength compared with polyethylene unburdened with resin. The leaching rate of ¹³⁷Cs from the resin-burdened polyethylene product was very small-only 0.1% leached out in one year. In respect of decomposition by radiation, the amount of gases evolving upon absorbing a dose of 10⁹ rad was 10 ml/g. The effect of radiation on the mechanical strength was also studied.
It is concluded from above results that solidification of radioactive spent ion exchange resin by incorporation in plastics is one of the best methods devised so far for treating spent resins.

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The effects of the presence of a central cavity on the space- and time-dependent neutron energy spectra in both thermal and fast neutron systems are analyzed theoretically with use made of the multi-group one-dimensional time-dependent S_n method. The thermal neutron field is also analyzed for the case of a fundamental time eigenvalue problem with the time-dependent P₁ approximation. The cavity radius is variable, and the system radius for graphite is 120 cm and for the other materials 7 cm.
From the analysis of the time-dependent S_n, calculations in the non-multiplying systems of polythene, light water and graphite, cavity heating is the dominant effect for the slowing-down spectrum in the initial period following fast neutron burst, and when the slowing-down spectrum comes into the thermal energy region, cavity heating shifts to cavity cooling. In the multiplying system of ²³⁵U, cavity cooling also takes place as the spectrum approaches equilibrium after the fast neutron burst is injected.
The mechanism of cavity cooling is explained analytically for the case of thermal neutron field to illustrate its physical aspects, using the time-dependent P₁ approximation. An example is given for the case of light water.

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