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Boundary conditions in the spherical-harmonic method
~aclor Scienu:and Technology (J.N.E. Parts A/a). 1961, Vol. 14. pp. 215 to 216. PcrgamonI’rcSsLtd. I’rinrcdin NorlhcrnIreland
ABSTRACTS AND TITLES OF FUTURE PAPERS Atomnaya
Energiya
Vol. 10, No. 1 Time variation of the space and energy distributions of the neutrons from a puked source: I. G. DYAD’KIN and E. P. BATALINA.
The reddening of minerals in uranium-bearing veins:
A treatment is given of the time variation of the distribution and energy spectrum of neutrons from a pulsed source. (Transient states of. this kind occur in geophysics, in the detection of oilbearing strata, for example.) It is_ found that the time distribution for neutrons of any one energy has a Poisson distribution at almost all significant times. A formula is given for the spectrum in space and time: this variations in the energy implies that the variation of that spectrum in space is independent of the variation in time for certain ranges of distances and times. The two modes of variaticn are correlated in a fashion that can be allowed for outside those ranges. A formula is given for the mean-square moderation length as a function of time. All the relationships are presented as simple formulas having clear physical meanings.
Descriptions are given of the various types of hematitization shown by siderite, ankerite, and iron manganocalcite in veins containing uraninite. It is found that the process can occur without relation in space to the uraninite either before or after orogenesis and for various reasons. The carbonates may bc oxidized as a result of contact with hydro-thermal solutions; alternatively, the solutions may bring in hematite formed elscwhere in finely divided form. The process is radiogenic in origin when it occurs in regions surrounding lenses containing uraninite. Attention is directed to the practical importance of the various types of hematitization as signs of the presence of uranium in regions containing hydro-thermal veins.
Yu.
M.
DYMKOV and B. V. BRODIN.
The relation of structure to anisotropy in the thermal expansion for uranium, neptunium, and plutonium: N. T. CHEBOTAREV.
The yields of fission fragments produced from *W and 230Puby fast neutrons: E. K. BONYUSHKIN, Yu. S. ZAMYATNIN, V. V. SPEKTOR, V. V. RACHEV, V. R. NEGINA, and V. N. ZAMYATNINA. Radiochemical methods have been used to measure the absolute yields of some fission products produced from *W and *30Pu by 14.5-MeV neutrons and by neutrons having a fiuion spectrum. The shape of the curve representing the yield as a function of mass is discussed. The difference between the mean masses of the light and heavy groups is shown to be related to the mass number of the fissile isotope.
The best temperature for the regenerative water-heating system of a nuclear power station having a water-cooled and water-moderated reactor: Yu. D. ARSEN’EV.
It is shown that the anisotropy in the thermal expansion of some in the modifications of U, Np, and Pu is related to changes structures of those modifications. It is found that in every cast the anisotropy is caused by the weakening of four covalent bonds as the temperature rises, those bonds being variously placed with respect to the crystallographic directions. The relationships give a clearer conception of sonic properties peculiar to these three metals.
and thermal expansion of 0 and ‘1 plutonium: Structure KONOBEEVSKII and N. T. CHEBOTAREV.
S. T.
The base-point method is used to determine the best value for t,, the temperature of regenerative heating, the best being that giving the minimum calculated consumption of electrical energy. It is shown that the t, for a nuclear power station having a double water circuit is close to the maximum one as determined from the parameters of the steam leaving the first stage of the turbine.
New ideas on the structures of the A and ‘1 forms of plutonium are presented on the supposition that the bonds become increasingly covalent as the temperature decreases. The structures are considered as resulting from quite small deviations from an ideal face-centred lattice, the deviations being produced by four covalent bonds. It is found possible to explain some of the anomalous properties of the 8 and 11forms, in particular the increased atomic volumes and the negative values for the volume thermal-expansion coefficients.
Boundary conditions in the spherical-harmonic method: RUMYANTWJ.
G. YA.
Some aspects of means of locating radioisotopes and the problem of safe storage: P. V. ZIMAKOV and V. V. KULICHENKO.
Equations are deduced by using spherical harmonics applied to a single-speed kinetic equation. The equations are analysed to derive the conditions at the boundary between two scattering media. It is found that those conditions define completely the solution obtained in an approximation of any order (the socalled P_v approximations are envisaged), including even orders. Great practical interest attaches to the possibility of using approximations of even order; for example, the method needed for P2 is not very laborious, being the elementary theory of diffusion revised without substantial increase in complexity. (So far, even-order approximations, in particular P,, have not been used in calculations.)
It is claimed that fission products can be stored or disposed of quite safely if liquid wastes are transformed to solids. Materials such as glasses have.considerable advantages as regards firmness of binding in minimum volumes. An analysis is given of the chemical basis of such modes of disposal, and a dikussion is given of some aspects of the behaviour and state of fission fragments trapped by fusion in such materials. Results are given from fractional chemical and X-ray analyses to show that such materials are inhomogeneous, and that some features of the response to leaching can be explained on that basis. It is found that the radiation tends lo favour an increase in the proportion of crystalline fractions.
215
ABSTRACTS AND TITLES OF FUTURE PAPERS Atomnaya
Energiya
Vol. 10, No. 1 Time variation of the space and energy distributions of the neutrons from a puked source: I. G. DYAD’KIN and E. P. BATALINA.
The reddening of minerals in uranium-bearing veins:
A treatment is given of the time variation of the distribution and energy spectrum of neutrons from a pulsed source. (Transient states of. this kind occur in geophysics, in the detection of oilbearing strata, for example.) It is_ found that the time distribution for neutrons of any one energy has a Poisson distribution at almost all significant times. A formula is given for the spectrum in space and time: this variations in the energy implies that the variation of that spectrum in space is independent of the variation in time for certain ranges of distances and times. The two modes of variaticn are correlated in a fashion that can be allowed for outside those ranges. A formula is given for the mean-square moderation length as a function of time. All the relationships are presented as simple formulas having clear physical meanings.
Descriptions are given of the various types of hematitization shown by siderite, ankerite, and iron manganocalcite in veins containing uraninite. It is found that the process can occur without relation in space to the uraninite either before or after orogenesis and for various reasons. The carbonates may bc oxidized as a result of contact with hydro-thermal solutions; alternatively, the solutions may bring in hematite formed elscwhere in finely divided form. The process is radiogenic in origin when it occurs in regions surrounding lenses containing uraninite. Attention is directed to the practical importance of the various types of hematitization as signs of the presence of uranium in regions containing hydro-thermal veins.
Yu.
M.
DYMKOV and B. V. BRODIN.
The relation of structure to anisotropy in the thermal expansion for uranium, neptunium, and plutonium: N. T. CHEBOTAREV.
The yields of fission fragments produced from *W and 230Puby fast neutrons: E. K. BONYUSHKIN, Yu. S. ZAMYATNIN, V. V. SPEKTOR, V. V. RACHEV, V. R. NEGINA, and V. N. ZAMYATNINA. Radiochemical methods have been used to measure the absolute yields of some fission products produced from *W and *30Pu by 14.5-MeV neutrons and by neutrons having a fiuion spectrum. The shape of the curve representing the yield as a function of mass is discussed. The difference between the mean masses of the light and heavy groups is shown to be related to the mass number of the fissile isotope.
The best temperature for the regenerative water-heating system of a nuclear power station having a water-cooled and water-moderated reactor: Yu. D. ARSEN’EV.
It is shown that the anisotropy in the thermal expansion of some in the modifications of U, Np, and Pu is related to changes structures of those modifications. It is found that in every cast the anisotropy is caused by the weakening of four covalent bonds as the temperature rises, those bonds being variously placed with respect to the crystallographic directions. The relationships give a clearer conception of sonic properties peculiar to these three metals.
and thermal expansion of 0 and ‘1 plutonium: Structure KONOBEEVSKII and N. T. CHEBOTAREV.
S. T.
The base-point method is used to determine the best value for t,, the temperature of regenerative heating, the best being that giving the minimum calculated consumption of electrical energy. It is shown that the t, for a nuclear power station having a double water circuit is close to the maximum one as determined from the parameters of the steam leaving the first stage of the turbine.
New ideas on the structures of the A and ‘1 forms of plutonium are presented on the supposition that the bonds become increasingly covalent as the temperature decreases. The structures are considered as resulting from quite small deviations from an ideal face-centred lattice, the deviations being produced by four covalent bonds. It is found possible to explain some of the anomalous properties of the 8 and 11forms, in particular the increased atomic volumes and the negative values for the volume thermal-expansion coefficients.
Boundary conditions in the spherical-harmonic method: RUMYANTWJ.
G. YA.
Some aspects of means of locating radioisotopes and the problem of safe storage: P. V. ZIMAKOV and V. V. KULICHENKO.
Equations are deduced by using spherical harmonics applied to a single-speed kinetic equation. The equations are analysed to derive the conditions at the boundary between two scattering media. It is found that those conditions define completely the solution obtained in an approximation of any order (the socalled P_v approximations are envisaged), including even orders. Great practical interest attaches to the possibility of using approximations of even order; for example, the method needed for P2 is not very laborious, being the elementary theory of diffusion revised without substantial increase in complexity. (So far, even-order approximations, in particular P,, have not been used in calculations.)
It is claimed that fission products can be stored or disposed of quite safely if liquid wastes are transformed to solids. Materials such as glasses have.considerable advantages as regards firmness of binding in minimum volumes. An analysis is given of the chemical basis of such modes of disposal, and a dikussion is given of some aspects of the behaviour and state of fission fragments trapped by fusion in such materials. Results are given from fractional chemical and X-ray analyses to show that such materials are inhomogeneous, and that some features of the response to leaching can be explained on that basis. It is found that the radiation tends lo favour an increase in the proportion of crystalline fractions.
215