On the use of the average chord length

The average chord length has been traditionally used in reactor physics for the estimation of escape probabilities for bodies of small optical size and in elementary formulas in shelfshilding analysis. In this work, the rôle of the average chord length in the estimation of transmission probabilities of homogeneous bodies is analyzed and the correct chord length distribution is derived from the incoming angular flux distribution. The concept of average projection area is used to derive a generalization of Dirac's original formula to the case of an angular flux uniformly entering a non-convex body.     

On generalization of uniaxial stress-strain relation

Different forms of constitutive relations have been advanced for elastic, plastic and elastic-plastic behaviour of materials. It is shown that the various forms of the stress-strain relationship are specialized forms of generalization of a single stress-strain relation. For example, it is shown how the laws of elastic deformation, and the incremental and total deformation relationship for plastic behaviour are derivable from the Ramberg-Osgood relation.     

On a generalization of the Telford equation for aerosols

A linearized form of the coagulation equation for aerosols, known as the Telford equation, has been generalized to include diffusion, deposition, settling and condensational growth. The relationship between this equation and those of linear gas kinetic theory and neutron diffusion is elucidated and clarified. The linearized equation is shown to be useful for studying dilute radioactive aerosols and can be of value in following the consequences of a minor accidental release in a reactor environment. The linearity of the equation makes it amenable to many standard analytical and numerical solutions and it has great advantages over the conventional non-linear aerosol coagulation equation.Several exact, analytical solutions are obtained for the space-time-volume distribution function following a localized, pulsed release of monodisperse aerosol.     

On the average probability distribution of peak ground acceleration in the U.S. continent due to strong earthquakes

An estimate is made of the average probabilities of different magnitudes of peak horizontal ground acceleration due to seismic events in that part of the United States east of the Rockies. Past history is used to provide an average seismicity and future earthquakes are assumed to occur randomly with regard to location and time. With the seismic correlations employed, the average probability per year that an acceleration ≥0.15 g will occur at any point is about 10⁻³, while the average probability per year of an acceleration ≥0.3 g at a random site is about three times smaller. The very considerable uncertainties in these estimates are illustrated in part by examining differences which would arise with a different choice of seismic correlations.     

Determination of the average137Cs contamination density of soil

Scientific and Industrial Association “Taifun.” Translated from Atomnaya énergiya, Vol. 76, No. 3, pp. 212–217, March, 1994.     

Mitigation of systematic uncertainty in the average cross-section of JENDL

JENDL 3.2 in spite of its utility to fast reactor program has large systematic uncertainty whose correlation coefficient is very close to 100%. In order to avoid singularity in processing the covariance matrices in JENDL library, a correlation coefficient of 90% is chosen arbitrarily. In order to avoid such arbitrariness and reduce the systematic uncertainty, we use the technique of determinant inequalities developed by us to estimate the bounds for the systematic uncertainties and demonstrate its utility in the U-235 total cross-section.     

Measurement of the average neutron generation lifetime in IBR-2

The purpose of this work was to measure the lifetime of a neutron generation in an IBR-2 core as a function of its state and the core environment. The main problem was to study the possibility of decreasing the duration of a neutron pulse. Different measurement methods were used. The main one was the α-Rossi method. For comparing with experiment, the lifetime was estimated by a computational method. It was shown that the results obtained by all measuring methods used agree with one another. For the standard state of a reactor, the lifetime of neutrons in the IBR-2 core is 62 ± 2 nsec. The contribution of individual elements of the core and its surroundings to the total lifetime of a neutron generation is presented. It is noted that in experiments with part of the radiation shielding moved away there are discrepancies in the estimate of the effective fraction of the delayed neutrons of a factor of 1.5 as compared with the standard state of the reactor. No explanation has been found for such a discrepancy. __________ Translated from Atomnaya énergiya, Vol. 103, No. 3, pp. 166–172, September, 2007.     

沉积物中石英氧空位平均寿命的研究

采用热活化技术,用E心的电子自旋共振信号估算出沉积物中石英氧空位心的平均寿命,实验结果表明,二级动力学方程更适于沉积物中石英氧空位心平均寿命的估算,塔里木盆地深层沉积物（4895－4908m)中石英氧空位心在27℃时的平均寿命为10^18年。     

The moderation length of neutrons

The neutron moderation length is an important constant without which is is impossible to deal with the design of nuclear reactors in all their aspects. A knowledge of the moderation lengths is especially necessary for the determination of the space distribution of the neutrons in a reactor, and for the calculation of the energy spectrum of the moderated neutrons.In the present work is given an approximate solution of the integral equations satisfied by the space moments of the neutron distribution function inan infinite medium with an infinite, plane, isotropic source. The energy-angle moments of the neutron scattering function are expressed in terms of experimentally determined angular distributions of neutrons of various energies in the case of anisotropic elastic scattering from nuclei. By using experimental results for the total cross section and for the angular distribution in the case of elastic scattering from the nuclei H¹, D², Be⁹, C¹², O¹⁶ the neutron moderation lengths were calculated for the moderators: water, heavy water, graphite, beryllium, and beryllium oxide.The results of the calculation were found to be in satisfactory agreement with experimental values.In conclusion the authors wish to thank Doctor of Physical and Mathematical Science G. I. Marchuk for useful discussions, and also B. S. Gudkov, Z. P. Drobyshev, and Z. I. Shemetenko for carrying out the calculations.     

Systematic behaviour of the average parameters required for the Los Alamos model of prompt neutron emission

A large number of fissioning systems have been studied in the frame of the Los Alamos model which showed interesting regular behaviours of the average model parameters (the energy release in fission 〈E_r〉, the total kinetic energy of the fission fragments 〈TKE〉, the average neutron separation energy 〈S_n〉 from the fission fragments, the prompt gamma-ray energy 〈E_γ〉 and the level density parameter 〈a〉 parameterized as 〈C〉 = A/〈a〉, where A is the mass number of the fissioning nucleus)) as well as of other quantities in connection with the prompt fission neutron emission (such as the total average prompt neutron multiplicity at thermal incident energy, the total average fission fragment excitation energy leading to prompt neutron emission, the total average prompt fission energy deposition, the average excitation energy given to the fragments, and the average center-of-mass energy of prompt neutrons and so on) and to elaborate systematics of model parameters.