Thermal Neutron Density Research Articles

An application of slowing down kernels to thermal neutron density fluctuations in nuclear reactors

The backward equation for the space and energy-dependent probability generating function of the density fluctuations in a nuclear reactor, has been reduced to a more tractable form by the application of a slowing down kernel technique. Simple working expressions have been obtained for the variance, the correlation function and the power spectral density (P.S.D.) in terms of the infinite medium slowing down kernel. The method includes the effects of detectors, delayed neutrons and slowing down time. In addition, the frequency characteristics of the detection apparatus have been accounted for. It is shown that the dominant break frequency, of the fundamental mode component in the power spectral density, is markedly dependent on the slowing down lengths of the delayed neutrons, a result that can lead to appreciable corrections to the experimentally calculated neutron lifetime in certain systems. A general formalism accounting for slowing down, delayed neutrons and detector geometry is developed, and is applied to detectors of various shapes. Marked differences in the P.S.D. are noted for the different detectors in an infinite medium; however, for the finite medium, the effect of detector geometry is not so important and it is shown that, in certain circumstances, experiments can be analysed according to the simple, infinite medium-infinite detector formula.

A new method for the exact measurement of thermal neutron distribution in an elementary cell

Exact measurement of thermal neutron density distribution in an elementary cell necessitates the knowledge of the perturbations involved in the cell by the measuring device. A method has been developed in which a special stress is made to evaluate these perturbations by measuring the response from the perturbations introduced in the elementary cell. The unperturbed distribution was obtained by extrapolation to zero perturbation. The final distributions for different lattice pitches were compared with a thermos-type calculation and as a pleasing fact a very good agreement has been reached.

Minimum critical mass at limited uranium concentration

The maximum principle [1] is applied to the solution of the minimum critical mass problem assuming a limited uranium concentration, It is shown that a three-zoned system is optimal: the inner zone with the maximum permissible uranium concentration u0; the middle zone with uranium distribution corresponding to the constant thermal neutron density; the reflector. Results are derived for plane and spherical geometries.

Harmonic free determination of the thermal neutron absorption cross section of hydrogen by a pulsed source technique

A method, based on Fourier analysis of harmonics, has been developed for measuring the rate of decay of the fundamental mode of the thermal neutron density distribution which is established in a cylinder of water after thermalization of an injected burst of fast neutrons. Measurement of this decay for a range of water depths enables determination, by extrapolation, of the decay constant vΣa of an infinitely large system. The 2200 m sec-1 thermal neutron microscopic absorption cross section of hydrogen has thus been measured. The value obtained, 326 ± 3 mbn, is in good agreement with that obtained by most previous workers by a variety of other methods. The thermal neutron diffusion coefficient was also measured, although the experiment was not optimized for this. The value obtained, D = 35 200 ± 400 at 22 °C, also agrees very well with previous results.

The measurement of the radial thermal neutron density distribution in tubular fuel elements

An experimental study has been made of the radial thermal neutron density distribution inside tubular natural uranium fuel elements containing the organic coolant—monoisopropyldiphenyl. Using the activation method, the thermal neutron density distribution has been measured in 23 different versions of the fuel element. Theoretical neutron density distributions were obtained for these fuel elements by solving the one-velocity kinetic equation on an electronic computer. The experimental and theoretical results obtained for the neutron density distributions, shielding factors and the neutron density discontinuities at the outer coolant layer are presented in the form of graphs.

Measurement of the thermal neutron density distribution along the radius of sleeve-shaped fuel elements

This article is devoted to an experimental investigation of the thermal neutron density distribution along the radius of sleeve-shaped fuel elements consisting of natural uranium and an organic coolant, monoisopropyldiphenyl. The thermal neutron density distribution for 23 types of fuel element was measured by using the activation method. The theoretical neutron density distributions were determined for these fuel elements by solving the single-velocity kinetic equation by means of an electronic computer. The experimental and theoretical results are given in the form of neutron density distribution graphs, screening numbers, and neutron density jumps in the outside coolant layer.

The theory of a heterogeneous reactor with cylindrical fuel elements of finite radius

A consistent theory is developed for a heterogeneous reactor with cylindrical fuel elements of finite but small radius. The thermal neutron density in an element and in the moderator is written down, taking into account azimuthal dependence. Diffusion theory is applied throughout the volume of the reactor. Simple expressions are obtained for the diffusion length in parallel and perpendicular directions, with an accuracy up to the first power of the ratio of areas of the fuel element and of the unit cell. It is shown that the scattering mean free path for the perpendicular direction depends on the shape of the fuel element. In Section 5 a simple method is discussed for obtaining the diffusion tensor in the case of weak absorption and large distances between the elements.

A measurement of the neutron age in graphite by the pulsed source method

The ages of thermal neutrons from the D-D and D-T reactions have been measured in graphite using a pulsed source placed inside a prism. From the time dependence of the thermal neutron density the effective age of D-D neutrons, converted to graphite with a density of 1·6 g cm −3, was calculated to be {ce:inline-formula}τ eff = 355 ± 9cm 2 {/ce:inline-formula}.The slowing down of D-T neutrons can be expressed approximately in terms of two groups of neutrons: neutrons which have suffered a single inelastic collision only ( {ce:inline-formula}τ eff {/ce:inline-formula} = 600 cmz) and neutrons which have undergone several inelastic collisions ( {ce:inline-formula}τ eff {/ce:inline-formula}= 240 cmz). In determining the neutron age 'r, the relative contributions of the groups were taken as 0·65 and 0·25 respectively. A third group, representing neutrons which are slowed down by elastic collisions only, were ignored since their contribution is small (around 0·1) and their age is large.

The Depression of Thermal Neutron Flux and Density by Absorbing Foils

"The Depression of Thermal Neutron Flux and Density by Absorbing Foils." Nuclear Science and Engineering, 11(3), pp. 338–339

Pulse method of measuring neutron age in graphite

Using a pulse source located within a prism, the age of thermal neutrons from the reactions D-D and D-T in graphite was measured. From the time dependence of the thermal neutron density the author calculated the effective age of D-D neutrons τeff = 355 ± 9 cm2, recalculated for a graphite density equal to 1.6 g/cm3. The slowing down of D-T neutrons in graphite can be approximately expressed with the aid of two neutron groups: neutrons suffering but one inelastic collision when slowed down (τeff =600 cm2), and neutrons suffering several inelastic collisions (τeff = 240 cm2). In determining the age τ the relative contributions of both groups were assumed equal to 0.65 and 0.25, respectively. A third group is composed of neutrons slowed down only by means of elastic collisions. These neutrons may be neglected in the first approximation, since their contribution is small (about 0.1), while the increase is large.

Theory of heterogeneous reactors with cylindrical lumps of a finite radius

This article presents a consistent theory of heterogeneous reactors with cylindrical lumps of a finite, but small, radius. The density of thermal neutrons inside a lump and in the moderator is described by taking into account the azimuthal dependence. The diffusion theory is applied to the entire reactor volume. Simple expressions for the diffusion length in the parallel and perpendicular directions with an accuracy to the first power of the lump surface to cell surface ratio are obtained. It is shown that the average scattering length for the perpendicular direction depends on the lump shape. A simple method for determining the diffusion tensor for the case of weak absorption and large spacing between the lumps is considered in section 4.

A pulse method of measuring the age of neutrons in graphite: Z. Dlougy

The age of thermal neutrons from D--D and D--T reactions was measured in graphite. The thermal neutron density as a fumction of time was used for estimatmg the effective age of D--D neutrons, T/sub eff/ = 355 approximately 9 cm/sup 2/, for a graphite density of 1.6 g/cm/sup 3/. The slowing down of D--T neutrons in graphite is expressed by two neutron groups: neutrons that experienced only one inelastic interaction (T/sub eff/ = 800 cm/sup 2/) and neutrons experiencing several inelastic interactions (T/sub eff/ = 240 cm/sup 2/). In determining the age ?, the relative contributions of both groups were considered to be 6.65 and 0.25, respectively. A third group consisted of neutrons slowed down by elastic interactions only; the contribution (0.1) and age of the third group were very small and were not considered in the iritial approximation. (trauth)

The measurement of the absolute intensity of neutron sources by a comparison with the reaction T(d, n)He4

A method for the measurement of the absolute intensity of neutron sources by a comparison with the neutron intensity from the reaction T(d, n)He4 is described. For the comparison of the intensities a detector was used which has an almost constant sensititity for a wide range of neutron energies. The detector consisted of a graphite prism in which, at a definite distance from the source (“constant”-sensitivity distance), the density of thermal neutrons was measured. The sensitivity of such a detector is constant, to an accuracy of 1–2 %, in the interval of neutron energies 0.1–8 Mev and is 13% lower for neutrons of energy 14 Mev. In 1953 this method was used for the measurement of the absolute intensity of a Ra-α-Be source with an accuracy of 4%.

Intensity and Energy Spectrum of Fast Neutrons in Cosmic Radiation

The intensity and the energy spectrum of low energy neutrons at Mt. Norikura (2740 m above sea level and 25°N geomagnetic latitude) were obtained by observing recoil protons with the randomly operated high pressure cloud chamber filled with hydrogen gas at the pressure of 92 atm. The differential energy spectrum for neutrons in the energy range from 1 Mev to 15 Mev was found to be expressed by \begin{aligned} (1.2\pm 40\%){\times}10^{-3}{\times}E^{-1.25\pm 0.10}\text{cm}^{-2} \text{sec}^{-1} \text{sterad}^{-1} \text{Mev}^{-1}. \end{aligned} The neutron flux is in conformity with what one would expect from the density of thermal neutrons. Connecting the present data with the others which were obtained by many investigations in different energy ranges, the energy spectrum of neutrons ranging from 1 ev to 10 Bev are discussed.

Thermal Energy Relaxation Length of Ra-Be Neutrons in Water

Measurement of the density of thermal neutrons about a point Ra---Be source in infinite water medium has been extended to one meter. The thermal relaxation length is found to be constant at 9.58\ifmmode\pm\else\textpm\fi{}0.2 cm over a range in which neutron density changes by ${10}^{5}$.

The G.L.E.E.P. as an Absolute Standard of Thermal Neutron Density

The G.L.E.E.P. as an Absolute Standard of Thermal Neutron Density

Depression of the Thermal Neutron Density by a Detecting Foil

Depression of the Thermal Neutron Density by a Detecting Foil

Capture Cross Sections for Thermal Energy Neutrons

Cross sections for capture of thermal energy neutrons were measured for several elements. The method consisted in comparing, by a B${\mathrm{F}}_{3}$ ionization chamber, the density of thermal neutrons in water and in a solution of the element investigated. In order to avoid corrections for geometry, the effect of the substance was compared with that of boron solutions of different concentrations, and consequently the measurements directly give the ratio of the cross sections of the elements investigated to the cross section of boron. Data are given for N, F, Na, P, Cl, K, V, Mn, Co, As, Se, Br, Cd, I, Ba.