Slowing Down Of Neutrons Research Articles

Equivalence of Taylor Series Approximation with Transcendental Equation of Neutron Slowing Down Theory under Constant Cross Sections

Abstract Neutron moderation in an infinite homogeneous medium with constant cross sections, which is traditionally treated by Taylor series approximation methods, bears a close correspondence with the exact transcendental equation approach, as has been demonstrated by reducing the exact result to approximate forms. In this paper we give an alternative approach in which the convergence of the approximations to the exact result is derived by allowing the order of approximation to increase indefinitely. The approach is based on the fact that the usual approximations do not give a self consistent definition of the effective mass parameter. The present result can hence be considered as the slowing down counterpart of Davison's treatment of the one speed equation in the Pl approximation.

Neutron Slowing Down with Energy-Dependent Anisotropy of Scattering

The problem of neutron slowing down in an infinite medium with energy-dependent anisotropy of elastic scattering has been discussed. The scattering function, P(u′, Δu), is redefined and expanded in terms of Legendre polynomials and the energy-dependent coefficients of the expansion are determined; in this expansion of P(u′, Δu) it is possible to carry out matrix degeneration of the kernel of the slowing-down equation; the matrix separable kernel allows the transformation of the integral equation into a differential equation in terms of Green's slowing-down functions. In some cases it is possible to obtain analytically the Green's slowing-down functions. In general, these functions are determined by standard numerical methods for solving sets of differential equations.

Equivalence of Taylor Series Approximation with Transcendental Equation of Neutron Slowing Down Theory under Constant Cross Sections

Abstract Neutron moderation in an infinite homogeneous medium with constant cross sections, which is traditionally treated by Taylor series approximation methods, bears a close correspondence with the exact transcendental equation approach, as has been demonstrated by reducing the exact result to approximate forms. In this paper we give an alternative approach in which the convergence of the approximations to the exact result is derived by allowing the order of approximation to increase indefinitely. The approach is based on the fact that the usual approximations do not give a self consistent definition of the effective mass parameter. The present result can hence be considered as the slowing down counterpart of Davison's treatment of the one speed equation in the Pl approximation.

Generalized Continuous Neutron Slowing-Down Theory

Generalized Continuous Neutron Slowing-Down Theory

Slowing-down of neutrons in the presence of inelastic scattering

Slowing-down of neutrons in the presence of inelastic scattering

Neutron Slowing Down via Inelastic Scattering in Heavy Moderators—I. Steady State

The inelastic scattering of neutrons by nuclei has been treated historically as a stepchild of elastic scattering. Few analytical studies have been performed which focus attention on inelastic scattering as a primary energy transfer mechanism. In this paper, we consider neutrons slowing down in the presence of inelastic scatterers. We take the host nuclei to be very heavy, so that in an inelastic collision a precise amount of energy is lost in the laboratory system. The slowing-down equation we obtain in the steady state has the form of a differential difference equation. We study its solutions in a variety of cases (cross-section models) and compare them with those obtained from conventional approaches. The techniques and results presented may be useful in evaluating complicated algorithms for the machine solution of problems in fast-reactor physics.

A Generalized Model for the Elastic and Inelastic Slowing Down of Fast Neutrons

A Generalized Model for the Elastic and Inelastic Slowing Down of Fast Neutrons

Improvements to Neutron Slowing Down Theory for Fast Reactors

Continuous neutron slowing down theory has proved useful in problems associated with thermal reactors. There are, however, two principal problem areas which inhibit obtaining the full benefits of continuous neutron slowing down models in fast reactor problems. One problem area is the treatment of inelastic scattering. The second problem area is the treatment of scattering and absorption resonances in a mixture of several moderating materials. In this paper, new methods are advanced for each of these problem areas. These methods are shown to lead to a continuous neutron slowing down model of reasonable accuracy for fast reactor problems. The inelastic treatment is based on matching the solution for an easily solvable reference problem (the zero absorption case). The mixture treatments (several are considered) are based on averaging procedures over a scattering interval instead of at a single energy.

Reply to Comment on the Elastic Slowing Down of Neutrons in Fast Systems

"Reply to Comment on the Elastic Slowing Down of Neutrons in Fast Systems." Nuclear Science and Engineering, 46(1), p. 168

Comment on the Elastic Slowing Down of Neutrons in Fast Systems

Comment on the Elastic Slowing Down of Neutrons in Fast Systems

An Improvement to the G.G. Approximation in Neutron Slowing Down through the Method of Generalized Function

The neutron slowing down problem in an infinite homogeneous medium is treated within the G.G. approximation through the theory of generalized function (g.f.). As test function for defining the g.f.'s, the source importance for the slowing down is chosen. In place of the Taylor expansion of the collision term of slowing down equation in the G.G. method we expand the adjoint collision term of the importance equation. Solutions obtained with this method clearly reproduce the Placzek wiggles, which do not appear in corresponding solutions by the orthodox G.G. method using the same order of approximation, and our solutions are in very good agreement with the exact Placzek function.

An Improvement to the G. G. Approximation in Neutron Slowing Down through the Method of Generalized Function

The neutron slowing down problem in an infinite homogeneous medium is treated within the G.G. approximation through the theory of generalized function (g.f.). As test function for defining the g.f.'s, the source importance for the slowing down is chosen. In place of the Taylor expansion of the collision term of slowing down equation in the G.G. method we expand the adjoint collision term of the importance equation. Solutions obtained with this method clearly reproduce the Placzek wiggles, which do not appear in corresponding solutions by the orthodox G.G. method using the same order of approximation, and our solutions are in very good agreement with the exact Placzek function.

On Some Exact and Approximate Solutions of the Neutron Slowing Down Equation in Resonant Absorbing Media

On Some Exact and Approximate Solutions of the Neutron Slowing Down Equation in Resonant Absorbing Media

Some New Applications of Neutron Slowing Down Time Spectrometry

A lead neutron slowing-down-time spectrometer LESP (LEad Standard Pile or LEad neutron SPectrometer) with a number of novel features was devised. It was applied to measurements on the effective sensitivity of counters and on the effective absorption and total cross sections of reactor materials. The basic principle of this method centers around the correlation that exists between the average neutron energy and the neutron slowing-down-time after fast neutrons are pulsed into a block of heavy medium with small neutron absorption such as a large lead assembly. This is analogous to the well established time-of-flight spectrometry. The proposed method of spectrometry should be suitable for measurement of such effects as the resonance self and mutual shielding and geometrical heterogeneity. As trial experiment, the effective efficiency of a 235U fission chamber was measured and found to correspond fairly well with BNL-325 data. As another example, blocks of heavy resonance material such as natural uranium, ant...

An Exact Solution of The Neutron Slowing Down Equation

The slowing down equation for an infinite homogeneous monoatomic medium is solved exactly. The cross sections depend on neutron energy. The solution is given in analytical form within each of the l...

An Approximate Scattering Kernel for Neutron Slowing Down

An Approximate Scattering Kernel for Neutron Slowing Down

Transient Solutions of the Neutron Slowing Down Equation

Transient Solutions of the Neutron Slowing Down Equation

An Approximate Scattering Kernel for Neutron Slowing Down

An Approximate Scattering Kernel for Neutron Slowing Down

Some New Applications of Neutron Slowing Down Time Spectrometry

A lead neutron slowing-down-time spectrometer LESP (LEad Standard Pile or LEad neutron SPectrometer) with a number of novel features was devised. It was applied to measurements on the effective sensitivity of counters and on the effective absorption and total cross sections of reactor materials. The basic principle of this method centers around the correlation that exists between the average neutron energy and the neutron slowing-down-time after fast neutrons are pulsed into a block of heavy medium with small neutron absorption such as a large lead assembly. This is analogous to the well established time-of-flight spectrometry. The proposed method of spectrometry should be suitable for measurement of such effects as the resonance self and mutual shielding and geometrical heterogeneity. As trial experiment, the effective efficiency of a 235U fission chamber was measured and found to correspond fairly well with BNL-325 data. As another example, blocks of heavy resonance material such as natural uranium, antimony and tungsten were placed in the LESP for producing the standard neutron spectrum fields of these materials, and the neutron spectra and effective cross sections measured on these materials were compared with calculation. It is concluded that these new applications of the method are quite practical for measurements of such properties as the effective efficiency of neutron counters and group averaged cross sections.

Measurement of Neutron Slowing Down Time in Light Water, Ice, Paraffin and Santowax

Measurements of the neutron slowing down times in light water, ice, paraffin and santowax have been made by pulsed neutron technique. Bursts of D-T neutrons of 0.1μsee width were generated in moderator cubes of 40×40×40 cm3. The slowing down neutrons were detected by bare as well as energy-selective filter-covered BF3 counters, and analyzed with a 256-channel time analyzer. Slowing down times in the moderator were determined by interpreting the increment of the difference of events between the two counters as attributable to the fraction of the neutrons slowing down at the time of measurement below the cut-off energy of the filter. The measured slowing down times below 0.63 and 0.43 eV agreed well with theoretical values on the 0°K free gas model. On the other hand, the measured values below 0.20 eV were found to be appreciably greater than the theoretical, which would appear to indicate that he effect of thermal agitation and chemical binding come into play at this range of energy.