Free Gas Model Research Articles

Multiple scattering and transport of neutrons

The collision term in the quantum-mechanical transport equation of neutrons derived by Osborn et al. (1965) is reformulated with the aid of the S-matrix theory of scattering, and the usual transport equation is generalized to include the effect of multiple scattering of neutrons. It is shown that the random phase approximation is no longer necessary by virtue of the adiabatic switching off of interactions. A semi-quantitative analysis of the effect of multiple scattering is made on the basis of the free gas model, and it is concluded that the validity of the usual transport equation depends on the spatial resolution, the energy of the neutron under consideration and the energy spectrum of all neutrons. The usual transport equation is not valid for a very cold neutron (of energy below 00001 cV), and not generally valid for a cold neutron when the energy spectrum of the neutrons is softer than a Maxwellian. It is also inapplicable to a neutron of any energy when the spatial resolution is not much less than the mean free path of the neutron.

(n, α) reactions on heavy nuclei induced by 15.1 MeV neutrons

The energy spectra of α-particles from the (n, α) reactions on 141Pr, 165Ho, 175Lu, 181Ta and 197Au induced by 14 MeV neutrons at 0° have been measured with a n-type silicon surface barrier semiconductor. They cannot be accounted for by the statistical model, with the inclusion of the shell effect for the level density, which is derived from the free gas model for a two-fermion system. The angular distribution of α-particles from 141Pr is strongly forward-peaked. It seems that there is an appreciable contribution of direct processes to these reactions.

Excitation energy of a free fermi gas in the (n, 2n) channel

Fast neutron induced (n, 2n) cross sections are estimated in the framework of the free gas model. Since the observed excitation energy is measured from the effective Fermi surface of a real nucleus, a distinction is made between the model excitation energy and the experimentally observed excitation energy of a system. By removing the interactions in an actual nucleus, one can go over to the hypothetical free gas reference system. The interaction energies of a real system will then contribute to the total excitation energy of the free gas system. When nuclei with the same experimentally observed excitation energy are compared, the model excitation energies are altered depending on the nuclear interactions. These interaction energies change the observed excitation to the model excitation energy and convert a real system into a free gas system at matched excitation energies. The view point is used here to obtain quantitative estimates of the fast (n, 2n) cross sections at 6 MeV residual excitation. The calculations agree fairly well with the experimental results. The limitations of the present view point are discussed.

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.

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.

Nuclear Level Densities in Intermediate and Heavy Nuclei

The level densities of intermediate and heavy nuclei have been fitted to the free gas model formula with some improvement over previous fits. The predictions of tho model regarding cross section behaviour have been tested and found to lead to anomalous behaviour of the partial widths for incident neutron energies above 1�5 MeV.

Diffusion length calculations in water

An extensive series of calculations have been performed to determine the asymptotic neutron energy spectra and diffusion lengths in water poisoned by absorbers like boron, cadmium and gadolinium at different concentrations. The effect of chemical binding has been studied by comparing the results obtained by using the well-known Nelkin model of water with the free-gas model for hydrogen. Diffusion theory has been used in making the calculations; however, to test the validity of the diffusion approximation, in a few cases we have also made some transport theory calculations and compared the two results. We find that even for fairly large absorptions (i.e. for κ Σ min ≈ 0·7–0·8 ) diffusion theory gives results which compare well with those obtained by using transport theory.

The role of in-pore mass transport resistance in the reaction of porous solids with gases The air oxidation of large tubes of graphite

The rate of reaction between a gas and a porous solid at elevated temperatures is limited by in-pore mass transport resistance. A mathematical model is presented which allows the magnitude of this effect to be estimated. The mass transport resistance is considered as three constituent parts, diffusion, bulk flow due to superimposed pressure gradients and bulk flow due to volumetric changes in the chemical reaction. The effect of diffusional resistance is determined on the basis of a free gas model and Knudsen diffusion is not considered. The chemical rate is assumed to obey a simple order relationship with respect to the reactant gas. The theory has been verified by a study of the oxidation of large tubes of graphite exposed to air at the bore surface. Evidence of a diffusional effect was obtained from gas concentrations in the bore and at the external surface. The effect of superimposed bulk flow of gas through the graphite was examined, Good agreement between the observed results and those predicted from the theory was obtained at temperatures in the region 400–550°C. The effects on the calcualted results of carbon monoxide formation and the concentration dependence of the diffusion coefficient were examined. Under the experimental conditions employed these were found to be of the second order. The commonly assumed first order dependence of the graphite—oxygen reaction was found to be incorrect and support for a 0·6 order dependence obtained.

Effective Cadmium Cutoff Energies for Cylindrical Detectors with Cylindrical Filters

The effective cutoff energies for cylindrical detectors with cylindrical filters in isotropic neutron flux were studied. The reactor spectra used in calculating the effective cutoff energy were those for infinite homogeneous media using the free gas model of deuterium and carbon. The values of the effective cutoff energies for cylindrical geometry in isotropic neutron flux are intermediate between those in isotropic and beam neutron fluxes for slab geometry. Change of detector position in the filter considerably influences the value of the effective cutoff energy. The self-shielding effect is negligibly small in micro counters.

Effective Cadmium Cutoff Energies for Cylindrical Detectors with Cylindrical Filters

The effective cutoff energies for cylindrical detectors with cylindrical filters in isotropic neutron flux were studied. The reactor spectra used in calculating the effective cutoff energy were those for infinite homogeneous media using the free gas model of deuterium and carbon. The values of the effective cutoff energies for cylindrical geometry in isotropic neutron flux are intermediate between those in isotropic and beam neutron fluxes for slab geometry. Change of detector position in the filter considerably influences the value of the effective cutoff energy. The self-shielding effect is negligibly small in micro counters.

The calculation of removal cross sections between overlapping thermal groups

The use of two overlapping thermal groups has been recommended by a number of authors for the study of problems such as the variation of thermal spectra across lattice cells and flux peaking in water gaps. In this paper, the Kottwitz problem (two semi-infinite media at different temperatures, with neither sources nor absorption present) is used as an example and three different methods for calculating the removal cross sections between the groups are presented.Numerical values for the removal cross sections are quoted using the free gas model of thermalization. If the diffusion coefficient of a medium is independent of energy, its removal cross sections are found to be independent of temperature. The work requires extending to situations with finite absorption, and more sophisticated models of thermalization should be used.