On the anisotropy of a heterogeneous medium with respect to the diffusion of neutrons II

In this paper use is made of the results of paper [1]for investigating the anisotropy of the diffusion of neutrons in a stratified heterogeneous medium with (total) cylindrical and spherical symmetry. The method given in [5]is employed to carry out homogenization of the stratified heterogeneous medium which scatters the neutrons anisotropically for each elementary act of scattering. The plane source at infinity is at the same time parallel to the layers.     

On possible role of neutrons in appearance of delayed muons in MUON-T setup at the Tien Shan high-altitude station

The MUON-T setup operated at the Tien Shan high-altitude station of the Lebedev Physical Institute (3340 m above sea level) at a soil depth of ∼10 m (∼20 m m.w.e.). Muons with delay times of 30–150 ns with respect to the extensive air shower front were observed at this setup. Calculations showed that delay times of relativistic muons, taking into account their deviations in the geomagnetic field, do not exceed ∼30 ns. To elucidate the possible role of neutrons in the appearance of delayed events due to the n-p reaction in the plastic scintillator material, the problem of neutron transport in a medium with a density of 2 g/cm³ and a humidity of 10% was solved by the Monte Carlo method. Calculations for a point source of neutrons with energies of 5, 10, and 20 MeV (such neutrons can be generated, in particular, in cascades in soil from hadrons of the shower core) showed that the neutron flux decreases more than by a factor of 10⁴ at a distance of 2.8 m of soil from the source. Neither neutron crosses the boundary of 3m at the total statistics of 3 · 10⁵ events. Since the MUON-T setup is at a depth of 10 m, it is clear that neutrons from the atmosphere and soil upper layer are absorbed, scattered, and do not reach the detector. Thus, the formation of delayed muons in the MUON-T setup cannot be explained by these neutrons.     

A case study of the MSA approach to quantized polarizable media

The mean spherical approximation (MSA) has proved to be a very general and flexible method to analyze equilibrium statistical mechanical systems. In this note we test its accuracy against a simple one-dimensional model, i.e., a lattice gas of polarizable molecules where the internal degree of freedom is treated as quantized harmonic oscillators which interact via harmonic forces. This model can be solved exactly. We find a very good agreement between the MSA and exact solutions.2 The corresponding classical problem of polarizable particles was first solved in a mean spherical approximation (MSA) by M. Wertheim [J. Chem. Phys. 26:1425 (1973)]. He considered the model with nonfluctuating dipole moments. Later L. Pratt [Mol. Phys. 40:347 (1980)] and J. S. Høye and G. Stell [J. Chem. Phys. 73:461 (1980)] solved the corresponding classical problem in the MSA for particles with fluctuating dipole moments.     

Random walk on hierarchical comb structures

This paper examines random walks on an exactly solvable comb model of percolation clusters. The study shows that diffusion along the structure’s axis is anomalous. Generalized diffusion equations with fractional-order time derivatives are derived, and a generalization to the multidimensional case is carried out. The relationship between this problem and that of diffusion in a medium with traps is examined, and equations that describe diffusion in a medium with traps are derived. The paper also discusses the transition to ordinary diffusion due to the introduction of comb teeth of finite length, and analyzes the case of N teeth of different length. It is shown that the solution of this problem leads to the emergence of an N-channel diffusion equation. Finally, equations describing the diffusion of interacting electrons are derived. Zh. éksp. Teor. Fiz. 115, 1285–1296 (April 1999)     

Temperature dependence of magnetic neutron scattering by dislocations in nickel

Magnetic small-angle scattering of neutrons by dislocations in a plastically deformed nickel single crystal has been investigated between room temperature and 650 K. The results are in disagreement with calculations from the micromagnetic theory [1]. For scattering vectors Q with 1 × 10^?2 ? Q ? 7 × 10^?2 nm^?1 the intensity goes to zero much more rapidly with increasing temperature than predicted. Some possible explanations for this observation are discussed.     

Scattering of neutrons on a Bose condensate

The spectrum of noncondensate excitations in neutron scattering on bosons is obtained in the framework of the Bogoliubov models both for liquid ⁴He and a dilute gas. The problem is solved using a path-integral representation of the partition function of the system. We describe the influence of scattering of neutrons on a Bose condensate in a stationary (time-independent) picture in the Gibbs equilibrium ensemble. This influence is a stationary boson response, and it depends on the initial neutron momentum k, transfer momentum p, and the neutron-boson interaction λ, which is related to the scattering length. The contribution of the neutrons to the initial Bogoliubov spectrum is found to be important for “quasi-elastic” scattering on the noncondensate, while the contribution of deep inelastic scattering is small; no contribution from elastic scattering on the Bose condensate is found. In the case of liquid Helium, the response is unlikely to be observable for all values p. On the other hand, for a gas one may expect a visible effect, in particular for a small momentum transfer p and a small density of the Bose condensate ϱ.     

On the two methods of kinetic theory of ECRM

The kinetic theory based on the expansion of local field in the guiding center coordinate system, presented by paper[1]–[3], has successfully developed into a theoretical system. The mathematical background and physical explanation of setting up the guiding center coordinate system is expounded in the paper. By using the methods of the guiding center and waveguide coordinate systems respectively, the same dispersion equations for interaction of an axially symmetrical single momentum electron beam with TE_mn field in the circular waveguide are rigorously derived. A number of mistakes in paper[4] are indicated as well.     

Pomraning–Eddington approximation for radiative transfer in a homogeneous solid cylinder

Abstract

The radiative transfer in a solid cylinder containing a homogeneous turbid medium with anisotropic scattering is considered. The medium has a diffuse and specular reflecting boundary illuminated by an external incidence and contains an internal energy source. This general problem can be solved in terms of the solution of the corresponding source-free problem with a specular reflecting boundary and isotropic external incidence. The Pomraning–Eddington approximation is used to solve the source-free problem. Three different weight functions are used to verify the boundary condition to find the constants of the solution. The partial flux, the irradiance and the net flux at the boundary for the general problem are calculated.     

Model and theory for the determination of diffusion coefficients by Auger electron spectroscopy measurements and an application to oxygen diffusion along the [0001] and [101¯0] axes in single crystal zirconium

A simple hopping model of the diffusion of adsorbed species from a surface into the bulk of a material has been formulated and solved mathematically. The difference in the energy barriers for an atom moving between the atomic layers at the surface and in the bulk are explicitly considered. This model is also capable of describing the initial stages of diffusion, something that conventional solutions of the continuum diffusion equation cannot handle. Auger electron spectroscopy has been used to measure the dissolution rate of oxygen from Zr(0001) and Zr(101¯0) surface into the bulk. Satisfactory results were obtained by applying our model to the diffusion data for these two zirconium surfaces for two different heating schedules: (i) rapid temperature ramp-and-hold and (ii) continuous linear heating with respect to time. The resulting Arrhenius expressions for diffusion are: D = (0.115 ± 0.031)exp[(−44.45 ± 4.82)kcal/RT]cm²/s along Zr[0001] and D = (1.07 ± 0.26)exp[(−46.18 ± 4.22)kcal/RT]cm²/s along Zr[101¯0].     

Measurements of the diffusion parameters in diphenyl at temperatures from 20 °C to 170 °C

Diffusion coefficient, mean life time of thermal neutrons, coefficient of diffusion cooling and diffusion length in diphenyl at temperatures 20°, 40°, 60°, 80°, 110°, 140° and 170° C were measured by the pulse method. Their dependence on the temperature of diphenyl was deduced in an analytic form and the change of the neutron transport length was determined experimentally. No discontinuity of the diffusion coefficient at the melting point of diphenyl apart from that caused by density change was observed. The energy exchange cross sectionM ₂ is practically independent of temperature in the range from 20 °C to 170 °C and the deduced microscopic absorption cross section for hydrogen equals 337±2 millibarns. The thermalization of neutrons in diphenyl proceeds more slowly than in water and neutrons loose their energy predominantly by interaction with the C—H group of the diphenyl molecule.We are indebted to Mr. J.Jadavan and Mr. J.Jirou for their technical assistance during the measurements and setting up the measuring apparatus.     

Supplement to anti-proton scheme of β-disintegration

The author's previous paper [2]on the possibility of extending the known scheme of -disintegration by four other anti-proton variants is rendered more exact by distinguishing between the neutrino and the anti-neutrino.     

The halo of the exotic nucleus 11Li: a single Cooper pair

If neutrons are progressively added to a normal nucleus, the Pauli principle forces them into states of higher momentum. When the core becomes neutron saturated, the nucleus expels most of the wave function of the last neutrons outside to form a halo, which, because of its large size, can have a lower momentum. It is an open question how nature stabilizes such a fragile system and provides the glue needed to bind the halo neutrons to the core. Here, we show that this problem is similar to that of the instability of the normal state of an electron system at zero temperature solved by Cooper, a solution which is at the basis of BCS theory of superconductivity. By mimicking this approach using, aside from the bare nucleon-nucleon interaction, the long wavelength vibrations of the nucleus ¹¹Li, the paradigm of halo nuclei, as tailored glues of the least bound neutrons, we are able to obtain a unified and quantitative picture of the observed properties of ¹¹Li. Received: 9 May 2001 / Accepted: 17 November 2001     

Analytic solutions of the ground and excited states of the spin-weighted spheroidal equation in the case of s=2

By using the super-symmetric quantum mechanics (SUSYQM) method, this paper obtains the analytical solutions for the spin-weighted spheroidal wave equation in the case of s = 2. Based on the derived W 0 to W 4 the general form for the n-th-order super-potential is summarized and is proved correct by mathematical induction. Hence the ground eigenvalue problem is completely solved. Particularly, the novel solutions of the excited state are investigated according to the shape-invariance property.     

Search for scission neutrons using specific angular correlations in 235U fission induced by slow polarized neutrons

The experimental data concerning scission (or prescission) neutrons are very contradictory—the relative part of these neutrons in the prompt fission neutrons varies from 1 to 35% owing to arbitrary assumptions made in different analyses. To solve this problem, we have used a new alternative method to search for the scission neutrons. We have found the left-right asymmetry of prompt-fission-neutron (PFN) emission caused by sp-wave interference in the entrance channel of the reaction and the P-odd asymmetry of the PFN emission caused by parity nonconservation at the exit channel of the fission process. Both effects cannot reside in PFN evaporated by excited fission fragments. The scission (or prescission) neutrons are responsible for these effects. The text was submitted by the authors in English.     

T-odd asymmetries for products from the spontaneous fission of oriented nuclei

The problem of describing T-odd asymmetries in ternary fission reactions of oriented nuclei is solved for the first time on the basis of quantum theory. Estimates of the T-odd asymmetry coefficients in the angular distributions of the reaction products are obtained using the spin density matrix of the oriented fissioning nucleus. It is demonstrated that experiments on observing T-odd asymmetries in the spontaneous fission of oriented nuclei are of interest because the T-odd asymmetry coefficients can be around an order of magnitude greater than similar coefficients in the fission of unoriented target nuclei induced by polarized neutrons.     

Solutions of the Fokker-Planck equation describing the thermalization of neutrons in a heavy gas moderator

The thermalization of neutrons is described by a transport equation with a second order differential operator with respect to the energy. First this equation is transformed to an one-variable Fokker-Planck equation. Next an eigenfunction expansion and a polynomial expansion are used to solve the time-dependent Fokker-Planck equation. The eigenvalues are obtained either by solving a Schrödinger equation or by calculating 2×2 matrix continued fractions. Explicit results for the approach to equilibrium of a pulse of neutrons as well as the stationary distribution for 1/v absorption are presented. It is shown that the theory of the photoelectromotive force in semiconductors also leads to the same problem.     

On the relation between a fluctuating diffusion equation and long time tails in stationary random media

Ernst, Machta, Dorfman, and van Beijeren [J. Stat. Phys. 34:477 (1984);35:413 (1984)] have proposed that diffusion in a stationary random medium is described by a fluctuating diffusion equation involving a coarse-grained local diffusion coefficient K(r) and free volume fraction(r). We show that for a particular class of models [lattice diffusion with random transition rates and constant(r)], their prediction for the long time tail in the velocity autocorrelation function is the correct asymptotic limit.     

Structure of the generalized momentum of a charged test particle and the inverse problem in the general theory of relativity

The work of Sedov [1] examined the navigational problem which involves finding the metric tensor g_i of space of general relativity from the results of physical measurements. The problem of the approximate determination of g_i from the mutual deflection of test particles in gravitational fields was studied in [2], The problem of finding g_i from the second integrals of the geodesic equations in gravitational fields was solved in [3]. The connection of the first integrals of the Hamilton-Jacobi equation of the test particles with the symmetry of StÄckel spaces was investigated by Shapovalov [4, 5].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 60–64, July, 1981.