Spin–density correlations and magnetic neutron scattering in ferromagnetic metals

We obtain expressions for the spatial spin-density correlator and for effective and local magnetic moments in the dynamic spin-fluctuation theory. We derive formulas for the magnetic scattering cross section in the theory of itinerant electron magnets. We calculate magnetic characteristics of bcc Fe in the paramagnetic state and compare our numerical results with the polarized neutron scattering experiment. We show that the short-range order in bcc Fe persists up to a temperature much higher than the Curie temperature but at rather small distances (up to 5Å).     

Debye–Waller Factor in Neutron Scattering by Ferromagnetic Metals

We obtain an expression for the neutron scattering cross section in the case of an arbitrary interaction of the neutron with the crystal. We give a concise, simple derivation of the Debye–Waller factor as a function of the scattering vector and the temperature. For ferromagnetic metals above the Curie temperature, we estimate the Debye–Waller factor in the range of scattering vectors characteristic of polarized magnetic neutron scattering experiments. In the example of iron, we compare the results of harmonic and anharmonic approximations.     

Scattering of Magnetic Edge States

We consider a charged particle following the boundary of a two dimensional domain because a homogeneous magnetic field is applied. We develop the basic scattering theory for the corresponding quantum mechanical edge states. The scattering operator attains a limit for large magnetic fields which preserves Landau bands. We interpret the corresponding scattering phases in terms of classical trajectories. Communicated by Yosi Avron submitted 23/02/05, accepted 3/05/05     

Scattering by magnetic nanocylinders and the method of distorted waves in noncollinear fields

In the perturbation theory framework, we compute the cross section of scattering by a magnetic nanocylinder and a helicoid arbitrarily oriented in an external magnetic field. We are the first to obtain the matrix Green’s function for two media with an interface and noncollinear magnetic fields on the two sides of the interface. We show how to compute scattering by magnetic inclusions in one of the media.     

Scattering theory for the Schrödinger equation in some external time-dependent magnetic fields

We study the theory of scattering for a Schrödinger equation in an external time-dependent magnetic field in the Coulomb gauge, in space dimension 3. The magnetic vector potential is assumed to satisfy decay properties in time that are typical of solutions of the free wave equation, and even in some cases to be actually a solution of that equation. That problem appears as an intermediate step in the theory of scattering for the Maxwell-Schrödinger (MS) system. We prove in particular the existence of wave operators and their asymptotic completeness in spaces of relatively low regularity. We also prove their existence or at least asymptotic results going in that direction in spaces of higher regularity. The latter results are relevant for the MS system. As a preliminary step, we study the Cauchy problem for the original equation by energy methods, using as far as possible time derivatives instead of space derivatives.     

Kinetic Magnetohydrodynamics of Neutron Matter

Equations for the magnetohydrodynamics of neutron matter are derived within a microscopic approach based on the Landau theory of a Fermi liquid. Along with the strong short-distance nuclear interactions, the equations account for the weak long-distance magnetic interactions. Applications of the derived magnetohydrodynamic equations to the theory of shock waves in neutron matter are discussed.     

On criticality problems in energy dependent neutron transport theory

In this paper, we consider the criticality problem for energy dependent neutron transport in an isotropically scattering, homogeneous slab. Under a positivity assumption on the scattering kernel, we can find an expression relating the thickness of the slab to a parameter characterizing production by fission. This is accomplished by exploiting the Perron-Frobenius-Jentsch characterization of positive operators (i.e. those leaving invariant a normal, reproducing cone in a Banach space). We point out that those techniques work for classes of multigroup problems where the Case singular eigenfunction approach is not as feasible as in the one-group theory, which is also analyzed.     

Some useful properties of Legendre polynomials and its applications to neutron transport equation in slab geometry

In this paper, we describe a new scattering kernel and general theoretical scheme for the evolution of the discrete and continuum eigenvalue spectrum in one-dimensional slab geometry neutron transport equation. Firstly, some useful properties of the Legendre polynomials which revealed during the definition of the new scattering kernel are discussed. By using the scattering kernel in one-dimensional neutron transport equation we obtained an integral equation for angular part of the angular flux. For the solution of this integral equation and eigenvalue equations, some comments are given.     

On nonlinear neutron transport equations

The purpose of this paper is to investigate a class of time-dependent neutron transport equations in which the total and differential scattering cross sections are nonlinear functions of neutron density function. Sufficient conditions on the nonlinear cross sections are given to insure the existence, uniqueness and asymptotic stability of a solution in one, two, or three-dimensional space domains under various boundary and initial conditions. The approach to the problem is based on abstract analysis on nonlinear evolution equations which are closely related to nonlinear semigroup theory.     

Scattering from a spatially restricted atom,I

We prove the existence and completeness of the wave operators for a model describing the elastic scattering of a neutron from the nucleus of an atom which is harmonically bound to a certain site in an infinite lattice. We then solve a similar problem for proton scattering under the assumption that the nuclear charge distribution has a nontrivial symmetry group, and finally consider dissipative effects due to the other lattice atoms on the scattering.     

Electroweak Nucleon Decays in a Superstrong Magnetic Field

We study the influence of a magnetic field on the electroweak processes of nucleon decay in a degenerate ideal gas of neutrons, protons, and electrons situated in an external superstrong constant and homogeneous magnetic field with effects due to the interaction of nucleon anomalous magnetic moments with the magnetic field taken into account. For different values of the chemical potentials of degenerate fermions, we obtain expressions for probabilities of electroweak processes, which are assumed to be responsible for the chemical equilibrium in the central domain of a neutron star with a frozen superstrong magnetic field. We show that the difference between the neutron decay probabilities in the presence of a magnetic field B ≪ 10¹⁷ G and without this field is completely determined by changing the phase volume of electron states. We discuss the process of proton decay into a neutron, positron, and neutrino. This process is energetically allowed only when the interaction of nucleon anomalous magnetic moments with a superstrong magnetic field is taken into account. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 1, pp. 108–122, October, 2005.     

Criticality problems for slabs and spheres in energy dependent neutron transport theory

The steady-state equation for energy-dependent neutron transport in isotropically scattering slabs and spheres is formulated as an integral equation. The Perron-Frobenius-Jentzsch theory of positive operators is used to analyze criticality problems for transport in slab and spherical media consisting of core and reflector. In addition, with an adroit selection of diffusion-like solutions, this theory is used to obtain an expression relating the critical radius of a homogeneous sphere to a parameter characterizing fission production.     

Nonlinear Electromagnetic Delay of Electromagnetic Signals Propagating in the Magnetic Meridian Plane of Pulsars and Magnetars

We analyze the propagation of electromagnetic waves in the magnetic meridian planes of neutron stars with a strong magnetic field in the framework of the parameterized post-Maxwellian electrodynamics of the vacuum. The origin of these electromagnetic waves is the curvature emission of X-rays and gamma rays from high-energy electrons in the vicinity of the magnetic poles of neutron stars. We show that in the case of a slowly varying intensity of X-ray and gamma-ray emission, the delay of the slow normal mode of electromagnetic waves relative to the fast mode results in a shift of the time dependence of the intensity of the detected radiation with one polarization relative to that of the radiation with the orthogonal polarization. In the case of single X-ray or gamma-ray pulses, the delay effect results in the polarization of the detected pulse varying during the pulse length, the leading edge of all pulses being polarized normally to the magnetic equator plane of the neutron star. We note that the modern level of the experimental technique, in principle, allows observing the manifestations of the delay effect for signals of different polarizations.     

INVERSE SCATTERING IN A LAYERED MEDIUM

We present a uniqueness theorem in inverse scattering at a fixed energy for the wave equation in a layered medium. We accommodate the Faddeev theory of inverse scattering using the calculus of commutators.     

Operator-valued Chandrasekhar H-functions

Operator valued analogs of the Chandrasekhar H-function, that occur in the study of neutron transport in a slab with continuous energy dependence and anisotropic scattering, satisfy a system of nonlinear integral equations. An appropriate Banach space setting is found for the study of this system. We show that the system may be solved by iteration. We extend the domain of analyticity of H_r and H_t by means of bifurcation theory.     

Quantum Macroscopic Effects in a Degenerate Strongly Magnetized Nucleon Gas

A model of a degenerate gas consisting of neutrons that are in chemical equilibrium with degenerate protons and electrons in a stationary and homogeneous superstrong magnetic field is used to describe the state of the matter in central regions of strongly magnetized neutron stars. Expressions for thermodynamic quantities (such as energy density, particle density, pressure, and magnetization) characterizing a degenerate gas of neutrons, protons, and electrons are obtained. In these expressions, the contributions determined by the interaction between anomalous magnetic moments of fermions and the magnetic field are taken into account. Macroscopic effects that may occur in strongly magnetized neutron stars are discussed. We show that all thermodynamic quantities characterizing electrically charged fermions in a strong magnetic field are subject to nonperiodic oscillations caused by the interaction of the anomalous magnetic moments of protons and electrons with the magnetic field. We also show that if the nucleon density and the electron density exceed threshold values that are relatively small and depend on the magnetic field strength, all fermions are fully polarized with respect to the spin. The full spin polarization effect in neutrons is caused by the interaction between the anomalous magnetic moment and the magnetic field. The obtained results may prove useful in understanding processes that occur in the nucleus of a neutron star with a magnetic field frozen into the star.     

Volume integral equations for scattering from anisotropic diffraction gratings

We analyze electromagnetic scattering of transverse magnetic polarized waves from a diffraction grating consisting of a periodic, anisotropic, and possibly negative index dielectric material. Such scattering problems are important for the modelization of, for example, light propagation in nano‐optical components and metamaterials. The periodic scattering problem can be reformulated as a strongly singular volume integral equation, a technique that attracts continuous interest in the engineering community but has rarely received rigorous theoretic treatment. In this paper, we prove new (generalized) Gårding inequalities in weighted and unweighted Sobolev spaces for the strongly singular integral equation. These inequalities also hold for materials for which the real part of the material parameter takes negative values inside the diffraction grating, independently of the value of the imaginary part. Copyright © 2012 John Wiley & Sons, Ltd.     

Radiant Heat Transfer Through an Aerosol Suspended in a Transparent Gas

The scattering of radiation by an aerosol in the cover-gas regionof a fast breeder nuclear reactor has been studied by meansof the equation of radiative transfer for a grey atmosphere.Some new results have been obtained in the form of an integralequation for the radiation intensity and heat flux. A variationalmethod is employed to obtain numerical results and the accuracyof an elementary theory based upon discrete ordinates is assessed.The variational approach leads to computationally useful andaccurate results for several quantities of practical interest.The interdisciplinary nature of the work is stressed by virtueof its close connection with neutron transport theory and rarefiedgas dynamics.     

Decoupled field integral equations for electromagnetic scattering from homogeneous penetrable obstacles

We present a new method for the analysis of electromagnetic scattering from homogeneous penetrable bodies. Our approach is based on a reformulation of the governing Maxwell equations in terms of two uncoupled vector Helmholtz systems: one for the electric field and one for the magnetic field. This permits the derivation of resonance-free Fredholm equations of the second kind that are stable at all frequencies, insensitive to the genus of the scatterers, and invertible for all passive materials including those with negative permittivities or permeabilities. We refer to these as decoupled field integral equations.     

Equilibrium of a Degenerate Gas of Nucleons and Electrons in a Strong Magnetic Field

A model of a degenerate ideal gas of nucleons and electrons in a superstrong magnetic field is used to describe the state of matter in the central region of a strongly magnetized neutron star. The influence of a constant uniform superstrong magnetic field on the equilibrium conditions and the equation of state for the degenerate gas of neutrons, protons, and electrons is investigated in the framework of this model. The contribution determined by the interaction of the anomalous magnetic moments of the fermions with the magnetic field is taken into account. The influence of the superstrong magnetic field on the process of gravitational collapse of a magnetized neutron star is discussed under the assumption that the central region of the star consists mostly of degenerate neutrons. We show that if the densities of electrons, protons, and neutrons are relatively low depending on the field strength, the fermion gases in a superstrong uniform magnetic field become totally polarized with respect to the spin. We discuss the possibility of spontaneous magnetization occurring in a system of degenerate neutrons where the exchange interaction effects are taken into account.