General three-particle scattering theory

A unified treatment of three-particle scattering theory with a three-body force in addition to the usual pair interactions is developed. The relationship of the generalized AGS and Faddeev formalisms to each other as well as distinct versions of each corresponding to the two most natural techniques for handling the three-body potential are established. It is found, just as in the case without the three-particle force, that the AGS formalism appears to be more practical for considering elastic and rearrangement scattering in two-body channels. On the other hand, for scattering amplitudes with at least one three-body channel (breakup and the 3-to-3) the Faddeev version of the theory is preferable. Other advantages of each formalism depending upon the treatment of the three-body interaction are noted.     

General relations between neutrino and antineutrino scattering

Assuming Born approximation and that the neutrino covariants in the interaction are nonderivative, we obtain some simple relations between neutrino and antineutrino scattering on any target: the scattering may be elastic, inelastic or deeply inelastic. Some of these relations have been noted already in some special cases by making stronger assumptions and sometimes only by explicit calculation. Our derivations rest only on simple general considerations.     

Impedance theory of sound scattering and absorption: A constrained best absorber and the efficiency bounds of passive scatterers and absorbers

A constrained best absorber is defined as a body that absorbs the maximum incident sound power among all of the passive bodies of the same geometry under the condition that the sound power scattered by it is fixed. By solving a variational problem, the surface impedances of the constrained best absorber are determined and the efficiency bounds of passive scatterers and absorbers are found. The range of all the allowable values of the absorption and scattering powers of an arbitrary passive body is represented graphically. For the boundaries of this range, analytical formulas are derived. Some of the properties of constrained best absorbers are considered, and illustrative examples are presented.     

Impedance theory of sound absorption: The best absorber and the black body

The impedance theory of scattering (which was proposed by the author—see Acoust. Phys. 52, No. 5 (2006)) is used as the basis for studying the extremum properties of the absorption and scattering sound powers of arbitrary elastic bodies in an arbitrary acoustic medium. Impedance-type conditions are obtained for the surfaces of a best absorber, a perfect scatterer, and a so-called Macdonald body. The absorbing and scattering properties of these objects are studied in comparison with the Kirchhoff black body. Illustrative examples are presented.     

A phenomenological theory of light scattering by surfaces: I. General theory

A phenomenological theory of light scattering by surfaces is presented. The differential intensity of the scattered light is found in terms of autocorrelation functions characteristic for the distribution of matter in the surface layer. Local field factors are found.     

Low frequency sound scattering from spherical assemblages of bubbles using effective medium theory

The determination of the acoustic field scattered by an underwater assembly of gas bubbles or similar resonant monopole scatterers is of considerable theoretical and practical interest. This problem is addressed from a theoretical point of view within the framework of the effective medium theory for the case of spherically shaped assemblages. Although being valid more generally, the effective medium theory is an ideal instrument to study multiple scattering effects such as low frequency collective resonances, acoustically coupled breathing modes of the entire assembly. Explicit expressions for the scattering amplitude and cross sections are derived, as well as closed form expressions for the resonance frequency and spectral shape of the fundamental collective mode utilizing analytical S-matrix methods. This approach allows, in principle, a simultaneous inversion for the assembly radius and void fraction directly from the scattering cross sections. To demonstrate the validity of the approach, the theory is applied to the example of idealized, spherically shaped schools of swim bladder bearing fish. The analytic results of the theory are compared to numerical first-principle benchmark computations and excellent agreement is found, even for densely packed schools and frequencies across the bladder resonance.     

The effect of diatom-diatom collisions on depolarized light scattering linewidths : I. General theory

With the use of an appropriately generalized Waldmann-Snider collision (super-) operator, a unified kinetic theory treatment of depolarized light scattering (both depolarized Rayleigh and rotational Raman) and their related linewidths is presented for gases of rigid rotor molecules. Explicit expressions are given, both exactly and within a distorted wave Born approximation, for the various state-to-state (i.e. rotational quantum number dependent) collision processes which can contribute to any observed linewidths due to diatom-diatom collisions. The results of this paper are employed in the calculation of the depolarized linewidths for the hydrogen isotopes in the following article.     

Renormalization group and relations between scattering amplitudes in a theory with different mass scales

In the Yukawa model with two different mass scales, the renormalization group equation is used to obtain relations between scattering amplitudes at low energies. By considering fermion-fermion scattering as an example, a basic one-loop renormalization group relation is derived which gives the possibility to reduce the problem to the scattering of light particles in the “external field” substituting a heavy virtual state. Applications of the results to problems of searches for new physics beyond the Standard Model are discussed.     

On the theory of multiple scattering of sound waves by spherical particles in liquid and elastic media

Two independent systems of equations are derived for describing the scalar and vector potentials of the sound field in a liquid or elastic medium containing discrete inhomogeneities. One of the systems determines the sound field as the sum of the fields scattered by the particles according to the law of scattering by a single particle with the oscillation amplitudes governed by the properties of the inhomogeneous medium. The other system determines the sound field as the sum of the scattered fields formed in the inhomogeneous medium with the oscillation amplitudes of a particle in a homogeneous medium. Expressions relating the fields that occur in a medium consisting of N particles to the fields in a medium consisting of N − 1 particles are proposed. These expressions may simplify and diversify the methods used for computer simulation of sound fields with the aim to verify the calculations. The results of the study are valid for any particle concentrations under the condition that the scattering by a single particle is determined by its monopole, dipole, and rotary oscillations.     

Quasi-wavelet calculations of sound scattering behind barriers

Quasi-wavelets (QWs) are a representation of turbulence consisting of self-similar, eddy-like structures with random orientations and positions in space. They are used in this paper to calculate the scattering, due to turbulent velocity fluctuations, of sound behind noise barriers as a function of the size and spatial location of the eddies. The sound scattering cross-section for QWs of an individual size class (eddy size) is derived and shown to reproduce results for the von Kármán spectrum when the scattered energies from a continuous distribution of QW sizes are combined. A Bragg resonance condition is derived for the eddy size that scatters most strongly for a given acoustic wavenumber and scattering angle. Results for scattering over barriers show that, for typical barrier conditions, most of the scattered energy originates from eddies in the size range of approximately one-half to twice the size of the eddies responsible for maximum scattering. The results also suggest that scattering over the barrier due to eddies with a line of sight to both the source and receiver is generally significant only for frequencies above several kilohertz, for sources and receivers no more than a few meters below the top of the barrier, and for very turbulent atmospheric conditions.     

Tilt-invariant theory of rough-surface scattering: I

Abstract

The small-slope approximation (SSA) in rough-surface scattering theory uses the surface slope as a small parameter of expansion. But, from the physical point of view, the slope may not be a restrictive parameter because we can change the slope of a surface simply by tilting the coordinate system. We present the theory of rough-surface scattering in a coordinate-invariant form. The new method, tilt-invariant approximation (TIA), leads to a different expansion that does not require that the slope of a surface be small. For a small Rayleigh parameter this approximate solution provides the correct perturbation theory, for a large Rayleigh parameter it provides the Kirchhoff approximation with several correcting terms.     

Tilt-invariant theory of rough-surface scattering: I

The small-slope approximation (SSA) in rough-surface scattering theory uses the surface slope as a small parameter of expansion. But, from the physical point of view, the slope may not be a restrictive parameter because we can change the slope of a surface simply by tilting the coordinate system. We present the theory of rough-surface scattering in a coordinate-invariant form. The new method, tilt-invariant approximation (TIA), leads to a different expansion that does not require that the slope of a surface be small. For a small Rayleigh parameter this approximate solution provides the correct perturbation theory, for a large Rayleigh parameter it provides the Kirchhoff approximation with several correcting terms.     

Abstract scattering theory

The asymptotic condition is formulated for a system whose theory is more general than quantum mechanics. Its logic forms an orthocomplemented weakly modular -lattice. The set of states , consisting of all the probability measures on , is endowed with the most suitable metric physically, called here the natural one. In this space it is proved that the asymptotic condition implies the existence of two convex automorphisms _+- of which we call the wave-automorphisms. From these theS-automorphism _– ^–1 ₊ is defined and corresponds to the scattering operator in conventional quantum theory.     

Time dependent canonical perturbation theory I: General theory

In this communication, we reanalyze the causes of the singularities of canonical perturbation theory and show that some of these singularities can be removed by using time-dependent canonical perturbation theory. A study of the local and global properties (in terms of the perturbation parameter) is also undertaken.