Application of the diffraction trace formula to the three-disk scattering system

The diffraction trace formula derived previously and the spectral determinant are tested on the open three-disk scattering system. The system contains a generic and exponentially growing number of diffraction periodic orbits. In spite of this it is shown that even the scattering resonances with large imaginary part can be reproduced semiclassically. The nontrivial interplay of the diffraction periodic orbits with the usual geometrical orbits produces the fine structure of the complicated spectrum of scattering resonances, which are beyond the resolution of the conventional periodic orbit theory.     

The many-body problem within the Lee model

The structure of a field theoretical many-body problem is studied within the (non-static) Lee model. The explicit solvability of the renormalization problem allows the investigation of renormalization corrections in many-particle systems. Herefore, the renormalized equations are worked out for the N-V scattering and for the binding-energy problem of “N-V matter” — these cases taken in analogy to nucleon-nucleon scattering and nuclear matter. The N-V matter equations are obtained from a cluster expansion suitably defined for the field theoretical case. The ansatz for the correlated wave functions is chosen in such a way as to generate a two-hole-line expansion of the binding energy. The renormalized form of this field theoretical extension of Brueckner theory is discussed in detail revealing the medium effects on renormalization.     

Higher-order <Emphasis Type="Bold">?</Emphasis> corrections in the semiclassical quantization of chaotic billiards

In the periodic orbit quantization of physical systems, usually only the leading-order ? contribution to the density of states is considered. Therefore, by construction, the eigenvalues following from semiclassical trace formulae generally agree with the exact quantum ones only to lowest order of ?. In different theoretical work the trace formulae have been extended to higher orders of ?. The problem remains, however, how to actually calculate eigenvalues from the extended trace formulae since, even with ? corrections included, the periodic orbit sums still do not converge in the physical domain. For lowest-order semiclassical trace formulae the convergence problem can be elegantly, and universally, circumvented by application of the technique of harmonic inversion. In this paper we show how, for general scaling chaotic systems, also higher-order ? corrections to the Gutzwiller formula can be included in the harmonic inversion scheme, and demonstrate that corrected semiclassical eigenvalues can be calculated despite the convergence problem. The method is applied to the open three-disk scattering system, as a prototype of a chaotic system. Received 10 September 2001 and Received in final form 3 January 2002     

On the dielectric constant for a non-polar fluid,a comparison

Sullivan and Deutch recently showed how the Wertheim formula for the dielectric constant of a non-polar fluid can be obtained as the lowest order result in a systematic expansion. We compare the results of this procedure with the results obtained with the more usual analysis of deviations from Clausius-Mossotti. On the basis of some rigorous theoretical arguments and some numerical results we conclude that Wertheim's formula predicts deviations from Clausius-Mossotti accurately to second order in the density. For higher densities we find that higher order corrections in the systematic expansion are necessary to find agreement. It is concluded that Wertheim's formula is therefore only a valid improvement over Clausius-Mossotti for low and intermediate densities. Sullivan and Deutch derive an expression for the local field factor, which appears in light scattering, valid to lowest order. They compare this factor with experimental results and find that it agrees much better than the factor which follows from Clausius-Mossotti for liquid densities. We give a general expression and show that higher order corrections to Wertheim's theory change the local field factor by a few percent. On the basis of this we conclude that the better than one percent agreement found by Sullivan and Deutch is to some extent fortuitous.     

Binding corrections for reactions on the deuteron in the 3-3 resonance region

Binding corrections evaluated to all orders in a phenomenological nucleon-nucleon potential are compared with the leading term and with a double scattering correction in the Watson expansion for breakup and for coherent reactions on the deuteron at intermediate pion or photon energies. As principal result, we establish that for charged pion photoproduction, and for certain pion induced “spectator” reactions, the binding correction remains sufficiently small that truncation of the Watson expansion at terms of second order in the projectile-nucleon amplitudes is justifiable, but sufficiently large that it cannot be neglected in comparison with multiple scattering corrections. For the reactions π⁺d → π⁺p + spectator neutron and π^?d → π^?n + spectator proton, our theory predicts deviations from the simplest impulse approximation which become very large in well-defined kinematical regions, and should be easily accessible to experimental investigation.     

Mass corrections to scaling in deep inelastic processes

We study subasymptotic hadron target and quark-parton mass corrections to scaling in deep inelastic scattering, ignoring interactions. The results can be summarized using a modified scaling variable common to parton, light-cone and short-distance operator product expansion formalisms, but with model-dependent spectral conditions. The analysis is expected to break down near the kinematic boundaries because of the bound state nature of hadrons. Related effects probably also dominate mass corrections due to very light quarks, but the analysis should be applicable to the production of new heavy quarks in neutrino production. Experimental deviations from scaling in deep inelastic electroproduction do not seem to be describable in terms of mass corrections alone, suggesting that interaction effects may be important at large momentum transfers as suggested by the renormalization group.     

Quantum chaotic scattering with a mixed phase space: the three-disk billiard in a magnetic field

We study the classical and semiclassical scattering behavior of electrons in an open three-disk billard in the presence of a homogeneous magnetic field, which is confined to the inner part of the scattering region. As the magnetic field is increased the phase space of the invariant set of the classical scattering trajectories changes from hyperbolic (fully chaotic) to a mixed situation, where KAM tori are present. The "stickiness" of the stable trajectories leads to a much slower decay of the survival probability of trajectories as compared to the hyperbolic case. We show that this effect influences strongly the quantum fluctuations of the scattering amplitude and cross sections.     

Mean distribution of single-particle levels in thin-skinned potential wells and the macroscopic level density parameters of nuclei

A general leptodermous expansion for the density of single-particle levels in thin-skinned potential wells is derived and is used to study the finite size corrections to the macroscopic level density parameters of nuclei. With droplet model values for the potential parameters, the calculated level density parameters for nuclei along the β-stability line show systematic deviations from the experimental estimates. Possible reasons for these deviations are also discussed.     

Evidence for a deep bound-state level in the 4HeNaCl(001) potential

Through a systematic high-resolution study of the elastic bound state resonances observed in the inelastic background of the angular distributions of ⁴He scattering from the NaCl(001) surface, carried out at 90 K, we obtained clear and conclusive evidence that a deep level in the ⁴HeNaCl(001) interaction potential exists at −7.07 meV. Important deviations from the free-atom dispersion are observed, as expected for deep bound-state levels. We discuss the physical reasons why deep-level resonances, which are observed in inelastic scattering, may not be detectable in elastic scattering experiments. This finding appears to be crucial with respect to the theory of atom-surface potentials since former quantum-mechanical and close-coupling calculations excluded the existence of a deep level in ⁴HeNaCl(001) in agreement with elastic scattering studies but at odds with phenomenological predictions.     

Overlapping resonances and unitarity of the scattering matrix

An automatically unitary product expansion for a scattering matrix with arbitrary over-lapping resonances is discussed and used to derive sum rules for the resonance parameters. Problems with the implementation of time-reversal invariance are pointed out.     

Precise numerical results for limit cycles in the quantum three-body problem

The study of the three-body problem with short-range attractive two-body forces has a rich history going back to the 1930s. Recent applications of effective field theory methods to atomic and nuclear physics have produced a much improved understanding of this problem, and we elucidate some of the issues using renormalization group ideas applied to precise nonperturbative calculations. These calculations provide 11-12 digits of precision for the binding energies in the infinite cutoff limit. The method starts with this limit as an approximation to an effective theory and allows cutoff dependence to be systematically computed as an expansion in powers of inverse cutoffs and logarithms of the cutoff. Renormalization of three-body bound states requires a short range three-body interaction, with a coupling that is governed by a precisely mapped limit cycle of the renormalization group. Additional three-body irrelevant interactions must be determined to control subleading dependence on the cutoff and this control is essential for an effective field theory since the continuum limit is not likely to match physical systems (e.g., few-nucleon bound and scattering states at low energy). Leading order calculations precise to 11-12 digits allow clear identification of subleading corrections, but these corrections have not been computed.     

Allowance for the Coulomb interaction in the framework of an algebraic version of the resonating group method

The Coulomb proton interaction is taken into account in the problem of light atomic nucleus scattering using an algebraic version of the resonating group method. Specific formulas are obtained for calculating the elastic scattering phases. The elastic pα scattering phases, the positions of resonances and their widths are calculated for some NN potentials. Theoretical values of the quantities under consideration adequately describe experimental data.     

The isobar-doorway theory for pion-nucleus interactions

Pion-nucleus scattering and reactions are treated in a theory which explicitly introduces the pion-nucleon resonances. Using a separation in Hilbert Space, doorway states of isobar-nuclear systems are introduced and nonresonant processes are clearly separated from resonance interactions. With one choice of doorway states a multiple scattering series is derived which corresponds to the conventional theory with binding energy and other corrections included. When another choice the isobar-doorway model is derived, with parameterization explicitly related to specific dynamic effects, our framework provides a phenomenological model for treating meson-nucleus interactions to all orders. Moreover, the parameters of the model have clear theoretical significance which can extend our knowledge of strong interactions physics. A numerical study is given for elastic scattering.     

Modeling the characteristics of the waves scattering by a group of scatterers

The pattern equations method is extended to solving the diffraction problem on a group of bodies. The problem is reduced to solving an algebraic system of equations with respect to the expansion coefficients of the scattering patterns by using a series expansion of the scattering patterns in angular spherical harmonics. The explicit (asymptotic) solution of the problem is obtained in a case when the scattering bodies are far enough from each other.     

Line shapes and threshold resonances for the scattering of waves from surfaces

An analytical study of threshold resonances in scattering of scalar waves from periodic surfaces is presented. Resonances are found with a variety of line shapes which provide characteristic information on the surface potential. The analytical predictions on line shapes are supported numerically. These resonances should be observed in atom-surface scattering and in scattering of light from large-amplitude gratings. We think that these resonances may be important for the field enhancement on surfaces.     

Baryon-baryon and baryon-antibaryon interaction amplitudes in the spin-momentum operator expansion method

Partial-wave scattering amplitudes in baryon-baryon and baryon-antibaryon collisions and amplitudes for the production and decay of baryon resonances are constructed in the framework of the spin-momentum operator expansion method. The approach is relativistically invariant and it allows us to perform combined analyses of different reactions imposing analyticity and unitarity directly. The role of final-state interactions (triangle and box diagrams) is discussed.     

Light scattering by a finite obstacle and fano resonances

The conditions for observing Fano resonances at elastic light scattering by a single finite-size obstacle are discussed. General arguments are illustrated by consideration of the scattering by a small (relative to the incident light wavelength) spherical obstacle based upon the exact Mie solution of the diffraction problem. The most attention is paid to recently discovered anomalous scattering. An exactly solvable one-dimentional discrete model with nonlocal coupling for simulating diffraction in wave scattering in systems with reduced spatial dimensionality is also introduced and analyzed. Deep connections between the resonances in the continuous and discrete systems are revealed.     

Resonant states for the scattering of slow particles by screened potentials

Partial resonant situations for the scattering of slow particles with nonzero angular momenta by short-range screened Yukawa and Buckingham potentials are considered. The problem of electron scattering by a hydrogen atom placed in a plasma medium is discussed. A general scheme of resonances has been constructed in the Pais approximation.     

Herman–Wallis correction in vibrational CARS of oxygen

Light molecules are subject to vibration–rotation (VR) interaction, which implies corrections to the rigid rotor approximation and, in particular, corrections to spectral line intensities are related to the so‐called Herman–Wallis (HW) factor. This problem is outlined here for the spectral response of some medium‐weight diatomics in the gas phase and probed by means of vibrational coherent anti‐Stokes Raman scattering (CARS) used for diagnostic reasons in combustion science. However, different from other works on this subject, we specialized our analysis to oxygen and, since the peculiarity of its anti‐bonding molecular orbital, we find that the VR coupling is responsible for deviations that compete with the effect of Raman line widths typical of collisional environments of hot gases at room pressure. The HW correction is ultimately demonstrated to affect O₂ CARS thermometry in such a manner that the accuracy for measurements at high temperatures can be improved. Copyright © 2011 John Wiley & Sons, Ltd.