Showing papers on "Scattering length published in 1995"

Geometric scattering theory

Abstract: List of illustrations Introduction 1. Euclidean Laplacian 2. Potential scattering on Rn 3. Inverse scattering 4. Trace formulae and scattering poles 5. Obstacle scattering 6. Scattering metrics 7. Cylindrical ends 8. Hyperbolic metrics.

Time-dependent solution of the nonlinear Schrödinger equation for Bose-condensed trapped neutral atoms

Abstract: We present numerical results from solving the time-dependent nonlinear Schr\"odinger equation (NLSE) that describes an inhomogeneous, weakly interacting Bose-Einstein condensate in a small harmonic trap potential at zero temperature. With this method we are able to find solutions for the NLSE for ground state condensate wave functions in one dimension or in three dimensions with spherical symmetry. These solutions corroborate previous ground state results obtained from the solution of the time-independent NLSE. Furthrmore, we can examine the time evolution of the macroscopic wave function even when the trap potential is changed on a time scale comparable to that of the condensate dynamics, a situation that can be easily achieved in magneto-optical traps. We show that there are stable solutions for atomic species with both positive and negative s-wave scattering lengths in one-dimensional (1D) and 3D systems for a fixed number of atoms. In both the 1D and 3D cases, these negative scattering length solutions have solitonlike properties. In 3D, however, these solutions are only stable for a modest range of nonlinearities. We analyze the prospects for diagnosing Bose-Einstein condensation in a trap using several experiments that exploit the time-dependent behavior of the condensate.

Singular quasiparticle scattering in the proximity of charge instabilities.

Abstract: We analyze the dynamic scattering amplitude between quasiparticles at the Fermi surface in the proximity of a charge instability, which may occur in the high temperature superconductors. Within the infinite-$U$ Hubbard-Holstein model we find that in the absence of long-range Coulomb forces the scattering amplitude is strongly singular at zero momentum transfer close to the phase separation instability. In the presence of long-range Coulomb forces the singularity occurs at finite wave vectors. In both cases we show how normal state properties are largely affected by this scattering.

Calculation of electron-helium scattering.

Abstract: We present the convergent close-coupling theory for the calculation of electron-helium scattering. We demonstrate its applicability at a range of projectile energies of 1.5 to 500 eV to scattering from the ground state to n\ensuremath{\le}3 states. Generally, good agreement with experiment is obtained with the available differential, integrated, ionization, and total cross sections, as well as with the electron-impact coherence parameters up to and including the 3 $^{3}$D-state excitation. This agreement is shown to be overall the best of the currently used electron-helium scattering theories. On occasion, some significant discrepancies with experiment are observed, particularly for the triplet-state excitations.

Green function for multilayers: Light scattering in planar cavities.

Abstract: A compact and transparent plane-wave expansion of the complete Green function for an absorbing multilayered system is derived. The plane-wave solutions involved match, in the appropriate limit, the space-mode functions recently employed for quantization of the radiation field in a planar cavity and make this Green function particularly convenient for consideration of optical processes in realistic cavities and multilayers in general. This is illustrated by considering classically light scattering on a molecule in a planar cavity. It is demonstrated that the cross sections derived, besides generally describing light scattering on molecules embedded in a multilayer, correctly reproduce the effects of field confinement on light scattering in a planar cavity as predicted recently by the quantum-mechanical theory of Cairo et al. [Phys. Rev. Lett. 70, 1413 (1993)]. It is also pointed out that scattering into waves guided by the cavity lossy (metallic) mirrors may become an effective process in low-order microcavities. As a by product, a classical approach to spontaneous emission in absorbing planar cavities emerges from these considerations.

Inverse scattering problem for the Schrödinger equation with magnetic potential at a fixed energy

Abstract: In this article we consider the Schrodinger operator inR n ,n≧3, with electric and magnetic potentials which decay exponentially as |x|→∞. We show that the scattering amplitude at fixed positive energy determines the electric potential and the magnetic field.

The validity of form-factor, modified-form-factor and anomalous-scattering-factor approximations in elastic scattering calculations

Abstract: The validity of form-factor, modified-form-factor and anomalous-scattering-factor approximations in predictions of elastic photon-atom scattering is assessed with the aid of the state-of-the-art numerical calculation of Rayleigh scattering obtained using the second-order S-matrix theory, in the photon energy range from 100 eV to 1 MeV. A comparison is made with predictions from S-matrix theory in the same atomic model for representative low-Z (carbon, Z = 6) and high-Z (lead, Z = 82) elements to get a general idea of the validity of these simpler more approximate methods. The importance of bound–bound contributions and the angle dependence of the anomalous scattering factors is discussed. A prescription is suggested, with the assumption of angle independence, that uses simpler approaches to obtain the elastic scattering cross sections in the soft-X-ray regime at the level of accuracy of the S-matrix calculation, failing at large momentum transfers for high-Z elements. Predictions from this prescription are compared with experiment. With starting point the many-body elastic scattering amplitude, a detailed discussion is presented of the partition of the elastic scattering amplitude into Rayleigh and Delbruck scattering components. This partition of the optical theorem reveals contributions from bound–bound atomic transitions, bound pair annihilation and bound pair production that are not usually associated with elastic scattering. In the partitioned optical theorem for Rayleigh scattering, as in the many-body optical theorem for scattering from excited states, subtracted cross sections naturally appear. These terms are needed, in addition to the familiar terms for photoionization, to relate the real and imaginary parts of the scattering amplitude.

Detailed theoretical and experimental analysis of low-energy electron-N2 scattering.

Abstract: We have carried out a comprehensive theoretical and experimental study of electron scattering from molecular nitrogen at energies below 10.0 eV. In the theoretical component of this project we have generated differential and integral cross sections for elastic scattering and vibrational excitation in converged vibrational close-coupling calculations. In the experiments, we have measured differential cross sections for these processes at scattering angles from 20\ifmmode^\circ\else\textdegree\fi{} to 130\ifmmode^\circ\else\textdegree\fi{} in a crossed-beam experiment at a large number of energies between 0.55 and 10 eV and, in a complementary time-of-flight experiment, total cross sections at energies between 0.08 and 10.0 eV. The measured angular distributions have been extrapolated to 0\ifmmode^\circ\else\textdegree\fi{} and 180\ifmmode^\circ\else\textdegree\fi{} using a procedure based on a nonlinear least-squares fit constrained by known physical properties of the e-${\mathrm{N}}_{2}$ scattering matrix; numerical integration of the resulting extrapolated distributions yields integrated cross sections with almost no error beyond that inherent in the measured angular data. We find generally good agreement between the present experimental and theoretical cross section, particularly at energies near the ${\mathrm{\ensuremath{\Pi}}}_{\mathit{g}}$ resonance near 2.39 eV. In previous studies of scattering in this region, such comparisons have been made problematical by the difficulty of ascertaining the appropriate theoretical scattering energy. We recommend here a protocol for resolving this problem for both elastic scattering and vibrational excitation.

Exact determination of the phase in neutron reflectometry.

Abstract: We show that by using a known reference layer having three tunable values of scattering density, an exact determination of the complex amplitude R=ReR+i ImR for neutron specular reflection can be made for any unknown real potential (i.e., no absorption). This straightforward yet remarkable general result is valid even in the dynamical regime (where the conventional Born approximation fails) and makes it feasible to consider direct inversion methods for obtaining the scattering length density profile normal to the reflecting surface.

The geometrical approach to multidimensional inverse scattering

Abstract: We prove that in multidimensional short‐range potential scattering the high velocity limit of the scattering operator of an N‐body system determines uniquely the potential. For a given long‐range potential the short‐range potential of the N‐body system is uniquely determined by the high velocity limit of the modified Dollard scattering operator. Moreover, we prove that any one of the Dollard scattering operators determines uniquely the total potential. We obtain as well a reconstruction formula with an error term. Our simple proof uses a geometrical time‐dependent method.

Attenuation, dispersion, and anisotropy by multiple scattering of transmitted waves through distributions of scatterers

Abstract: Scattering of waves causes the coherent wave field to be attenuated and dispersed. These phenomena express the fact that the pulse loses coherence by which incoherent coda energy is created. First‐order scattering theory violates the law of energy conservation and therefore cannot be used when the wave field is strongly distorted. An approximation is proposed which estimates the interaction between different scatterers by considering only multiple forward scattering interactions. Internal of a single scatterer all multiple interactions are maintained. This approximation can only be valid for the first part of the wave field and sufficiently weak scattering conditions. The heterogeneous medium can then be described as an effective medium that is a function of the scatterer density and forward scattering amplitude and the background medium. Simulations of the multiple scattering process with isotropic scatterers in two dimensions show that the discrepancies between the exact and approximate solution are sma...

Estimation of nonisotropic scattering in western Japan using coda wave envelopes : application of a multiple nonisotropic scattering model

Abstract: Scattering by heterogeneities is an important factor controlling shapes oF seismograms. Analyzing horizontal component seismograms in the band 1.0-8 Hz of local earthquakes in western Japan, the author found that coda energy concentration just after the S wave arrival is more than expected for any multiple isotropic scattering model in uniform infinite medium. This behavior was seen even for deep earthquakes and became stronger with increase of frequency. To try to interpret this observation, nonisotropy is introduced into the multiple scattering model. The observed envelopes are compared with the model in order to estimate the amount of nonisotropy in scattering. Coda wave envelopes are synthesized using the Monte Carlo method for the nonisotropic scattering media. Two types of angular dependent scattering are considered as models of the nonisotropy with relation to the perturbation of seismic wave velocity in the lithosphere: perturbed media with exponential and Gaussian autocorrelation functions. It is found that forward scattering is dominant and the strength of sideways scattering is at least 10 times larger than that of backward scattering. The amount of the nonisotropic scattering means that correlation distance is estimated to be larger than several hundred meters in the case of Gaussian random media. 31more » refs., 17 figs.« less

An 18-state calculation of positron-hydrogen scattering

Abstract: We report results for positron scattering by ground-state atomic hydrogen in the energy range 0 to 80 eV. The calculations have been performed in an 18-state Ps(1s, 2s, 3s, 4s, 2p, 3p, 4p, 3d, 4d)+H(1s, 2s, 3s, 4s, 2p, 3p, 4p, 3d, 4d) approximation where the pseudostates (denoted by a bar) have been taken from Fon et al. (1981). Cross sections are presented for elastic scattering, positronium formation, total scattering and ionization. The elastic scattering results are in good agreement with accurate variational numbers at low energies and with other sophisticated, but very different, theoretical approximations at higher energies. We estimate that the elastic cross section is now known to better than 10%. The cross section for positronium formation is dominated by capture into the 1s state and is in fairly good agreement with the measurements of Weber et al. (1994). The results for the total cross section are generally consistent with the upper and lower bounds of Zhou et al. (1994) but are a little larger than other theoretical estimates at the higher energies. There is also a general theoretical problem concerning the degree to which the total cross sections for electrons and positrons merge at energies above 31 eV. The calculated ionization cross section is in agreement with the measurements of Jones et al. (1993).

Electron-atom collisions

Abstract: Preface 1. Introduction 2. Experimental techniques for cross-section measurements 3. Background quantum mechanics in the atomic context 4. One-electron problems 5. Theory of atomic bound states 6. Formal scattering theory 7. Calculation of scattering amplitudes 8. Spin-independent scattering observables 9. Spin-dependent scattering observables 10. Ionisation 11. Electron momentum spectroscopy References Index.

QCD sum rules, scattering length, and vector mesons in the nuclear medium.

Abstract: Mass shift of vector mesons in the nuclear medium is studied in two different approaches: the in-medium QCD sum-rule approach and the scattering-length approach. The latter is shown to be inapplicable to extract the hadron masses in the medium. Further elaboration of the in-medium QCD sum rules is also discussed.

Photoabsorption by ultracold atoms and the scattering length.

Abstract: It is shown that photoabsorption in a gas of ultracold atoms depends on the sign and magnitude of the scattering length in the scattering of a pair of atoms. Measurements of fluorescence in ${}^{7}$Li are interpreted to show that the triplet scattering length is negative and the singlet scattering length is positive.

Scattering of massless scalar waves by a Schwarzschild black hole: A phase-integral study.

Abstract: Plane scalar waves scattered off a Schwarzschild black hole are studied in the partial-wave picture. A new approximate formula for the relevant phase shifts is derived using the phase-integral method. This formula is, in principle, uniformly valid for all frequencies and agrees with well-known approximations for frequencies well above and below the top of the curvature potential barrier. The reliability of the phase-integral formula is assessed in two different ways. First we use the fact that higher orders of approximation are easily implemented in the phase-integral method. The accuracy of each phase shift can be estimated by the contribution to it by the following order of approximation. Second, we use the approximate phase shifts to construct physically meaningful quantities, such as the deflection function and cross section, for several scattering frequencies. The features of these quantities, especially those associated with the prominent black-hole glory in the backward direction, are in excellent agreement with results of previous studies of the problem. The new phase-shift formula is thus shown to be reliable and provides a useful and efficient tool, especially for intermediate and high frequencies.

Failure of the optical theorem for Gaussian-beam scattering by a spherical particle

Abstract: It is shown that when an electromagnetic wave with some degree of amplitude rolloff in the transverse direction is scattered by a spherical particle, the optical theorem is not valid. For such shaped beams the extinction cross section may be written as an infinite series in powers of the reciprocal of the beam width. The imaginary part of the forward-scattering amplitude is shown to be the first term in this series. Two approximations to the extinction cross section are presented for the special case of Gaussian-beam scattering. The first one is based on the dominance of diffraction in the forward direction for w0 ≳ a, where w0 is the beam half-width and a is the target particle radius. The second approximation, valid for w0 ≲ a, is based on transmission-compensating field interference.

Synthesis and SANS Structural Characterization of Polymer-Substituted Fullerenes (Flagellenes)

Abstract: Small-angle neutron scattering (SANS) has been shown to be an appropriate technique for the structural characterization of fullerenes in solvents with strong SANS contrast (e.g., CS 2 ) [Affholter, K. A. ; Henderson, S. J. ; Wignall, G. D. ; Bunick, G. J. ; Haufler, R. E. ; Compton, R. N. J. Chem. Phys. 1993, 99, 9224]. Since deuterated solvents (e.g., toluene-d 8 ) have a high scattering length density (SLD) which is close to that of C 60 and C 70 fullerenes, there is virtually no SANS contrast with the solvent, and these particles are practically invisible in such media. On the other hand, the negative scattering length of hydrogen means that the SLD of 1 H-containing materials is much lower, so they have a strong contrast with toluene-d 8 . Thus, SANS makes it possible to study the sizes and shapes of polymer-substituted fullerenes (flagellenes) [Samulski, E. T. ; DeSimone, J. M. ; Hung, M. O., Jr. ; Menceloglu, Y. Z. ; Jarnagin, R. C. ; York, G. A. ; Labat, K. B. ; Wang, H. Chem. Mater. 1992, 4, 1153]. Mono- and dipolystyrene-substituted C 60 were synthesized via termination of living anionic polymerization of styrene in an optimization of our previous work [Samulski et al.]. These materials were characterized by gel permeation chromatography (GPC) and small-angle neutron scattering (SANS). The extrapolated cross section at zero angle of scatter [dΣ/dΩ(0)] is a function of the number of pendant chains, so SANS can be used to assess the number of arms which are covalently attached to the fullerene core. Close agreement (±4%) between the measured and calculated values of dΣ/dΩ(0) and with independent estimates of the radius of gyration (R g ) and second virial coefficient (A 2 ) for a linear polystyrene calibration sample serves as a cross check on the validity of this methodology.

Elastic electron scattering by water molecules

Abstract: Elastic differential and momentum transfer cross sections are reported for electron scattering by H2O at impact energies ranging from 4 to 50 eV. The iterative Schwinger variational method in the fixed-nuclei, static-exchange approximation is used to calculate the low partial wave scattering amplitudes and the higher partial wave contributions are included via closure using the Born approximation for a point-dipole. Comparison of our calculated cross sections with recent experimental and other theoretical results is encouraging.

Simplified model of electron scattering using R-matrix methods

Abstract: The eigenchannel {ital R}-matrix method is used to describe a set of two-electron escape processes. This method is applied to calculate both bound state excitation and ionization cross sections for a simplified model of electron-hydrogen scattering and electron-He{sup +} scattering, in which only zero angular momentum states are considered. The results shown are calculated for incident electron energies ranging from 13.6--50 eV for electron-hydrogen scattering and from 54.4--200 eV for electron-He{sup +} scattering. A frame transformation technique is introduced to improve the stability of calculated ionization cross sections. The {ital R}-matrix results are compared with cross sections obtained from a convergent close-coupling approach and with other results.