Showing papers on "Scattering length published in 1986"

Quantum scattering in two dimensions

Abstract: A self‐contained discussion of nonrelativistic quantum mechanical potential scattering in two dimensions is presented The discussion includes, among other topics, partial wave decomposition in coordinate and momentum space, Lippmann–Schwinger integral equations of scattering for the scattering wavefunction and the transition operator, optical theorem, and the unitarity relation for the transition operator The present definition of the scattering amplitude in terms of the asymptotic wavefunction differs from the usual definition The present definition has certain advantages, for example, in writing the optical theorem and in studying the analytical properties of the scattering amplitude

3-D linearized scattering of surface waves and a formalism for surface wave holography

Abstract: Summary. Scattering of surface waves by lateral heterogeneities is analysed in the Born approximation. It is assumed that the background medium is either laterally homogeneous, or smoothly varying in the horizontal direction. A dyadic representation of the Green's function simplifies the theory tremendously. Several examples of the theory are presented. The scattering and mode conversion coefficients are shown for scattering of surface waves by the root of an Alpine-like crustal structure. Furthermore a ‘great circle theorem’in a plane geometry is derived. A new proof of Snell's law is given for surface wave scattering by a quarter-space. It is shown how a stationary phase approximation can be used to simplify the Fourier synthesis of the scattered wave in the time domain. Finally a procedure is suggested to do ‘surface wave holography'.

Magnetic structure of erbium.

Abstract: We present a synchrotron x-ray scattering study of the magnetic phases of erbium. In addition to the magnetic scattering located at the fundamental wave vector tau/sub m/ we also observe scattering from magnetoelastically induced charge modulations at the fundamental wave vector, at twice the fundamental, and at positions split symmetrically about the fundamental. As the temperature is lowered below 52 K the charge and magnetic scattering display a sequence of lock-in transitions to rational wave vectors. A spin-slip description of the magnetic structure is presented which explains the wave vectors of the additional charge scattering.

Small-angle scattering from porous solids with fractal geometry

Abstract: The fractal or Hausdorff dimensionality of an ideal random structure exhibiting self-similarity implies that the intensity of radiation scattered at small scattering vectors should have a power-law dependence on the magnitude of the scattering vector. However, for any real system, the scattering law must be modified by the introduction of a correlation length which reflects the finite overall size of the system. This concept can also be incorporated into the outer (Porod) part of the small-angle scattering where a non-integral power-law dependence can arise from interfaces of fractal character. The scattering law for the inner region of the small-angle scattering (corresponding to larger distances) is proportional to Q-D where D is the fractal dimensionality of the structure. The scattering law for the outer region (corresponding to smaller distances) is proportional to QD-6, where in this case D is the fractal dimensionality of the interface. This reflects the crossover from scaling based on mass per unit volume to one based on mass per unit area as the length of the examining probe (the inverse scattering vector) becomes shorter. An inverse correlation is predicted between the fractal dimensionality of the interface and the correlation length obtained using a nonfractal (Debye) model over a restricted range of scattering vectors. Measurements on shaly (argillaceous) rocks exhibit deviations from Porod scattering indicative of microscopically rough interfaces with D>2, and show the negative correlation between interfacial dimensionality and correlation length.

Use of general potentials in multiple-scattering theory.

Abstract: A mathematically transparent derivation of the multiple-scattering equations valid for a general non-muffin-tin potential, as applied to clusters of atoms with and without a surrounding outer sphere, is presented. These equations are shown to be a natural generalization of the analogous equations valid for muffin-tin potentials. An expression for the photoabsorption and electron scattering cross section in the framework of the multiple-scattering theory valid for a general potential is derived for what may be the first time, providing the necessary generalization for the similar expression valid in the muffin-tin case. A connection with the Green-function approach to the problem is also established via a generalized optical theorem.

The calculation of scattering cross sections for polarized x-rays *

Abstract: The scattering of low energy X-rays by atoms is dominated by coherent (Rayleigh) and incoherent (many times known as “atomic Compton”) scattering. As electron synchrotron storage rings become more widely used as sources of intense, polarized X-rays, it is important to be able to properly calculate the scattering cross sections since the polarization of the X-rays can be utilized to reduce the X-ray scattering. This paper reviews the methods of calculating the Rayleigh and atomic Compton scattering cross sections of polarized X-rays and presents analytical integrations of the cross sections over solid angles of circular detectors from point sources into 90°. Special attention is paid to the effects the scattering has on the background of spectra collected with energy dispersive detectors. It is shown that the ratio of scattering to fluorescence does not approach zero for small values of rR (r = detector radius, R = distance to detector).

Elastic scattering of polarised electrons from mercury and xenon

Abstract: Polarised electrons have been scattered elastically from mercury and xenon. The angular distribution of the parameters that describe the change in the electron polarisation caused by the scattering process has been measured in the energy range from 25 to 150 eV for mercury and from 40 to 350 eV for xenon. With these parameters, in conjunction with the absolute differential cross section, a complete analysis of the scattering amplitudes with respect to their magnitudes and their relative phase is performed for xenon.

Elastic electron scattering cross sections for Xe in the 1-100 eV impact energy region

Abstract: Relative differential elastic scattering cross sections for Xe have been measured in the 1-100 eV impact energy and 10-146 degrees angular ranges. The data were subjected to phaseshift analysis, but the normalisation was achieved at each impact energy by utilising total electron scattering, ionisation and total excitation cross sections. Comparison is made with other recent experimental and theoretical results.

Inelastic gas-surface scattering. I. Formalism.

Abstract: We present a method for calculating elastic and inelastic scattering probabilities for light particles, such as helium and molecular hydrogen, scattering from surfaces with which they weakly interact. The method is a unitary one-phonon approximation in which the scattering probabilities are calculated from thermally averaged amplitudes which are generated numerically. The thermal averaging procedure is more general than this application and could be applied to other systems with weak inelastic scattering. We also discuss an approximation for the gas-surface interaction potential that can greatly simplify calculations where it is applicable. Finally we present some preliminary results using this method to study rotationally mediated selective adsorption resonances in HD scattering from copper.

Elastic electron scattering from CH4 for collision energies between 0.2 and 5 eV

Abstract: Angular dependences of the elastic scattering of electrons from CH4 for impact energies between 0.2 and 5 eV in the angular range between 15 degrees and 138 degrees are presented. Absolute differential cross sections have been obtained. With the help of a phaseshift analysis, integrated cross sections are calculated. The Ramsauer minimum is found to be at a collision energy close to 0.45 eV. The sum of the integrated vibrationally elastic cross sections and the vibrational excitation cross sections yields the total cross sections. These data are compared with the recent data for sigma T of Ferch et al. (1985).

Interband-intraband electronic Raman scattering in semiconductors

Abstract: A certain kind of electron Raman scattering in semiconductors, which the authors have called 'interband-intraband electron Raman scattering' (IIERS), is discussed in detail. The IIERS process differential cross section is calculated without particular assumptions on the semiconductor band structure, allowing the study of a wide class of materials. Concrete applications are made to the cases of parabolic and Kane band structure models. The differential cross section of the IIERS is also studied for the critical points in the three-dimensional case. Special emphasis is made on the spectral frequency dependence for different polarisation of the incident and emitted light. Scattered light in the IIERS is displaced towards the low-frequency region providing spectral structure far from the incident light frequency.

Differential cross sections for elastic and inelastic scattering of electrons by N2O in the range from 10 to 80 eV

Abstract: Differential electron impact cross sections (DCS) for the elastic scattering and excitation of the 1 Pi and 21 Sigma + states of N2O have been measured using a crossed electron beam-molecular beam scattering technique. These measurements were performed at electron impact energies of 10 and 12 eV for elastic as well as at 15, 20, 30, 50 and 80 eV for elastic and inelastic scattering. DCS were obtained over a wide range of scattering angles, up to 150 degrees . The elastic DCS were put on an absolute scale by normalisation to the total electron scattering cross sections. The inelastic DCS are in relative units except for the case of 80 eV impact energy where it was possible to determine the elastic to inelastic intensity ratio and to obtain absolute DCS values. By extrapolation of DCS to zero and 180 degrees scattering angles, integral and momentum transfer cross sections were obtained.

Total reaction cross section for 12C on 12C, 40Ca, 90Zr, and 208Pb between 10 and 35 MeV/nucleon

Abstract: Elastic scattering angular distributions for $^{12}\mathrm{C}$ on $^{12}\mathrm{C}$, $^{40}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$ were measured for projectile energies between 10 and 35 MeV/nucleon Total reaction cross sections were extracted by an optical model analysis and compared to the prediction of the Glauber model This comparison suggests that the nucleus-nucleus total reaction cross section at intermediate and high energies is governed by the nucleon-nucleon cross section

Near-threshold vibrational excitation and elastic electron scattering from N2

Abstract: Angular dependences of the elastic scattering and the vibrational excitation of N2 have been measured for impact energies between 0.1 and 1.5 eV in the angular range from 15 to 135 degrees . Absolute differential and integrated cross sections are presented. The elastic scattering can be described reasonably well by the modified effective range theory for 0.1 eV. The integral vibrational excitation cross sections are in good agreement with swarm results.

Layer‐stripping solutions of multidimensional inverse scattering problems

Abstract: A layer‐stripping procedure for solving three‐dimensional Schrodinger equation inverse scattering problems is developed. This method operates by recursively reconstructing the potential from the jump in the scattered field at the wave front, and then using the reconstructed potential to propagate the wave front and the scattered field further into the inhomogeneous region. It is thus a generalization of algorithms that have been developed for one‐dimensional inverse scattering problems. Although the procedure has not yet been numerically tested, the corresponding one‐dimensional algorithms have performed well on synthetic data. The procedure is applied to a two‐dimensional inverse seismic problem. Connections between simplifications of this method and Born approximation inverse scattering methods are also noted.

Studies of electron‐molecule collisions: Applications to e‐H2O

Abstract: Elastic differential and momentum transfer cross sections for the elastic scattering of electrons by H2O are reported for collision energies from 2 to 20 eV. These fixed-nuclei static-exchange cross sections were obtained using the Schwinger variational approach. In these studies the exchange potential is directly evaluated and not approximated by local models. The calculated differential cross sections, obtained with a basis set expansion of the scattering wave function, agree well with available experimental data at intermediate and larger angles. As used here, the results cannot adequately describe the divergent cross sections at small angles. An interesting feature of the calculated cross sections, particularly at 15 and 20 eV, is their significant backward peaking. This peaking occurs in the experimentally inaccessible region beyond a scattering angle of 120 deg. The implication of this feature for the determination of momentum transfer cross sections is described.

Neutron scattering lengths and neutron-electron interaction

Abstract: After a discussion of the electromagnetic contributions to the neutron-nucleus scattering length we report on methods for the determination of scattering lengths and on precision techniques which allow the separation of the electromagnetic from the nuclear scattering length We used this effect for a new determination of the effective neutron-electron scattering length to be -(132±004) × 10 -3 fm and for the separation of the electric polarization scattering of the neutron At the present status of the experiment we obtain polarization scattering lengths from experiments on Pb and Bi which correspond to an electric polarizability of the neutron of (3±4) × 10 -3 fm 3 , in agreement with theoretical predictions

Elastic and inelastic scattering of polarised 7Li from 120Sn

Abstract: The differential cross section and analysing powers iT11, TT20, T20, T21 and TT30 have been measured for both the elastic scattering of 44 MeV polarised 7Li from 120Sn and for projectile excitation to the 1/2 state at 478 keV. The data have bee fitted with coupled-channels calculations which include ground-state reorientation of the 7Li and coupling to excited states of 7Li. The sensitivity of the different observables to a number of coupling schemes is discussed. The potentials were derived from a double folding model which explicitly includes the 7Li deformation.

Construction of two-dimensional Schrödinger operator with given scattering amplitude at fixed energy

Abstract: The classical necessary properties of the scattering amplitude (reciprocity and unitarity) are, provided its L/sub 2/ norm is small, sufficient for the existence of a two-dimensional Schrodinger operator with the given scattering amplitude at fixed energy

The calculation of the differential cross sections for recoil protons in 4He-p Scattering

Abstract: The equation relating phase shift to energy given by the effective range theory for charged particle reactions and the effective range parameters which can well fit the experimental data of P- 4 He elastic scattering have been used to obtain the phase shifts and differential cross sections of protons in p- 4 He elastic scattering. Thereafter the differential cross section of recoil protons in 4 He-p elastic scattering are calculated through the principle of detailed balance and compared with the experimental data and Rutherford cross sections. Better consistency between experimental and theoretical values than in previous work is achieved.

Low-energy scattering of muonic hydrogen on helium and lithium nuclei

Abstract: The energy dependence of the formation rates of the hydrogen-helium and hydrogen-lithium mesomolecules and the elastic cross sections for the scattering of muonic hydrogen on helium and lithium are calculated. The Ramsauer-Townsend effect is predicted for the elastic scattering. The elastic cross section for the t mu atom attains the magnitude of the atomic dimensions. The electron screening effect is shown to be essential for the elastic scattering.

Three-body calculation of neutron-deuteron elastic scattering in the energy region from 2.5 MeV up to 50 MeV

Abstract: The three-body Faddeev equations for neutron-deuteron scattering are solved in the energy region from 2.5 MeV to 50 MeV of the incident neutron energy with small energy steps. Higher-rank separable potentials are used in the1 s 0 wave and in the3 s 1—3 d 1 waves, while rank-1 separable potentials are used in1 p 1,3 p 0,1,2 1 d 2 3 d 2,3 waves. The calculation is compared with experiments for the total cross section, the total break-up cross section, the differential cross section and the analyzing power of neutron-deuteron scattering. The improvements in the agreement as compared to previous calculations are impressive in many cases. Especially, the calculated total cross section agrees with the experiment below 30 MeV within the error bars, which are as small as 1%. A discussion on the numerical accuracy is given. General aspects of the calculated cross section are discussed. It is pointed out that thes-wave asymptotic normalization of the deuteron wave function (A s ) is important.

Differential cross section for coherent photon scattering from 4He at 180 MeV.

Abstract: We report the measurement of the differential scattering cross section for coherent photon scattering (nuclear Compton scattering) from /sup 4/He at an average energy of 180 MeV. This represents the first direct observation of the coherent process on a complex nucleus above the pion threshold. The results are compared with the predicton of a claculation utilizing the isobar-hole formalism.