Scattering Wave Function Research Articles

Convergence of energy-differential ionization cross sections obtained from aT-matrix approach withR-matrix wave functions

The T-matrix approach, as formulated by Pindzola et al. [Phys. Rev. A 62, 062718 (2000)] for calculating the single-differential ionization cross section (SDCS) has been further investigated. Using the ``intermediate-energy R-matrix method'' to obtain the full scattering wave function needed in the matrix element, we performed several case studies for the Temkin-Poet S-wave model of e-H scattering to study the dependence of the results on the box radius and the number of states included. Despite encouraging results before reaching convergence, we conclude that the method will ultimately not yield the correct form of the SDCS but instead will still suffer from unphysical oscillations.

Scattering of SH-wave by multiple circular cavities in half space

In this paper, an analytic method is developed to address steady SH-wave scattering and perform dynamic analysis of multiple circular cavities in half space. The scattered wave function used for scattering of SH-waves by multiple circular cavities, which automatically satisfies the stress-free condition at the horizontal surface, is constructed by applying the symmetry of the SH-wave scattering and the method of multi-polar coordinates system. Applying this scattered wave function and method of moving coordinates, the original problem can be transformed to the problem of SH-wave scattering by multiple circular cavities in the full space. Finally, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the infinite algebraic equations to the finite ones. Numerical examples are provided for case with two cavities to show the effect of wave number, and the distances between the centers of the cavities and from the centers to the ground surface on the dynamic stress concentration around the cavity impacted by incident steady SH-wave.

The Schwinger multichannel method (SMC) calculations for Zeff were off by a factor of Z

Our previously reported Z eff values were in accidental agreement with experiment. They were actually underestimated by a factor of Z. In order to full understand the nature of the discrepancies with experimental data, we carried out several tests for positron–He collisions. We first tried many different (Cartesian Gaussian) basis sets in a single-excitation configuration–interaction (CI) framework. Then, we included single- and double-excitations of the target in the CI expansion (CISD) of the scattering wave function. Finally, we tried to mimic the virtual positronium cusp. It seems that cusp description should indeed be further improved.

Bound and scattering wave functions for a velocity-dependent Kisslinger potential for l > 0

Using formal scattering theory, the scattering wave functions are extrapolated to negative energies corresponding to bound-state poles. It is shown that the ratio of the normalized scattering and the corresponding bound-state wave functions, at a bound-state pole, is uniquely determined by the bound-state binding energy. This simple relation is proved analytically for an arbitrary angular momentum quantum number l > 0, in the presence of a velocity-dependent Kisslinger potential. The extrapolation relation is tested analytically by solving the Schrodinger equation in the p-wave case exactly for the scattering and the corresponding bound-state wave functions when the Kisslinger potential has the form of a square well. A numerical resolution of the Schrodinger equation in the p-wave case and of a square-well Kisslinger potential is carried out to investigate the range of validity of the extrapolated connection. It is found that the derived relation is satisfied best at low energies and short distances.

On the classical behavior, coherent and incoherent contributions to scattering of atoms from a surface

In this work we calculate the coherent and incoherent contributions to the diffraction probability of atoms scattered by a surface. We are interested in exploring the relative importance of each of these contributions, and compare them with results obtained from molecular dynamics calculations. To achieve this goal, we employed a method developed by Heller that consists of writing the incident plane wave as a sum of Gaussian wave packets, propagating them independently by using the time dependent Schrödinger equation, and constructing the scattered wave function by adding coherently the scattered packets. For the system studied, the molecular dynamics results show the largest intensity in the specular region and also display a classical rainbow structure. On the other hand, the quantum results exhibit diffraction features, with the coherent contribution accounting for most of the total intensity probability.

Statistics of interior current distributions in two-dimensional open chaotic billiards

The probability current statistics of two-dimensional open chaotic ballistic billiards is studied both analytically and numerically. Assuming that the real and imaginary parts of the scattering wave function are both random Gaussian fields, we find a universal distribution function for the interior probability current. As a by-product we recover previous analytic forms for wave function statistics. The expressions bridge the entire region from GOE to GUE type statistics. Our analytic expressions are verified numerically by explicit quantum mechanical calculations of transport through a Bunimovich billiard.

Nucleon-nucleon optical model for energies up to 3 GeV

Several nucleon-nucleon potentials, Paris, Nijmegen, Argonne, and those derived by quantum inversion, which describe the $\mathrm{NN}$ interaction for ${T}_{\mathrm{Lab}}<~300 \mathrm{MeV},$ are extended in their range of application as $\mathrm{NN}$ optical models. Extensions are made in r space using complex separable potentials definable with a wide range of form factor options including those of boundary condition models. We use the latest phase shift analysis SP00 (FA00, WI00) of Arndt et al. from 300 MeV up to 3 GeV to determine these extensions. The imaginary parts of the optical model interactions account for loss of flux into direct or resonant production processes. The optical potential approach is of particular value as it permits one to visualize fusion, and subsequent fission, of nucleons when ${T}_{\mathrm{Lab}}>2 \mathrm{}\mathrm{GeV}.$ We do so by calculating the scattering wave functions to specify the energy and radial dependences of flux losses and of probability distributions. Furthermore, half off the energy shell t matrices are presented as they are readily deduced with this approach. Such t matrices are required for studies of few- and many-body nuclear reactions.

Coulomb effects in nucleon-deuteron polarization-transfer coefficients

Coulomb effects in the neutron-deuteron and proton-deuteron polarization-transfer coefficients ${K}_{y}^{{y}^{\ensuremath{'}}},$ ${K}_{z}^{{x}^{\ensuremath{'}}},$ ${K}_{y}^{{x}^{\ensuremath{'}}{x}^{\ensuremath{'}}\ensuremath{-}{y}^{\ensuremath{'}}{y}^{\ensuremath{'}}},$ and ${K}_{y}^{{z}^{\ensuremath{'}}{z}^{\ensuremath{'}}}$ are studied at energies above the deuteron breakup threshold. Theoretical predictions for these observables are evaluated in the framework of the Kohn variational principle using correlated basis functions to expand the three-nucleon scattering wave function. The two-nucleon Argonne ${v}_{18}$ and the three-nucleon Urbana IX potentials are considered. In the proton-deuteron case, the Coulomb interaction between the two protons is included explicitly and the results are compared to the experimental data available at ${E}_{\mathrm{lab}}=10,19,22.7 \mathrm{MeV}.$ In the neutron-deuteron case, a comparison to a recent measurement of ${K}_{y}^{{y}^{\ensuremath{'}}}$ by Hempen et al. at ${E}_{\mathrm{lab}}=19 \mathrm{MeV}$ evidences a contribution of the calculated Coulomb effects opposite to those extracted from the experiment.

Time-dependent coupled-channel calculations of positronium-formation cross sections in positron-hydrogen collisions

We demonstrate the usefulness of the time-dependent coupled channel (TDCC) method in theoretical studies of atomic rearrangement collisions. In the TDCC method, coupled-channel partial differential equations for scattering wave functions are solved time dependently. We develop the Hankel-interpolation method, which is used to transform wave functions from an initial coordinate to a final coordinate system. By using this method, reaction cross sections of rearrangement collisions can be directly extracted from solutions of TDCC equations. We calculate positronium-formation cross sections in positron-hydrogen collisions in which a considerable number of theoretical calculations and precise experiments have been made. The present results for positron energies of 6.8--35 eV are in excellent agreement with the recent experiment of Zhou et al. [Phys. Rev. A 55, 361 (1997)].

Optical Potentials and Propagators for Elastic and Inelastic Scattering from Many-Body Targets

The usual textbook one-particle Green's function possesses a self-energy that is known to be an optical potential for elastic scattering. The introduction of an optical potential reduces the complex many-body scattering problem into a tractable one-body problem. In this work the definition of Green's functions is extended. The defined inelastic functions are shown to possess self-energies that can be expressed in closed form in terms of the target states. It is proven that these self-energies are optical potentials for inelastic scattering. The properties of these potentials and working equations for the scattering wave functions are discussed. Particular emphasis is put on elucidating the substantial differences arising in the scattering of a projectile distinguishable from the target's particles and in the scattering of indistinguishable particles.

Capacitance theory of open quantum systems with classical contacts

We consider semiconductor devices composed of a small quantum structure as the active device region and two classical environments constituting the source- and the drain contact. The contacts are taken as free electron gases with infinite conductivity defining the chemical potentials in the contacts. The transport through the quantum structure is described in the Landauer–Büttiker formalism using electronic scattering wave functions which determine the electron density in the quantum system. In our Hartree approximation these charges and the induced charges in the contacts are the sources of the self-consistent Coulomb field. As a particular quantum structure we study a GaAs heterostructure device consisting of a two-dimensional electron gas sandwiched between a gate contact and an AlGaAs blocking barrier [see V.T. Dolgopolov et al., Phys. Low-Dim. Struct. 6 (1996) 1]. We demonstrate the quantitative agreement of our theory with the experimental results.

Polarization observables inp−dscattering below 30 MeV

Differential and total breakup cross sections as well as vector and tensor analyzing powers for $p\ensuremath{-}d$ scattering are studied for energies above the deuteron breakup threshold up to ${E}_{\mathrm{lab}}=28 \mathrm{MeV}.$ The $p\ensuremath{-}d$ scattering wave function is expanded in terms of the correlated hyperspherical harmonic basis and the elastic S matrix is obtained using the Kohn variational principle in its complex form. The effects of the Coulomb interaction, which are expected to be important in this energy range, have been rigorously taken into account. The Argonne AV18 interaction and the Urbana URIX three-nucleon potential have been used to perform a comparison to the available experimental data.

Inelastic electron scattering at metal surfaces: the role of elastic scattering

Recently it has been demonstrated (Nazarov, Phys. Rev. B. 59 (1999) 9866) that the characteristics of elastic scattering of electrons near a surface dramatically influence the outcome of inelastic scattering. In this paper we present the results of the jellium model time dependent local density approximation calculations for simple metal surfaces using low energy electron diffraction elastic scattering wave functions in the kinematic approximation.

Direct calculation of the scattering amplitude without partial-wave analysis

Two developments in scattering theory are reported. We show, in a practical way, how one can calculate the scattering amplitude without invoking a partial-wave expansion. First, the integral expression for the scattering amplitude $f(\ensuremath{\theta})$ is simplified by an analytic integration over the azimuthal angle. Second, the full scattering wave function that appears in the integral expression for $f(\ensuremath{\theta})$ is obtained by solving the Schr\"odinger equation with the finite element method. As an example, we calculate electron scattering from static hydrogen (the Hartree potential). With minimal computational effort, we obtain accurate and stable results for the scattering amplitude.

Annihilation probability density in positron scattering by He

We have calculated annihilation probability densities in positron collisions against the He atom. Our scattering wave functions were obtained with the Schwinger multichannel method [J. S. E. Germano and M. A. P. Lima, Phys. Rev. A $47,$ 3976 (1993)]. It has been found that direct annihilation, in which electronic cloud deformation shields the nuclear repulsive potential effectively attracting the positron to a binary encounter, dominates the annihilation process at low impact energies. Closer to the real positronium formation threshold, the signature of virtual positronium has been noticed. At room temperature, significant annihilation probability has been observed over a somewhat extended region.

Quantum Monte Carlo treatment of elastic exciton-exciton scattering

We calculate cross sections for low energy, elastic, bulk, s-wave exciton-exciton scattering within the single-band effective mass approximation. Unlike previous theoretical approaches, we give a complete, nonperturbative treatment of the four-particle scattering problem. Diffusion Monte Carlo is used to calculate the essentially exact energies of scattering states, from which phase shifts are determined. For the case of equal-mass electrons and holes, which is equivalent to positronium-positronium scattering, we find ${a}_{s}{=2.1a}_{x}$ for scattering of singlet excitons and ${a}_{s}{=1.5a}_{x}$ for triplet excitons, where ${a}_{x}$ is the excitonic radius. The spin dependence of the cross sections arises from the spatial exchange symmetry of the scattering wave functions. A significant triplet-triplet to singlet-singlet scattering process is found, which is similar to the reported effects in recent experiments and theory for excitons in quantum wells. We also show that the scattering length can change sign and diverge for some values of the mass ratio ${m}_{h}{/m}_{e},$ an effect not seen in previous perturbative treatments.

Coherent electron-phonon coupling and polaronlike transport in molecular wires

We present a technique to calculate the transport properties through one-dimensional models of molecular wires. The calculations include inelastic electron scattering due to electron-lattice interaction. The coupling between the electron and the lattice is crucial to determine the transport properties in one-dimensional systems subject to Peierls transition since it drives the transition itself. The electron-phonon coupling is treated as a quantum coherent process, in the sense that no random dephasing due to electron-phonon interactions is introduced in the scattering wave functions. We show that charge carrier injection, even in the tunneling regime, induces lattice distortions localized around the tunneling electron. The transport in the molecular wire is due to polaron-like propagation. We show typical examples of the lattice distortions induced by charge injection into the wire. In the tunneling regime, the electron transmission is strongly enhanced in comparison with the case of elastic scattering through the undistorted molecular wire. We also show that although lattice fluctuations modify the electron transmission through the wire, the modifications are qualitatively different from those obtained by the quantum electron-phonon inelastic scattering technique. Our results should hold in principle for other one-dimensional atomic-scale wires subject to Peierls transitions.

Uniform semiclassical IVR treatment of the S-matrix

A new, uniform, semiclassical, initial value representation expression is obtained for the S-matrix in the case of collinear collisions. The derivation is based on an asymptotic analysis (for large inter-fragment distances) of a uniform semiclassical integral expression for the time independent scattering wave function. Although this derivation specifically treats the case of the collision of an atom with a harmonic diatom, the final expression is generalized to arbitrary collinear collisions. The various properties of the expression and its relation to existing semiclassical methods are discussed. Numerical tests are performed for the well-known Secrest–Johnson system. Among other important advantages, the present treatment is a well-defined, uniform, semiclassical approximation that is capable of good accuracy and high computational efficiency, requiring a relatively small number of classical trajectories to obtain converged S-matrix elements for a given energy and initial state.

Multiple scattering of electrons in solids and molecules: A cluster-model approach

A method for the simulation of electron scattering and diffraction in solids and molecules within the cluster approach is presented with explicit applications to photoelectron diffraction, electron scattering in molecules, and low-energy electron diffraction. No approximations are made beyond the muffin-tin model, and, in particular, an exact representation of the free-electron Green function is used. All multiple-scattering paths are accounted for up to an order of scattering that ensures convergence. The method relies upon a convenient separation of the free-electron Green function in rotation matrices and translations along the z axis, which greatly reduces the computation time and storage demand. The evaluation of the multiple-scattering expansion is implemented using the fully convergent recursion method, which permits one to perform an iterative refinement of the final-state wave function, as expressed in the basis set of spherical harmonics attached to each atom of the cluster. Examples are offered in which the direct multiple-scattering expansion and the more elaborated simultaneous relaxation method fail to converge, whereas the recursion method leads to convergence. The computation time needed by the resulting computer program of electron diffraction in atomic clusters to determine the self-consistently scattered wave function is proportional to ${N}^{2}{(l}_{\mathrm{max}}{+1)}^{3},$ where N is the number of atoms in the cluster and ${l}_{\mathrm{max}}$ is the maximum angular momentum for which the scattering phase shifts take non-negligible values. Within this method it is possible to establish that in practical cases $N>1000$ might be needed for a convergence of the cluster size, although the angular averaging inherent in many experiments may reduce this. The recursion method was also modified to reduce the effort in computing angular distributions of photoelectrons and low-energy diffracted electrons, which now require negligible time for each angle of emission once the wave function has been determined for a given electron energy. Angle and energy distributions of core-level photoemission, elastic scattering of electrons from a free molecule, and low-energy electron diffraction in large-unit-cell surfaces are calculated.

SCATTERING OF PLANE SH-WAVE BY A CYLINDRICAL HILL OF ARBITRARY SHAPE

The problems of scattering of plane SH-wave by a cylindrical hill of arbitrary shape is studied based on the methods of conjunction and division of solution zone. The scattering wave function is given by using the complex variable and conformal mapping methods. The conjunction boundary conditions are satisfied. Furthermore appling orthogonal function expanding technique, the problems can finally be summarized into the solution of a series of infinite algebraic equations. At last, numerical results of surface displacements of a cylindrical arc hill and of a semi-ellipse hill are obtained. And those computational results are compared with the results of finite element method (FEM).