Elastic scattering of electrons and positrons by cadmium atoms

ABSTRACT

The differential, integrated elastic, total and momentum transfer cross sections along with Sherman function for the elastic scattering of electrons and positrons by cadmium atoms have been evaluated from the partial wave solution of the Dirac relativistic scattering equations for a projectile-atom complex potential at the energy range 6.4 eV < E < 1.0 keV. For various scattering quantities, a comparison of our results exhibits better agreement with the experimental data than the other available theoretical values.     

Quasi-elastic and elastic charge-exchange differential cross sections (critical review)

More than 50 years ago the charge-exchange of one nucleon in the quasi-elastic nucleon deuteron scattering was proposed to determine the spin independent, or the spin dependent parts of the elastic backward neutron proton differential cross section. For this purpose two measurements are to be performed using unpolarized particles only. Such a suggestion was very attractive for experimentalists, since at that time polarized beams were rare and polarized targets were nonexistent. One experiment consists in the inclusive measurement of the charge-exchange quasi-elastic nucleon deuteron differential cross section. The energy of the fast outgoing nucleon is to be approximately the same as that of the incident nucleon. The intrinsic momenta of the remaining two identical nucleons should be small. The impulse approximation has been assumed, i.e. in the final state of the two nucleons their interaction can be neglected. The quasi-elastic result is to be compared with the elastic np differential cross section in the backward direction at the same energy. The theory related the ratio R _QE (π) of the quasi-elastic to the elastic np charge-exchange differential cross sections to the spin dependent part of the np backward elastic scattering amplitude. Several experiments in the nucleon kinetic energy interval below 1 GeV were carried out, where the R _QE (π) values were determined. Recently the energy interval was extended up to 2 GeV by successful experiments at the JINR VBLHE Nuclotron. The quasi-elastic results can be compared with the values of the analogous quantity R _np (π) for the np elastic scattering, calculated from the phase shift analyses below 1.3 GeV. The present paper is a critical review checking expressions for R _np (π) in different amplitude representations, listing numerical values of elastic np quantities and results of existing quasi-elastic experiments. Conclusions and statements of some authors and the validity of the relevant theory is discussed.     

Correlation functions in the theory of atomic collision cascades: Ion location and the distribution in depth and size of damage clusters

Abstract

Simple depth distribution functions of ion bombardment damage predict the spatial extension of the cumulative damage caused by a beam of ions. Correlation functions need to be considered when more detailed information is desirable, such as the average size or depth of individual damage clusters, the average location of an ion within its damage cluster, and the fluctuations of these quantities. In this paper we establish an integral equation for the pair correlation function, coupling the individual ion range with the deposited energy. This pair correlation function determines the damage caused by all those ions that come to rest at a specific penetration depth. Solutions of the integral equation are found by standard methods. Explicit results are presented for elastic scattering governed by power cross sections. The depth distribution of damage clusters turns out to be significantly narrower than the gross damage distribution at all mass ratios except for M ₁ ? M ₂, and the size distribution appears insensitive to depth when measured perpendicular to the ion beam, but varying with depth when measured parallel. Predictions on ion location suffer from a surprizingly sensitive dependence on the scattering cross section. A note on the fluctuation of the sputtering yield by individual ions concludes the paper.     

Two-dimensional scattering of electromagnetic waves from a permeable inclusion in an anisotropic medium

Integrodifferential equations for the cross section of the scatterer and a collocation method are used to obtain a numerical solution of the problem of scattering of an H-polarized wave by an anisotropic layer of a three-layer dielectric structure. Zh. Tekh. Fiz. 68, 84–88 (January 1998)     

Integration of the nonlinear Schroedinger equation with a self-consistent source

It is shown that the nonlinear Schroedinger equation with a self-consistent source admits investigation by the inverse scattering method for the Dirac operator. The conditions are found under which the solutions of the nonlinear Schroedinger equation with a self-consistent source describe the creation and annihilation of solitons.     

Relativistic Description of 3He (e, e�� p)2H

The relativistic distorted-wave impulse approximation is used to describe the ³He(e, e?? p)²H process. We describe the ³He nucleus within the adiabatic hyperspherical expansion method with realistic nucleon-nucleon interactions. The overlap between the ³He and the deuteron wave functions can be accurately computed from a three-body calculation. The nucleons are described by solutions of the Dirac equation with scalar and vector (S?CV) potentials. The wave function of the outgoing proton is obtained by solving the Dirac equation with a S?CV optical potential fitted to elastic proton scattering data on the residual nucleus. Within this theoretical framework, we compute the cross section of the reaction and other observables like the transverse-longitudinal asymmetry, and compare them with the available experimental data measured at JLab.     

Correlation effects in electron-ion collisions in a strong laser field

We examine elastic and inelastic scattering of electrons by ions in intense laser light. A method of numerical investigation of the scattering characteristics based on regularizing the Coulomb singularity is proposed. We show that over a broad range of parameter values the transport scattering cross section is weakly dependent on the intensity of the high-frequency field. We detect a significant modification of the dependence of the effective inelastic scattering cross section. We also show that the energy exchange with the field is determined by a fairly small group of electrons, called the representative electrons. Finally, we propose a qualitative model that explains our results by the fact that the leading contribution is provided by inelastic collisions of electrons with relatively small impact parameters traversing the region important for the interaction at large angles. Zh. éksp. Teor. Fiz. 115, 463–478 (February 1999)     

Spin structure of the “Forward” nucleon charge-exchange reaction <Emphasis Type="Italic">n</Emphasis> + <Emphasis Type="Italic">p</Emphasis> → <Emphasis Type="Italic">p</Emphasis> + <Emphasis Type="Italic">n</Emphasis> and the deuteron charge-exchange breakup

The structure of the nucleon charge-exchange process n + p → p + n is investigated basing on the isotopic invariance of the nucleon-nucleon scattering. Using the operator of permutation of the spin projections of the neutron and proton, the connection between the spin matrices, describing the amplitude of the nucleon charge-exchange process at zero angle and the amplitude of the elastic scattering of the neutron on the proton in the “backward” direction, has been considered. Due to the optical theorem, the spin-independent part of the differential cross section of the process n + p → p + n at zero angle for unpolarized particles is expressed through the difference of total cross sections of unpolarized proton-proton and neutron-proton scattering. Meantime, the spin-dependent part of this cross section is proportional to the differential cross section of the deuteron charge-exchange breakup d + p → (pp) + n at zero angle at the deuteron momentum k _d = 2 k _n (k _n is the initial neutron momentum). Analysis shows that, assuming the real part of the spin-independent term of the “forward” amplitude of the process n + p → p + n to be smaller or of the same order as compared with the imaginary part, in the wide range of neutron laboratory momenta k _n > 700 MeV/c the main contribution into the differential cross section of the process n + p → p + n at zero angle is provided namely by the spin-dependent term.     

s-wave and p-wave scattering in a cold gas of Na and Rb atoms

Using improved experimentally based X¹Σ⁺ and a³Σ⁺ molecular potentials of NaRb, we apply the variable phase method to compute new data for low energy scattering of ²³Na atoms by ⁸⁵Rb atoms and ⁸⁷Rb atoms. These are the scattering lengths and volumes, numbers of bound states and effective ranges, which we use to obtain the low energy spin-change cross section as functions of the system temperature and the isotope masses. From an analysis of the contributions of s-wave and p-wave scatterings to the elastic cross section we estimate temperatures below which only s-wave scattering is dominant. We compare our quantal results to data obtained from the semiclassical approximation. We supply evidence for the existence of a near zero energy p-wave bound state supported by the singlet molecular potential.     

Interactions of charmed mesons with nucleons in the ¯<Emphasis Type="Italic">p</Emphasis><Emphasis Type="Italic">d</Emphasis> reaction

We study the possibility to measure the elastic ΦN (Φ≡J/ψ,ψ(2S), ψ(3770), χ_2c) scattering cross section in the reaction ˉp+d→Φ+n _sp and the elastic D(ˉD)N scattering cross section in the reaction ˉp+d→D ⁻ D ⁰ p _sp. Our studies indicate that the elastic scattering cross sections can be determined for Φ momenta about 4–6 GeV/c and D/ˉD momenta 2–5 GeV/c by selecting events with p _t≥ 0.4 GeV/c for Φ's and p _t(p _sp) ≥ 0.5 GeV/c for D/ˉD-meson production. Received: 8 November 1999     

Resonance elastic scattering of light by a quantum well with statistically uneven boundaries

A theory is formulated for the elastic scattering of light through quasi-two-dimensional exciton states in a quantum well with randomly uneven walls. The nonlocal exciton susceptibility is expressed in terms of random functions describing the shape of the quantum well boundaries up to and including linear terms in the unevenness height. The resonance elastic scattering cross sections in the presence of arbitrary statistical unevenness are calculated in the Born approximation for all channels in which the initial and final states are represented by an electromagnetic TM or TE mode. The spectral and angular dependences of the scattering probability are calculated with the unevenness characterized by Gaussian correlation functions. It follows from numerical estimates that elastic scattering in quantum wells should be observed for unevenness having an rms height of the order of the thickness of an atomic monolayer. Fiz. Tverd. Tela (St. Petersburg) 41, 330–336 (February 1999)     

Studying the ω<Emphasis Type="Italic">N</Emphasis> elastic and inelastic cross section with nucleons

We explore the possibility to measure the elastic and inelastic ωN cross section in p+d→d+ω+p _sp and p+A reactions. Our studies indicate that the elastic scattering cross sections can be determined for ω momenta above 1 GeV/c in p+d reactions by gating on high proton spectator momenta whereas the ωN absorption cross section down to low relative ω momenta is most effectively studied in p+A reactions at beam energies 2.0–2.7 GeV. Received: 15 October 1999     

Elastic scattering of e∓ by Na atoms

ABSTRACT

The differential, integrated elastic, momentum transfer, viscosity and total cross-sections along with Sherman function for the elastic scattering of electrons and positrons by sodium atoms have been calculated within the framework of complex projectile–atom optical potential model at the impact energies 0.1 ≤ E_i ≤ 10⁴ eV for both the projectiles. The relativistic Dirac partial wave techniques, with accurate analytical charge densities, are used to obtain the scattering amplitudes. The present results produce satisfactory agreement with the experimental measurements and other theoretical calculations available in the literature.     

Asymptotic coefficients for atoms and ions

We derive convenient analytical formulas in the effective-range approximation for the asymptotic coefficient C _κ of the radial wave function at infinity and for the average radius of the system. A comparison with the results of numerical calculations (done by the Hartree-Fock method) for multi-electron atoms and ions reveals that this approximation has good accuracy for valence s-electrons in all atoms from hydrogen to uranium. We calculate the values of the scattering lengths and the effective ranges for electron-atom and electron-ion scattering. We also examine the quasiclassical approximation for C _κ. Finally, we discuss the logarithmic increase in the effective ranges of ns states as n→∞. Zh. éksp. Teor. Fiz. 115, 521–541 (February 1999)     

Scattering of massless fermions by Schwarzschild and Reissner-Nordstrm black holes

We study the scattering of massless Dirac fermions by Schwarzschild and Reissner-Nordstrm black holes. This is done by applying partial wave analysis to the scattering modes obtained after solving the massless Dirac equation in the asymptotic regions of the two black hole geometries. We successfully obtain analytic phase shifts, with the help of which the scattering cross section is computed. The glory and spiral scattering phenomena are shown to be present, as in the case of massive fermion scattering by black holes.     

解相对论Dirac方程计算低能电子弹性散射截面的分波法

本文给出一个基于解相对论Dirac方程计算低能电子弹性散射截面的方法,比较Thomas-Fermi-Dirac(TFD)势及Hartree-Fock(HF)势对散射截面计算的影响,计算了C、Al、Cu、Ag、Au等多种元素在0.01~10keV能量范围的弹性散射截面,比较分析Mott模型、Pendry模型以及屏蔽的Rutherford截面之间的差异。     

On the theory of multiple scattering

In this paper a kinetic equation is derived for the distribution function in the variable q=2 sin(ϑ/2) for the case of a scattering cross section of general form under the assumption that the region of multiple scattering (the diffusion region) is small. The limits of the kinetic equation are discussed, with no restrictions imposed on the scattering angles. It is found that the equation has a solution in the form of an integral. Finally, it is established that the solution is applicable over the entire range of angles, from 0 to 180°. Zh. éksp. Teor. Fiz. 116, 418–435 (August 1999)     

Determination of the neutron electric form factor from the reaction 3 He(e,e'n) at medium momentum transfer

The electric form factor of the neutron G_En has been determined in double polarized exclusive ³ He(e,e'n) scattering in quasi–elastic kinematics by measuring asymmetries A _⊥, A _∥ of the cross section with respect to helicity reversal of the electron, with the nuclear spin being oriented perpendicular to the momentum transfer q in case of A_⊥ and parallel in case of A_∥. The experiment was performed at the 855 MeV c. w. microtron MAMI at Mainz. The degree of polarization of the electron beam and of the gaseous ³ He target were each about 50%. Scattered electrons and neutrons were detected in coincidence by detector arrays covering large solid angles. Quasi–elastic scattering events were reconstructed from the measured electron scattering angles ϑ_e, φ_e and the neutron momentum vector p _n ^′ in the plane wave impulse approximation. We obtain the result <G _En>_{(0.27 < Q2c2/GeV2 < 0.5)}= 0.0334 ± 0.0033_stat± 0.0028_syst which is averaged over the indicated range of Q ², the squared momentum transfer. This G _En value is significantly smaller than measured from the D(e,e'n) reaction under similar kinematical conditions. To what extent final state interactions in ³He quench the G _En result is subject of calculations currently in progress elsewhere. Received: 29 April 1999     

Positron-lithium scattering with the inclusion of positronium formation

Detailed studies have been made of elastic scattering and positronium formation in low energy collisions of positrons with lithium atoms for the two partial wavesl=0,1. For this system, as for all alkali atoms, the positronium formation channel is open even at zero positron energy. A two-channel version of the Kohn variational method is used with trial functions containing many variational parameters, and reasonably well converged results are obtained. The s-wave positronium formation cross section is infinite at zero positron energy but it then falls rapidly to become several orders of magnitude smaller than the elastic scattering cross section which has a maximum value of approximately 100 ₀ ² at a positron energy of 0.5 eV. For p-wave scattering the positronium formation cross section rises to a value of approximately 10 ₀ ² at an energy of 0.1 eV, with the elastic scattering cross section rising to a maximum of approximately 60 ₀ ² just below the first excitation threshold at 1.84 eV.     

Cascade processes in a plasma oscillator

A theoretical and numerical analysis is made of the dynamics of nonlinear electron-beam scattering of a wave reflected by the emitting device of a plasma oscillator. It is shown that a counterpropagating plasma wave can interact nonlinearly with other waveguide modes of the system and with charge-density beam waves, leading to changes in the operation of the oscillator. It is established by means of a numerical simulation that the generation efficiency is reduced as a result of scattering of the counterpropagating wave and stimulated emission of a strong-potential plasma wave with phase velocity v _ph=ω/k _z≪c. Zh. éksp. Teor. Fiz. 112, 1299–1311 (October 1997)