Order Born Approximation Research Articles

Calculation of cyclotron resonance linewidth due to ionized impurities and longitudinal optical phonons

Abstract The cyclotron resonance linewidth for free carriers in semiconductors is calculated, starting from the Kubo formula. Ionized impurity and LO phonon scattering are taken into account. The absorption spectrum is investigated in the Relaxation Kernel approach and the scattering is treated in the lowest order Born approximation. For T >15 K, excellent agreement is obtained with the measurements of Matsuda et al. in InSb. No adjustable parameters are introduced.

Elastic scattering of electrons by helium atoms in high energy higher order Born approximation

The differential cross-sections forē-helium elastic scattering are calculated by using Yateshigh-energy higher order Born approximations, through 0 (KiEmphasis>−2) of the incident electron momentum, and comparisons have been made with the recent theoretical and experimental results.

On higher order Born approximations in atomic scattering calculations

It is pointed out that all higher order odd Born amplitudes calculated in the closure approximation vanish in the forward direction for elastic scattering of structureless charged particles by hydrogen atoms. The consequences of this result on elastic scattering of charged particles by complex atoms and on other approximate theories are also discussed.

4 OPW calculations of electronic transport coefficients of aluminium containing point defects

The scattering of conduction electrons on dilute point defects in aluminium was investigated, for zero temperature, by pseudopotential calculations considering the realistic form of the Al Fermi surface (FS) and band structure. The 4-OPW wavefunctions, band velocities and FS curvatures were calculated for 1,300 pointsk on 1/48 (cubic symmetry element) of the FS. The scattering potentials were obtained as follows: for the impurities Ge, Mg, Zn, and Ga tabulated pseudopotentials were used and rescreened for the electron density of Al, the vacancy was treated as a missing Al atom and the [100] dumbbell interstitial as two Al atoms with a vacancy in between (always with strain field corrections). The scattering matrixP kk′ was obtained in first order Born approximation. The linearized Boltzmann equation was solved numerically by iteration, for zero magnetic field and for a reduced set of 109 points on 1/48 FS, to yield the anisotropic transport relaxation timesτ k and lifetimesτ 0 . Theτ k were interpolated for the 1,300 points again and inserted into low-field FS integrals for the galvanomagnetic coefficients which depend sensitively on the details of the FS and the anisotropy ofτ k . Without any free parameter, our results agree very well with experimental data for the case of Ge, Mg, and Zn impurities, and less so for the homovalent Ga impurities and for the self-defects. The diffusion thermopower was also calculated.

αspectroscopic factors inCa40

In the $^{36}\mathrm{Ar}$($^{6}\mathrm{Li}$,$d$)$^{40}\mathrm{Ca}$ reaction, at a bombarding energy of 17 MeV, angular distributions have been measured for all levels below 7 MeV excitation. Unnatural-parity states are weak. For natural-parity states, the angular distributions are characteristic of direct $\ensuremath{\alpha}$ stripping, even as far backward as 160\ifmmode^\circ\else\textdegree\fi{} for the strong states. The data have been analyzed with zero-range distorted-wave Born approximation in order to extract relative $\ensuremath{\alpha}$-particle spectroscopic factors.NUCLEAR REACTIONS $^{36}\mathrm{Ar}$($^{6}\mathrm{Li}$,$d$), $E=17.0$ MeV; measured $\ensuremath{\sigma}({E}_{d},\ensuremath{\theta})$; $^{40}\mathrm{Ca}$ levels deduced ${S}_{\ensuremath{\alpha}}$. DWBA analysis. Enriched gas target.

Coherent excitation of then=3 level of hydrogen in a field free region

The theory of coherent excitation of then=3 level of atomic hydrogen by electron impact is studied using density matrix techniques. A set of multipole parameters is defined which allows to characterise coherently excited states with different angular momenta. Numerical results of these parameters, calculated in first order Born approximation, are tabulated for several energies and angles. Angular distribution and polarization of Balmer-α radiation are expressed in terms of the initial multipole parameters for the case that scattered electrons and emitted photons are detected in coincidence. The theory of cascade effects is briefly considered and applied to the case where scattered electrons and Lyman-α photons are detected in coincidence, generalising earlier formulations. Most of the formulas presented here are quite general and can be applied, for example, to an analysis of light emitted by beam foil excited hydrogenic levels.

Transition temperature of a two-band superconductor with nonmagnetic impurities

The problem of nonmagnetic impurities in a two-band superconductor has been investigated for the case of strong scattering of a conduction electron from an impurity. We use the Green's function method and introduce a t-matrix to treat the scattering. We find that the transition temperature T/sub c/ calculated in the present theory differs significantly from its value obtained by using the lowest order Born approximation. In general, the present theory gives a softening of the depression in T/sub c/ by the impurities.

Energy shifts in the relative coordinates treatment of the collinear collision between an atom and an oscillator. Exponential repulsive potential

The treatment of the kinetic term which may be taken as the perturbation when the collision between an atom and an oscillator is described with relative coordinates is shown to require the use of energy shifted basis functions in the calculation of the transition probabilities. For an exponential repulsive potential, a simple analytical formula is obtained for one quantum jumps in the first order Born approximation, which has a simple relationship with the first order Born distorted wave expression, and which lead to better results than the other available analytical formulas.

Charge exchange to the continuum for light ions in solids

Electron capture into ionized states of fast ions (H+, H2+, He+) in carbon and gold foils is investigated. Velocity of ejected electrons are measured in the forward direction and a characteristic cusp-shaped peak is found for electrons ejected with velocity equal to that of the incoming ions. The spectra are interpreted by a theory of charge exchange to the continuum, based on an atomic physics ion-atom collision model. As with proper charge exchange, a second order Born approximation is necessary to calculate the high energy cross sections.

Kinetic Theory of Nonequilibrium Alignment Phenomena in Atomic Vapors

Nonequilibrium alignment phenomena in gases of polyatomic molecules (Senftleben-Beenakker effect, flow birefringence) have been studied extensively during the last decade. Similar effects should also exist for atoms with nonzero electronic orbital angular momentum. The Waldmann- Snider equation (considered as Boltzmann equation for reacting mixtures) is used to derive an expression for the tensor polarization caused by a flow field in such atomic vapors. As a simple special case 2P-atoms are treated as an effective two level system (fine structure doublet). They can be tensor-polarized in the state with j = 3/2. An ansatz is made for the nonspherical interaction potential between 2P-atoms. The scattering amplitude is calculated in first order Born approximation which is reasonable for the high temperatures necessary. The relevant cross sections and collision integrals are evaluated. The temperature dependence of the alignment and its order of magnitude are discussed. Although the effect is rather small it should be detectable by optical methods (flow birefringence). The connection of flow birefringence and collisional alignment is elucidated.

Corrections to the Bethe-Bloch formula for average ionization energy loss of relativistic heavy nuclei Close collisions

Corrections to the Bethe-Bloch formula for a average ionization energy loss of relativistic nuclei are calculated by numerically integrating the exact Mott cross section. Results are tabulated in the form of a correction term Φ( β, Z) for nuclei with Z = 6, 12, 26, 36, 52, 60, 75, 80, 92, 104 and 114 and velocities corresponding to β = 0.85, 0.90, 0.95, 0.97, 0.99 and 0.999. These results are compared with closed form corrections obtained from the second and third order Born approximations. Close agreement is found between the corrections from the Mott and third order Born approximations for Z ≤ 60 and β ≥ 0.85.

Spin waves in a dilute Heisenberg antiferromagnet

A Green function calculation for spin waves in a dilute antiferromagnet is presented. By generalizing a calculation of Kaneyoshi (1969) it is shown that in a second order Born approximation the spin wave modes become unstable at C*=0.296. Diagrammatic techniques are given from which selective summations may be performed. A possible candidate for experiments is indicated.

Self-Consistent Dispersion-Theoretic Electron-Positron Scattering Amplitude

A method is outlined for the construction of dispersion-theoretic electromagnetic scattering amplitudes for processes in which bound states may appear; in particular, the electron-positron system is examined. A Lorentz-covariant spinor amplitude is exhibited which is analytic, cutoff independent, and crossing symmetric, which has the correct double-spectral functions through second order in the fine-structure constant $\ensuremath{\alpha}$, and which reduces to the usual Born approximation in lowest order. Moreover, the amplitude displays Regge asymptotic behavior and the positronium Regge poles. Self-consistency requires that the positronium poles appear at the correct position and with the proper residue, and that the amplitude possesses a well-defined Jacob-Wick expansion. It is found that this second-order amplitude provides a suitable basis for iterative calculation of the higher-order terms using the same procedure.

Dispersive effects in elastic electron scattering by vibrational nuclei

The effects of virtual nuclear excitations for elastic electron scattering by a quantized liquid drop are estimated with the second order Born approximation.

Excitation of the one-nucleon continuum of 12C by electron scattering at low momentum transfer

Inelastic electron scattering cross sections are calculated for excitation energies above the one particle threshold in 12C. The nuclear problem has been treated in the framework of the eigenchannel theory of nuclear reactions using the 1p-1h-approximation. The treatment of the electron is restricted to first order Born approximation. The numerical results obtained for negative parity states up to J π = 4 − are presented together with new experimental data from the Darmstadt Linac.

Notes on the Influence of Spin on the Electrical Conductivity in Strong Magnetic Fields

AbstractThe longitudinal and transverse electrical conductivity for a system of free electrons interacting with short‐range impurities is calculated. Since in the lowest order Born approximation the transverse conductivity diverges, and the longitudinal conductivity shows unphysical zeroes for certain values of the magnetic field, higher order t‐matrix treatment is required. We obtain spin splitting of the Shubnikov‐de Haas oscillations for spin independent and spin dependent scattering. Compared with the transverse case, the first (0+) maximum is absent in the longitudinal case, provided that no spin flip occurs. Spin flip in the scattering process, however, gives rise to a 0+ maximum. Apart from this fact, the spin flip causes no remarkable change in the oscillatory behaviour of the conductivity.

Possibility of Extracting Anisotropy Parameters from Total Cross-Section Measurements. II

The total (integrated) cross section for the collision of an atom and a diatomic molecule (rigid rotor) is computed in the distorted-wave Born approximation (DWBA) in order to see how information concerning the anisotropic potential can be obtained from such measurements. It is seen that the anisotropy parameters can be obtained most directly from the amplitude of the oscillatory contribution to the cross section. The frequency of the oscillations is determined by the velocity dependence of the rainbow angle of the spherically symmetric distorting potential and (to lowest order) contains no dependence on the anisotropy. Elastic and inelastic transitions are treated.

Higher Order Born Approximations for the Inversion of Love Wave Dispersion

Summary The procedure for the inversion of Love wave dispersion has been extended to the case of an arbitrary number of homogeneous layers overlying a uniform half-space. With this process the iterative inversion procedure can proceed as often as required for convergence subject to the limitation of the Born approximation.

Momentum-spin correlations in photoelectric effect and in single quantum positron annihilation

The transverse polarization of photoelectrons and the photon emission asymmetry with respect to the polarization plane in single quantum annihilation of transversely polarized positrons is calculated in the lowest non-vanishing order Born approximation. The effects are of the same nature and of the same order of magnitude as the polarization and asymmetry effects in Mott scattering. The momentum spin correlation in quantum theory of radiation is shown to be proportional to the imaginary part of the matrix element integrals. The fact that the correlation only occurs in the second order Born approximation, the first order Born approximation matrix element integrals being real, is closely related to time reversal invariance.

High-energy behaviour of electromagnetic scattering cross-sections

The theory of the renormalization group is used in order to show that for large momentum transfer the perturbation expansion in α of the differential cross-section for the scatteringo f an electron by a potential in first order Born approximation is expanded in terms of the effective parameter (α/π) ln (q2/m2). (q=invariant momentum transfer,m=electron rest mass;q/m≫1.)