Dipole Correction Research Articles

The polarisation of electrons elastically scattered from argon

Spin polarisation is calculated for the elastic scattering of electrons by argon atoms at energies from 10 to 100 eV. The target atom is represented by a frozen core in a continuum relativistic Hartree-Fock calculation with dipole and quadrupole polarisation corrections. Parameters of the model polarisation potential are obtained from independent calculations. Exchange is calculated exactly for both large and small components of the scattered wavefunction. Effects of incomplete orthogonality between the core and scattered electron are investigated and found to be minimal. The results are in good agreement with earlier theoretical investigations, but in only partial agreement with available experimental data.

A relativistic approach to the elastic scattering of electrons by argon

Phase shifts and total and differential cross sections are calculated for the elastic scattering of unpolarised electrons by argon atoms in the impact energy range of 0.1 to 40 eV. The target atom is represented by a frozen core in a continuum relativistic Hartree-Fock calculation with dipole and quadrupole polarisation corrections. Exchange is calculated exactly and the parameters of the model polarisation potential are fixed by independent calculations. The results are in good agreement with experiment and with some of the non-relativistic coupled Hartree-Fock calculations; they demonstrate the importance of core polarisation effects as well as of relativistic effects at low incident energies.

The electric dipole of a guiding center and the plasma momentum density

Pfirsch [Z. Naturforsch., Teil A 39, 1 (1984)] has shown that the charge and current density in the guiding-center representation have contributions from electric dipole moments and magnetic dipole corrections. These moments are interpreted in terms of elementary guiding-center theory, and their role in the expression for the total momentum density is explained.

Rydberg states of helium: Relativistic and second-order corrections.

In this paper the corrections of relative order (Z\ensuremath{\alpha}${)}^{2}$ to all multipole polarizabilities of a hydrogenic ion of nuclear charge Z are computed, with use of third-order perturbation theory with nonrelativistic wave functions. To accomplish this, the spin-independent part of the Pauli Hamiltonian of order ${\ensuremath{\alpha}}^{2}$ is treated as a perturbation along with the usual Coulomb interaction expanded in a multipole series. The leading (dipole) correction is in agreement with the previous results of Zon et al. In addition, the previously discussed second-order energy shift has now been calculated analytically. Both of these corrections are applied to the high-lying Rydberg states of helium, yielding small but important corrections to the fine-structure splittings.

A Microprocessor Based Function Generator Mor Superconducting Dipole Correction Coils

A Microprocessor Based Function Generator Mor Superconducting Dipole Correction Coils

Interstitial potential differences, electronegativity differences, and effective ionic charges in zinc-blende-type semiconductors

Simple semi-empirical self-consistent pseudopotential calculations of various semiconductors, fitted to the empirical band structures, lead to interstital potential differences that can be described by an ionic model such that the ionic charges are proportional to the differences of the PHillips electronegativities for the participating ion species, e*/e≃0.76𝒟X. The results are applied to dipole corrections in heterojunction lineups.

Isabelle Closed Orbit Correction System

The proposed closed orbit correction system for the ISABELLE storage accelerators is described. Results given include the initial orbit displacement error expected, the degree of correction that is expected by moving quadrupoles and by exciting dipole correction coils, the limitations on orbit correction due to the number and location of the probes (pickup electrodes) and the accuracy requirements on the power supplies that stem primarily from the need to keep the two narrow beams in proper collision with each other.

The dipole expansion method for plasma simulation

The dipole expansion technique for determining the grid charge density and the electrostatic forces due to a system of extended charges is presented. In this scheme a charge (monopole) and a dipole moment, both extended, are assigned to the nearest grid point. The corresponding calculations of the force require the determination of the electric field and its gradient. The approach aims to minimize the number of operations per particle at the expense of more operations per grid point. The technique is appealing on physical grounds, since it helps one to relate numerical approximations to physical concepts. We also present a modified version, the subtracted dipole scheme (SUDS). In this version the field calculations do not take significantly longer than in nearest-grid-point calculations. This is particularly important in two- and three-dimensional simulations. We also discuss an optimization of the coding, particularly for the operations that must be done for each particle (computing its contribution to the charge density and updating its position and velocity). For example, this optimization has given a one-dimensional, nearest-grid-point code (lowest order in the multipole expansion scheme) that takes ∼1.8 μsec/particle on the IBM 360/91. We assess the value of the dipole correction by comparing dipole and nearest-grid-point simulations. Finally the relation between the dipole expansion (or SUDS) and charge sharing is discussed.

Preaveraged potential and the third virial coefficient of polar gases

The third virial coefficient of polar gases has been calculated on a preaveraged 12-6-6 potential model. The nonadditive corrections due to dipole, dispersion and repulsion three body interactions have also been computed. It has been found that while the dipole and dispersion nonadditive corrections are always positive, the repulsion nonadditive correction is negative. The net effect of these corrections is sizeable in the temperature range of our interest. The theoretical results have been compared with the experimental data of ammonia and methyl fluoride. The agreement between theory and experiment is reasonable in view of the large uncertainties in the experimental data. The overall agreement between experimental values and those obtained on the preaveraged potential for polar gases is comparable to that of the Lennard-Jones (12-6) model for nonpolar gases.

Relativistic Correction to Bremsstrahlung from a Plasma

An electron-ion dipole correction of − 15VT2/8c2 to the transverse bremsstrahlung spectrum is found by including relativistic corrections to the electron kinetics. This correction is of the same order as the electron-ion and electron-electron k2λD2 corrections.

Nonadiabatic Theory of Electron-Hydrogen Scattering

A rigorous theory of the $s$-wave elastic scattering of electrons from hydrogen is presented. The Schr\odinger equation is reduced to an infinite set of coupled, two-dimensional partial differential equations. A zeroth order scattering problem is defined by neglecting the coupling terms of the first equation. An exact relation is derived between the phase shift of this zeroth order problem and the true phase shift. The difference between these is contained in a rapidly convergent series whose terms correspond adiabatically to multipole distortions of the hydrogen by the incoming electron. The physical significance of the zeroth order problem is discussed, and its recognition is considered basic to the understanding of the scattering problem. The exchange approximation for $s$-wave scattering is shown to be a variational approximation of the zeroth order problem. A perturbation theory is introduced to calculate the higher order corrections. The dipole correction has an increasingly important quantitative effect in the limit of zero energy. The effect of the long-range part of this correction on the scattering length can be expressed by a formula in terms of inverse powers of a long-range parameter $R$. Phase shifts for both singlet and triplet scattering are calculated, including up to quadrupole terms. The convergence is such that this number of terms should yield better than four-place accuracy. Uncertainties in our calculated values decrease the accuracy to approximately three significant figures.