Inclusion Of Relativistic Corrections Research Articles

Relativity versus exchange currents inO16(e,e′p)

The 16O(e,e'p) reaction in the quasi-elastic region has been studied in several experiments to determine spectroscopic factors, hence, the degree to which $^{16}$O looks like a closed shell. By varying the kinematics, experimentalists are able to extract response functions which comprise the cross section. However, analysis of the response functions separately produces very different spectroscopic factors. Two calculations led to different conclusions as to whether exchange currents can eliminate the discrepancies. Neither calculation considered relativistic corrections. The purpose of the article is to investigate the disagreement as to whether exchange currents are the solution to obtaining consistent spectroscopic factors, and to show that relativistic corrections have a much greater influence on providing this consistency. This calculation employs the recoil corrected continuum shell model, a model that uses a realistic interaction, and produces non-spurious scatterings states that are solutions to the coupled channels problems. Pionic and pair contributions to the exchange currents were calculated as developed by Dubach, Koch, and Donnelly. Relativistic effects are included by use of the direct Pauli reduction. Contributions of the exchange currents are shown to be insufficient to provide consistent spectroscopic factors. However, the inclusion of relativistic corrections, that can be large, lead to more consistent spectroscopic factors and cross sections. The influence of channel coupling is also shown to be significant. Tests of current conservation show that inclusion of the direct Pauli reduction produces small increases in its violation. Response functions which depend on the transverse current are sensitive to the lower component of relativistic wave functions, and hence, would provide a measure of the appropriateness of any relativistic model.

DFT calculation of NMR δ(113Cd) in cadmium complexes

We have tested several DFT protocols, at the non-relativistic and relativistic ZORA (scalar and spin–orbit) levels, for the calculation of the 113Cd chemical shifts, δ(113Cd), for a number of cadmium complexes accounting for both different local coordination environments on the metal center, involving N, O and S ligands, and different geometrical arrangements. Moreover, suitable models as reference compounds for δ(113Cd) evaluation have been set up in order to propose a complete computational approach to calculate δ(113Cd) for cadmium complexes. Inclusion of relativistic corrections did not lead to any sensible improvement in the quality of results and, in this context, non-relativistic method, namely: B3LYP/Sadlej(Cd); 6-31g(d,p) (light atoms), showed to be the best approach to calculate δ(113Cd) for the classes of compounds investigated.

Simulation of the Hydrogen Ground State in Stochastic Electrodynamics-2: Inclusion of Relativistic Corrections

In a recent paper the authors studied numerically the hydrogen ground state in stochastic electrodynamics (SED) within the the non-relativistic approximation. In quantum theory the leading non-relativistic corrections to the ground state energy dominate the Lamb shift related to the photon cloud that should cause the quantum-like behaviour of SED. The present work takes these corrections into account in the numerical modelling. It is found that they have little effect; the self-ionisation that occurs without them remains present. It is speculated that the point-charge approximation for the electron is the cause of the failure.

A converging equation of state of a weakly nonideal hydrogen plasma without mystery

A detailed independent derivation of the equation of state of a weakly nonideal hydrogen plasma is presented. The impetus for this work was the demand for high accuracy of the equation of state of the solar plasma in relation to the problems of modern helioseismology, accuracy sufficient for reproducing the velocity of sound on the Sun from optical measurement results with errors not exceeding 10−4. The existing equations for the second virial coefficient in the expansion of the Helmholtz thermodynamic potential for a system of electrons and protons in powers of the activities of these particles involve certain procedures for the removal of the arising divergences that provoke questions and require independent verification. The suggested equation of state is used to qualitatively estimate the accuracy of various physical and chemical models. The speed of sound and adiabatic exponent calculated along the solar trajectory are presented for a model hydrogen plasma. The calculations were performed with the inclusion of relativistic corrections, electron degeneracy effects, radiation pressure in the plasma, Coulomb interaction in the Debye-Huckel approximation with diffraction and exchange corrections, and converging contributions of bound and scattering states.

The age of the Sun and the relativistic corrections in the EOS

We show that the inclusion of special relativistic corrections in the revised OPAL and MHD equations of state has a significant impact on the helioseismic determination of the solar age. Models with relativistic corrections included lead to a reduction of about with respect to those obtained with the old OPAL or MHD EOS. Our best-fit value is which is in remarkably good agreement with the meteoritic value for the solar age. We argue that the inclusion of relativistic corrections is important for probing the evolutionary state of a star by means of the small frequency separations , for spherical harmonic degrees and radial order .

THE SEMIRELATIVISTIC EQUATION VIA THE SHIFTED-l EXPANSION TECHNIQUE

The semirelativistic wave equation which appears in the theory of relativistic quark–antiquark bound states, is cast into a constituent second order Schrödinger-like equation with the inclusion of relativistic corrections up to order (v/c)2 in the quarks speeds. The resulting equation is solved via the Shifted-l expansion technique (SLET), which has been recently developed to get eigenvalues and wave functions of relativistic and nonrelativistic wave equations. The Coulomb, Oscillator, and the Coulomb-plus-linear potentials used in [Formula: see text] phenomenology are tested. It is observed that, the energy eigenvalues can be explained well upon the more commonly used nonrelativistic models, when such a dynamical relativistic corrections are introduced. In particular, it provides a remarkable accurate and simple analytic expression for the Coulomb ground-state energy problem, a result which is in the right direction at least to serve as a test of this approach.

Orthogonalized linear combinations of atomic orbitals. IV. Inclusion of relativistic corrections.

The relativistic corrections to the band-structure calculation have been implemented in the orthogonalized linear combinations of atomic orbitals method. A two-step process is suggested such that the scalar-relativistic effects due to the spin-independent mass-velocity and Darwin terms are treated first. Spin-orbit interaction is then included on the basis of the spin-polarized band structures. All other higher-order corrections are ignored. Test calculations on scalar-relativistic corrections are demonstrated in the elemental methods Ni, Nb, and Ce with increasing atomic mass numbers. The results are in very good agreement with the established results using other band methods. The full relativistic band structure is calculated for ferromagnetic Fe. It is shown that the effect of spin-orbit interaction in Fe is of considerable importance compared with the scalar-relativistic correction.

Highly correlated systems. Ionization energies of first row transition metals Sc–Zn

The low-lying ionization potentials of the first row transition metal atoms Sc–Zn are calculated using fourth-order Mo/ller–Plesset perturbation theory (MP4) and quadratic configuration interaction (QCI) techniques with large spd and spdf basis sets. Two ionic states have been considered for each atom yielding a total of 20 different ionization processes which we have included in this study. For Sc+–Cu+, the ionic states considered have dns1 and dn+1 orbital occupations and for Zn+, the d10s1 and d9s2 states were studied. The MP4 method accurately reproduces the ionization potentials of Sc–Fe, but is found to be inadequate for Co–Zn. In contrast, the QCI technique performs uniformly for all ionization energies with a mean deviation from experiment of only 0.13 eV (with the spdf basis set) after inclusion of relativistic corrections.

Oscillator strengths for transitions from 3s4s and 3s4p levels calculated in the magnesium sequence, MgI–MnXIV using the multiconfiguration optimized potential model

Oscillator strengths for downward transitions from the 3s4p and 3s4s levels in the Magnesium isoelectronic sequence are reported. These, as well as lifetimes for these levels, have been calculated for MgI to MnXIV using the Multiconfiguration Optimized Potential Model (MCOPM) with inclusion of relativistic corrections. Generally, the level splittings are reasonably accurate but at certain level crossings - occurring near Sv and C1VI - considerable energy level accuracy is required to ensure accurate relativistic mixing coefficients and transition rates. Corrections have been applied to the energies in these cases.

Relativistic effects in neutrino (Antineutrino) disintegration of the deuteron

The cross section of neutrino disintegration of the deuteron with inclusion of relativistic corrections is calculated. The transition only to1S0-state is taken into account, so the results are valid for reactor and meson factory energies. Comparison with earlier works is given. It is shown, that accurate choice of bound state wave function is essential for the final results. The relativistic approach developed in this work should be used as a starting point for calculations of meson exchange current corrections.

L X-ray production cross sections of Au, Bi and U by protons of energy 0.3 to 1.8 MeV

Partial L X-ray production cross sections for proton bombardment of Au, Bi and U have been systematically measured in the energy range 0.3 to 1.8 MeV. This targets have been used in transmission geometry. For Bi and U, detailed low-energy measurements are reported here for the first time. Intensity ratios Ialpha /Ibeta ,Ialpha /Igamma and Ialpha /Il have been as a function of proton energy. Data are compared with the theoretical predictions of the PWBA and the PWBA with Coulomb deflection and binding corrections. There are indications that inclusion of relativistic corrections in the PWBA substantially improves the agreement with experiment.

Relativistic corrections for variational wavefunctions

A consistent procedure based on a suggestion of Boys and Price is recommended for the simple inclusion of relativistic corrections in the Breit approximation into variational wavefunctions. A previous discussion is criticized as introducing error terms of the same order as the quantities being studied.

Electronic Structure of Palladium

A detailed investigation of the electronic structure of palladium is presented in terms of two different band models: (1) ab initio calculations using the augmented-plane-wave method, and (2) calculations using the combined interpolation scheme augmented by inclusion of relativistic corrections. The width and position of the $d$-band complex are found to be particularly sensitive features of the electronic structure of palladium. A highly detailed density-of-states histogram, and estimates for the first and second derivatives of the density of states at the Fermi energy are derived. In addition, detailed comparisons are made with Fermi-surface-static susceptibility, and specific-heat experimental results. Estimates for the effects of manybody enhancements suggest that paramagnons raise the effective mass at the Fermi energy by only about 41%. Owing to the strong $s\ensuremath{-}d$ hybridization in palladium, the Fermi surface is made up almost entirely of $d$-like states. Because the Fermi energy in palladium falls near the strongly spin-orbit split levels at $X$ and $L$, spin quenching reduces the effective $g$ factor at the Fermi energy from 2 to about 1.65. This increases an estimate of the effective Stoner-enhancement factor from 10 to about 15.