Polarization Corrections Research Articles

Calculation of the relativistic correction energies of Ne-like ions with orbital polarization correction

This paper reports the theoretical calculation of Breit, self-energy, and vacuum polarization corrections in the Ne-like system using multi-configuration Dirac-Fock method with the orbital polarization. The relations of these corrections with the atomic number and the orbital symmetries are shown and the calculated correction energies are compared with other calculated results. Our Breit correction energies are all smaller by 1eV as maximum than the other theoretical Breit correction energies and the differences reveal ystematical relation with atomic number. It is found that the configuration interactions have great effect on Breit corrections while the orbital polarization has much smaller effect on Breit corrections. The self-energy and vacuum polarization obtained by our calculation are much different from that in previous literatures for some transitions.

Non-Abelian Aharonov-Bohm scattering of spin 1/2 particles

We study the low energy regime of the scattering of two fermionic particles carrying isospin $\frac{1}{2}$ and interacting through a non-Abelian Chern-Simons field. We calculate the one-loop scattering amplitude for both the nonrelativistic and also for the relativistic theory. In the relativistic case we introduce an intermediate cutoff, separating the regions with low and high loop momenta integration. In this procedure purely relativistic field theory effects as the vacuum polarization and anomalous magnetic moment corrections are automatically incorporated.

Polarization effect in stopping of swift partially screened heavy ions: Perturbative theory

We report a calculation of the polarization correction – also called Barkas or Z13 effect – to the electronic energy loss of screened heavy ions above the Bohr velocity. For distant collisions we extend the classical calculation of Ashley et al. (Phys. Rev. B 5 (1972) 2393) to a screened projectile, while for close collisions we make use of an argument by Lindhard. The variation of energy loss with impact parameter is illustrated for Li on C for different charge fractions and projectile velocities v. Stopping numbers are shown at fixed charge fraction as a function of velocity, and for a velocity-dependent equilibrium charge.The polarization correction is found to be sizable over most of the velocity range covered by Bohr theory (the classical regime), but for the three ions for which results are reported, Li, C and Ar, very similar curves are found when stopping numbers are plotted against the Bohr parameter mv3/Z1e2ω, where ω is a characteristic resonance frequency of the target.The polarization correction is similar in magnitude to the leading term over a wide velocity range below mv3/Z1e2ω≃3. Therefore the perturbative approach presented here, which includes only one order beyond the leading term, cannot be expected to deliver very accurate results. This work will therefore be followed up by a nonperturbative evaluation of the stopping cross-section.

Electronic stopping of swift lithium and carbon ions

An attempt is made to estimate stopping powers for swift nonrelativistic heavy ions in the velocity range where projectile screening is significant. In contrast to existing tabulations and computer codes, our calculations take account of the fact that Bohr's classical approach is superior in this velocity regime to the Bethe theory. A theoretical scheme for estimating stopping powers at a fixed projectile charge, developed recently by one of us, has been expanded so as to account for charge equilibrium. Both target and projectile excitation/ionization are taken into account. The agreement with available experimental data appears promising in the considered velocity range (v0<v<2Z1v0) considering the fact that shell and polarization corrections still need to be incorporated.

Delocalization and new phase in americium: Density-functional electronic structure calculations

Density-functional electronic structure calculations have been used to investigate the high pressure behavior of Am. At about 80 kbar (8 GPa) calculations reveal a monoclinic phase similar to the ground state structure of plutonium (\ensuremath{\alpha}-Pu). The experimentally suggested \ensuremath{\alpha}-U structure is found to be substantially higher in energy. The phase transition from fcc to the low symmetry structure is shown to originate from a drastic change in the nature of the electronic structure induced by the elevated pressure. A calculated volume collapse of about 25% is associated with the transition. For the low density phase, an orbital polarization correction to the local spin density theory was applied. Gradient terms of the electron density were included in the calculation of the exchange/correlation energy and potential, according to the generalized gradient approximation. The results are consistent with a Mott transition; the $5f$ electrons are delocalized and bonding on the high density side of the transition and chemically inert and nonbonding (localized) on the other.

Observation of a triple correlation in ternary fission: is time reversal invariance violated?

In ternary fission, besides the two main fission fragments, a third (usually light) charged particle is emitted. A triple correlation has been studied involving the momenta for a specific fission fragment p ̂ f , the momenta of the ternary particle p ̂ t and the spin of the polarized cold neutron inducing fission σ ̂ . The correlation observable B= σ ̂ ·[ p ̂ f × p ̂ t ] reverses sign upon time reversal and thus a non-vanishing value for the expectation value 〈 B〉 could possibly be due to TRI being violated. However, final-state interactions or specific properties of the emission mechanism for ternary particles could equally well lead to a non-zero 〈 B〉 with TRI being perfectly conserved. The reaction chosen was 233U(n,f). An unexpectedly large correlation was observed. From the raw data the value for 〈 B〉 is 〈 B〉=−(0.78±0.02)×10 −3 with the sign corresponding to light fragments. Corrections for neutron polarization, geometric efficiency, resolution of detectors and background increase this figure by a factor of (1.5±0.3).

Correction of the influence of baseline artefacts and electrode polarisation on dielectric spectra

The deconvolution of biological dielectric spectra can be difficult enough with artefact-free spectra but is more problematic when machine baseline artefacts and electrode polarisation are present as well. In addition, these two sources of anomalies can be responsible for significant interference with dielectric biomass measurements made using one- or two-spot frequencies. The aim of this paper is to develop mathematical models of baseline artefacts and electrode polarisation which can be used to remove these anomalies from dielectric spectra in a way that can be easily implemented on-line and in real-time on the Biomass Monitor (BM). We show that both artefacts can be successfully removed in solutions of organic and inorganic ions; in animal cell and microbial culture media; and in yeast suspensions of varying biomass. The high quality of the compensations achieved were independent of whether gold and platinum electrodes were used; the electrode geometry; electrode fouling; current density; the type of BM; and of whether electrolytic cleaning pulses had been applied. In addition, the calibration experiments required could be done off-line using a simple aqueous KCl dilution series with the calibration constants being automatically calculated by a computer without the need for user intervention. The calibration values remained valid for a minimum of 3 months for the baseline model and indefinitely for the electrode polarisation one. Importantly, application of baseline correction prior to polarisation correction allowed the latter's application to the whole conductance range of the BM. These techniques are therefore exceptionally convenient to use under practical conditions.

Transition intensities in rare gas triatomic ions: DIM versus point-charge approximation

Diatomics-in-molecule (DIM) approach is compared with the point-charge approximation for transition moments in Rg 3 + and is shown to be its extension capable of accurately reproducing the direct ab initio results. Relevant polarization corrections to the point-charge approximation are proposed. The developed procedure is applied to construction of transition moment and intensity (oscillator strength) 3D-surfaces of Ne 3 +. They are used to evaluate the photoabsorption spectra of the bound species and of the Ne + Ne 2 + collisional system. The major absorption band of Ne 3 + is predicted to be red-shifted by 200 nm from that for the diatomic ion, and the absorption spectrum of Ne 2 + is found to be significantly affected in collisions with Ne.

Energies, fine structures, and transition rates of the core-excited states in BeII

The energies and fine structures of some doubly excited resonances of lithiumlike beryllium are calculated using the saddle-point variational method. A restricted variational method is used to extrapolate a better nonrelativistic energy. Relativistic and mass polarization corrections are included. Oscillator strengths, transition rates, and wavelengths are also calculated. The results are compared with other theoretical and experiment data in the literature. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 656–661, 2000

Energies, fine structures, and transition rates of the core‐excited states in BeII

The energies and fine structures of some doubly excited resonances of lithium like beryllium are calculated using the saddle-point variational method. A restricted variational method is used to extrapolate a better nonrelativistic energy. Relativistic and mass polarization corrections are included. Oscillator strengths, transition rates, and wavelengths are also calculated. The results are compared with other theoretical and experimental data in the literature.

Formulation of nuclear polarization correction with the Feynman photon propagator

The leading order process of the nuclear polarization (NP) is formulated with the Feynman photon propagator. The present treatment incorporates the whole contributions due to the Coulomb and transverse interactions as well as their interference in the Coulomb gauge. An explicit formula is given in the point-nucleus limit for hydrogen-like heavy ions. The numerical method is also discussed.

Relativistic many-body and QED effects on the hyperfine structure of lithium-like ions

The hyperfine splitting of the ground state of three-electron ions is studied in detail with the help of the multi-configuration Dirac-Fock method. We study the role of the magnetic electron-electron interaction and of the negative energy continuum. An all-order evaluation of some vacuum polarization corrections is performed. The Bohr-Weisskopf effect is evaluated in a simple model.

Calculations of 2Po resonances in Be II

The positions and the widths of 21 2Po resonances in Be II between 1 1S0 and 2 1P thresholds are calculated using a saddle-point complex-rotation method. Relativistic and mass polarization corrections to the autoionization energy are included. Below threshold (1s2s)3S our results agree well with other calculations and experiments. We make an identification of states above the (1s2s)3S threshold. For the region above 2 3S, our present results for Be II are contrasted with those for Li I (Wu L J and Chung K T 1997 J. Phys. B: At. Mol. Opt. Phys. 30 1173). We discuss the dependence of the widths on the atomic number.

Ab initio study of anisotropic magnetism in uranium compounds

We have applied two methods to investigate the origin in the electronic structure of the unusual magnetic behavior of the uranium monochalcogenides and monopnictides. First, we have carried out spin-polarized electronic structure calculations based on the full-potential linearized muffin-tin orbital (FPLMTO) method with only spin-polarization (orbital polarization only via spin-orbit coupling) and also with orbital polarization correction. Second, we have carried out first-principles calculations synthesizing (1) a phenomenological theory of orbitally driven magnetism using a model Hamiltonian which incorporates explicitly the hybridization-induced and Coulomb exchange interactions on an equal footing, and (2) FPLMTO electronic structure calculations allowing a first-principles evaluation of the parameters entering the model Hamiltonian. Within the purely band calculation greater success is obtained for the zero-temperature ordered moments for the more itinerant compounds (US and UP), while the synthesis of phenomenology and electronic structure method gives better agreement with experiment for the more localized pnictides (UBi, USb). Results for the ordered moments and ordering temperatures are presented, and the validity and limitations of the two methods are discussed.

Spin-orbit interaction in the field of an optical vortex of a few-mode fiber

A quantum-mechanical analog of the spin-orbit interaction operator \(\hat V\) is constructed for the fields of optical CV vortices and TE and TM modes in an optical fiber. It is shown that the polarization correction δβ to the propagation constant, which is the mean value of this operator, is a measure of the “level splitting” of the propagation constant \(\tilde \beta \) in the scalar case. The difference in the operation of the individual parts of the operator \(\hat V\) on the fields of CV vortices and on the fields of TM and TE modes is indicative of the presence of two different physical processes — circular and linear birefringence in the locally isotropic optical fiber. The conversion of the “scalar” field \(\tilde e\) to a vector field e1 as a consequence of the spin-orbit interaction operator can be regarded as resulting from a re-radiation of the additional field e1 by the vortex field \(\tilde e\), which rotates around the optical axis of the fiber. In this picture the additional field e1 can be regarded as being a “relativistic” correction to the vortex field for the distortions of the main field \(\tilde e\) and arising as a result of the rotation of the field of the optical vortex in the medium of the few-mode fiber.

The 2s 12p 4 autodetachment resonance in the C − negative ion

The calculations of the photodetachment cross section for the C − negative ion has been performed within the newly-developed many-body theory method, the RPAE interchannel interaction and dynamic relaxation and polarization corrections being included. The 2s 12p 4 shape resonance is shifted to a higher photon energy and broadens as compared to the resonance parameters determined earlier within the RPAE, which is consistent with the experimental evidence and the recent R-matrix calculations.

Radiative corrections to the hyperfine-structure splitting of hydrogenlike systems

We present a complete calculation of the leading nonrecoil radiative corrections to the $1s$ hyperfine-structure splitting of highly charged hydrogenlike ions. In particular, we have investigated how the radiative corrections for ions with a high nuclear charge number $Z$ are affected by using an extended nuclear magnetization. We also present the first complete evaluation of the Wichmann-Kroll part of the vacuum polarization correction to all orders in $(Z\ensuremath{\alpha})$. To unambiguously incorporate this effect we have also calculated the vacuum polarization correction to the measured nuclear magnetic moment. Total theoretical results are collected for the experimentally interesting ions ${}^{209}{\mathrm{Bi}}^{82+},$ ${}^{207}{\mathrm{Pb}}^{81+},$ ${}^{185}{\mathrm{Re}}^{74+},$ and ${}^{165}{\mathrm{Ho}}^{66+}.$ Also the low-$Z$ region is considered in order to compare with the known part of the $(Z\ensuremath{\alpha})$ expansion.

Relativistic and many-body effects in K, L, and M shell ionization energy for elements with $\mathsf{10 \leq Z \leq 100}$ and the determination of the 1s Lamb shift for heavy elements

We report on a calculation of K, L and M inner-shell ionization energy in atoms with atomic numbers in the range . Many-body effects are evaluated for all n =1, 2, and 3 hole states. Those include correlation and effects due to the auto-ionizing nature of the hole states (Auger shift). For high Z we add recent corrected nuclear polarization, and several second-order vacuum polarization corrections. K and L ionization energies are compared with experimental X-ray absorption edges measurements. Excellent agreement with rare gazes and metal vapor measurements is found. We also compare our calculations with X-ray transition energies for all K and L lines that involve K, L and M holes. Finally we use K X-ray lines to deduce an hydrogenlike 1 s Lamb shift for several heavy elements, with far better accuracy than has been obtained by direct measurements of hydrogenlike ions.

Core polarization and oscillator strength ratio anomaly in potassium, rubidium and caesium

The problem of the anomalous ratios of the oscillator strengths in the heavy alkali principal series, though known for almost 70 years, still attracts the attention of both theorists and experimentalists. Our present fully relativistic model potential calculations demonstrate that the spin-orbit interaction cannot be solely responsible for the observed anomalies in potassium, rubidium and caesium and that they result from the interplay of spin-orbit interaction, core-valence electron correlation (core polarization) and cancellation observed in transition integrals. The role of core polarization is carefully studied. It is shown that in the case of the empirically adjusted model potential the most important correction is not the inclusion of polarization potential but the allowance made for the additional induced dipole moment in the dipole moment operator of transition. Also the form employed to represent the correction to the dipole moment is important, if one wishes to avoid any adjustment in core polarization corrections. It is also shown that the employment of J-dependent effective model potentials (J = total angular momentum) is essential in reproducing relativistic effects in f-value ratios.

Topological phase of optical vortices in few-mode fibers

It has been found that as they propagate, the natural optical vortices of a few-mode parabolic fiber acquire a topological phase in addition to the dynamic phase. The magnitude of this phase is numerically equal to the polarization correction to the propagation constant of the CV and IV vortices. An analysis revealed that this phase is a new type of optical manifestation of the topological Berry phase. The already known Pancharatnam and Rytov-Vladimirski $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}$$ . phases are associated with changes in the magnitude and direction of the angular momentum flow of the wave. In the fields of natural vortices of a few-mode fiber all the explicit parameters of the wave remain unchanged during propagation. However, the direction of the momentum density vector of the vortex undergoes cyclic variations along the trajectory of the energy flow line. These cyclic variations of the implicit vortex parameter are responsible for the new type of topological phase. Unlike the study made by van Enk (Ref. 6), where the topological phase was only related to the angular momentum for the lowest-order Gaussian beams (l=±1), this topological phase describes guided vortices with any values l of the topological charge. The results can be used to estimate the stability of CV and IV vortices relative to external perturbing influences on the optical fiber.