Spin Polarization Parameters Research Articles

Cross sections and spin polarizations for e+/- scattering from cadmium.

Various scattering cross sections such as differential, integrated-elastic, momentum-transfer, and total cross sections, and the spin-polarization parameters for both the elastic and the total scatterings of electrons and positrons from cadmium atoms in the impact-energy range of 6.4--300 eV, have been calculated relativistically by solving the Dirac equation. For the pure elastic-scattering case, the projectile-target interaction is represented by a real model potential that includes the static potential (attractive), a parameter-free polarization potential (attractive) and an electron-exchange potential for the electrons scattering, and the static potential (repulsive) and a parameter-free polarization potential (attractive) different from that of electrons scattering for the positrons scattering from cadmium. For the total scattering, which includes both the elastic-scattering and the inelastic-scattering processes, the total interaction is represented by a complex potential by adding a model absorption potential as its imaginary part. It has been observed that the agreement of the calculated differential cross section (DCS) curves for the elastic scattering of electrons from cadmium is reasonable with the previously measured values of DCS while the agreement is good with the recently measured values of DCS.

Theoretical Calculations for Elastic Scattering of Electrons from Xe Atom

The differential cross sections and spin polarization parameters for the spin-electrons elastically scattered from spinless Xe atoms are calculated by relativistic partial expansion method. In the processes the incident electrons are treated as moving relativistically in an effective central potential V(r) which is calculated by relativistic self-consistent-field method with Slater local exchange approximations. The validity of the theoretical method can be accessed by detailed comparison with recent complete experimental data.

Angle- and spin-resolved photoelectron spectroscopy in the region of the 6s6p2 autoionisation of Tl

An angle-, energy- and spin-resolved photoionisation experiment was performed in the region of the 6s6p2 autoionisation resonances of thallium. Using monochromatic circularly polarised synchrotron radiation the energy dependence of the spin-polarisation parameters A, xi and alpha and the angular asymmetry parameter beta of the differential cross section were determined. In the wavelength region investigated these dynamical parameters show a pronounced variation which agrees well with the results of the random phase approximation with exchange' calculation by Cherepkov (1980). A detailed discussion of the resonance behaviour for the autoionising states is given in terms of dipole-matrix elements and phaseshift differences which are extracted from the experimental data.

Spin polarisation and differential cross sections in elastic low-energy scattering of electrons from mercury

The spin polarisation parameters S, T, U and differential cross sections are calculated for low-energy electrons elastically scattered from mercury atoms. Additionally the moduli and the relative phases of the scattering amplitudes are calculated. The applied theoretical method is based on the scattering Dirac-Fock equation, where the exchange is calculated exactly. The scattering potential is a combination of two terms: the frozen-core Dirac-Fock potential and the polarisation model potential with one adjustable cut-off parameter. The results obtained are in very good agreement with the recent experimental and theoretical data of the spin polarisation parameters. Some discrepancies are noted in the case of the absolute differential cross sections.

Low- and intermediate-energy photoionisation of palladium

The results of calculations of the atomic photoionisation cross sections, angular distribution asymmetry parameters, branching ratios and spin polarisation parameters for the 4d, 4p, 4s, 3d and 3p subshells of palladium are reported. Calculations have been performed for a photon energy range of about 0.34-28.0 au. The positions of the Cooper minima in the 4d and 4p photoionisation cross sections are located in the continuum. Also, the study shows the 4s and 3p Cooper minima to be in the discrete part of the spectrum. The centrifugal barrier faced by the continuum f electrons causes a 'shape resonance' in the 4d and 3d cross sections and also affects the branching ratio for the sigma (nd5/2): sigma (nd3/2) cross sections. The branching ratio in the 4d cross section is influenced by the fact that the Cooper minima in the individual relativistic dipole, 4d5/2,3/2 to in f7/2,3/2 channels occur at different photon energies. Threshold effects and dynamical factors such as the occurrence of Cooper minima have a marked effect on the energy dependence of the spin polarisation parameters.

Spin-resolved photoionisation of lead above the Pb+ (6s26p) 2P3/2 - threshold

The spin-polarisation parameters for photoelectrons from lead atoms (6s26p2)J = 0 were measured in the wavelength range between the second threshold [Pb+ (6s26p) 2P3/2] and 100 nm in an angle-resolving experiment using circularly polarised vuv-radiation from the storage ring BESSY. Beyond this threshold (λ = 135.3 nm), the photoionisation cross section is strongly perturbed by autoionisation resonances. Especially, a strong enhancement of the generally weak Pb+ (6s26p) 2P3/2 photoionisation cross section occurs. Theoretical calculations by Radojevic [15] attribute these resonances to the 6s6p3-configuration of lead. By use of the measured spin-polarisation parameters A, ξ and α which show pronounced variations in the region investigated for both final ionic states 2P1/2 and 2P3/2 a detailed discussion of the resonances is performed.

Photoionization cross-section, angular-distribution, and spin-polarization calculations for the 3pand 3dsubshells of krypton

Calculations of photoionization cross sections, angular-distribution asymmetry parameters, and spin-polarization parameters for photoelectrons ejected from the 3p and 3d subshells of krypton have been performed in the relativistic random-phase approximation. The six relativistic dipole channels originating in the spin-orbit-split 3d levels and the five channels originating in the 3p levels were coupled to incorporate the more important intrashell correlations. In the sensitive region above the 3p threshold, both intrashell and intershell coupling were included in order to minimize truncation errors. The 3p cross section is seen to go through a dip at \ensuremath{\simeq}17 eV above the threshold. A plausible physical basis for this feature is discussed. The 3d cross section shows a delayed onset due to the centrifugal barrier faced by the continuum f waves. The spin-polarization parameters for the photoelectrons in the threshold regions are moderately influenced by rapidly varying strengths in the various dipole channels.

Energy dependence of the electron spin polarisation parameters for Hg 5d photoionisation with circularly polarised light

Circularly polarised VUV radiation from the storage ring BESSY was used to measure all three spin polarisation parameters of photoelectrons from the Hg 5d shell in the photon energy range from threshold to approximately 35 eV. The experimental results are compared with theoretical calculations in the relativistic and non-relativistic random-phase-approximation scheme (RRPA and RPAE respectively) and Dirac-Slater (DS) calculations. A discussion of the influence of relativistic and potential barrier effects on the experimental data is given.

Electron spin resonance study of azoalkane and imine radical cations

Radical cations of azoalkanes have been observed for the first time in a low-temperature matrix by e.s.r. spectroscopy. The e.s.r. data show that they are π-cations despite photoelectron studies which indicate the HOMO for an azoalkane to be the σ(n-) orbital. Interestingly, these species appear to be stable, at least up to ca. 160 K, and show no tendency to fragment to form alkyl radicals. This contrasts with the solution-phase behaviour of these species, which are intermediates in the oxidation of azoalkanes, and give rise to carbocations and alkyl radicals. Imines form similar π-radical cations which show a greater tendency to decompose. The structures and stabilities of these cations are discussed. Attempts to observe the corresponding azoalkane anions in solid matrices resulted only in the formation of alkyl radicals, and so we conclude that the anions decompose by fragmentation, although they have been studied in solution under steady-state conditions. Previously derived coupling parameters predict isotropic 14N hyperfine couplings for these species which are larger than those observed. Therefore, new values are calculated, and these fit well with the observed couplings. In this way, spin polarisation parameters are obtained for individual contributions to the couplings, as opposed to previous approaches which treat them collectively.

Theoretical spin-polarization parameters of molecular photoelectrons: Application to hydrogen halides.

The nonrelativistic formulation of Cherepkov [J. Phys. B 14, 2165 (1981)] of the spin-resolved photoionization cross sections is extended from the Hund's coupling case (a) to case (c) for the description of the ion molecular state. The spin-polarization parameters are analyzed in terms of a generalization of the partitioning scheme developed by Thiel [Chem. Phys. 77, 103 (1983)] for the study of the \ensuremath{\beta} asymmetry parameter. This scheme allows a detailed analysis of different l contributions to spin-polarization parameters and, in the case of a single predominant term, a straightforward evaluation of these parameters. In the framework of the frozen-core static-exchange approximation, this formulation is used for the calculation and the interpretation of the spin-polarization parameters in the case of the \ensuremath{\pi}np outer-shell and d inner-shell photoionizations of the HBr and HI molecules in the energy region of Cooper minima and shape resonances.

Spin polarisation of electrons elastically scattered from mercury

Spin polarisation parameters have been calculated for the elastic scattering of electrons from mercury atoms at incident energies up to 180 eV. These results were obtained by solving the Dirac equations, which included relativistic Dirac-Fock static and non-local exchange potentials plus a non-relativistic polarisation potential. A comparison with recent experiments of the results for the spin polarisation parameters S, T and U as well as for the difference in phase between the direct and exchange scattering amplitudes yields very good agreement at energies above 15 eV. The authors also present results for elastic differential, total and momentum transfer cross sections.

Spin-Polarization Measurements in the Autoionization Region of Mercury

The autoionization region of mercury was investigated with spin- and angle-resolved photoelectron spectroscopy between the Hg+ (5d9 6s2)2D5/2 and Hg+ (5d9 6s2)2D3/2 thresholds. Spin-polarization parameters A and ξ and intensity were measured separately for the photoelectrons corresponding to the two final ionic states accessible (2S1/2, 2D5/2) as function of the radiation wavelength. The data are dominated by structure due to autoionization resonances and differ quantitatively for the two peaks in the photoelectron spectra. The results are compared with earlier measurements below the 2D5/2-threshold.

Experimental characterization of the Xe 5p photoionization by angle- and spin-resolved photoelectron spectroscopy

Spin- and angle-resolved photoelectron spectroscopy with elliptically polarized radiation has been used to fully characterize the dynamics of photoelectron emission from free Xe atoms in the 5p-autoionization and continuum region. An advantageous reaction geometry and its experimental realization at the storage ring BESSY are discussed. The three independent experimental parameters which characterize the angular dependence of the photoelectron spin-polarization vector are reported for the wavelength range from 100nm to 40 nm. The results are compared with theoretical predictions based on RRPA-, RPAE- and semiempirical MQDT-calculations. The combination of existing data for the differential photoionization cross section with the spinpolarization parameters is used to completely decouple the photoionization channels: The transition matrix elements and their relative phases are determined separately for every single dissociation channel. The results are discussed in the context of the MQDT. Correlation effects and the influence of spin-orbit interaction on the continuum states most clearly show up when the Dill-Fano angular-momentum-transfer formalism is applied.

Low-energy photoionization of alkali-metal atoms: Relativistic random-phase-approximation calculations.

A complete theoretical survey of low-energy photoionization cross sections, angular asymmetry, and spin-polarization parameters for the ground states of the alkali-metal atoms Li, Na, K, Rb, and Cs, including virtual core excitations in a gauge-independent relativistic random-phase approximation (RRPA) is presented and compared with length- and velocity-form Dirac-Fock results and with available experimental data. The ab initio RRPA formulation substantially improves the agreement of cross sections with experiment at energies above the Cooper minimum.

Characteristic features of spin polarisation for outer subshells of mercury

The variation of the photoelectron spin polarisation parameters ( eta and delta ) relative to the 5d, 5p and 4f subshells of mercury has been determined in the relativistic Dirac-Slater approximation. The influences of both Coulomb and non-Coulomb phaseshifts are emphasised. The authors' results are compared with other theoretical results and experimental measurements when available. They are discussed in terms of the relative importance of relativistic effects in both the initial discrete and final continuum states.

Theoretical study of the spin-orbit autoionization in molecules application to the HI photoionization spectrum

A theoretical study of the spin-orbit autoionization in molecules with 2Π state ion cores is presented. The multichannel quantum defect theory is used with an ab initio calculation of the relevant electronic quantities. In the application to the HI photoionization spectrum the energy positions of the observed resonances between the 2Π1/2 and 2Π3/2 ionization thresholds are well reproduced. The importance of the l mixing especially for the π3σ channels is stressed. An attempt to include the S-uncoupling part of the rotational operator in the calculations gives rise to additional autoionization peaks, associated with a new type of rotational autoionization specific to 2Π-state cores. Theoretical predictions are also made for the angular distribution and spin polarization parameters of the photoelectron in the 1155–1168 Å energy range.

Resonances of the photoelectron spin-polarization parameters in the 5p autoionization range of xenon.

The spin-polarization parameters for photoelectrons from xenon atoms have been measured in the wavelength range between 96 and 100 nm in an angle-resolving experiment using circularly polarized synchrotron radiation. Theoretical calculations (relativistic random-phase approximation and multichannel quantum defect theory) generally reproduce the wavelength dependence of the parameters, but there are some systematic deviations from the experimental data.

Application of the relativistic local-density approximation to photoionization of the outer shells of neon, argon, krypton, and xenon

Parameters describing the low-energy photoionization of the outer shells of the rare gases Ne, Ar, Kr, and Xe have been calculated using a relativistic generalization of the time-dependent local-density approximation. The resulting photoionization cross sections, angular-distribution asymmetry parameters, and spin polarization parameters are presented here. The results are found to be in good agreement with those from the relativistic random-phase approximation (RRPA), even though the present theory is simpler, formally and computationally, than the latter. These results, and those of the RRPA, are generally in good agreement with experiment, illustrating the utility of the present approach to photoionization, especially for heavy atoms in which both relativistic and correlation effects are important.

ESR-Spectroscopic Investigations on the Radical Cations of p-Phenylene Diamines and Related Compounds. The Determination of the Various Spin Polarisation Parameters

Article ESR-Spectroscopic Investigations on the Radical Cations of p-Phenylene Diamines and Related Compounds. The Determination of the Various Spin Polarisation Parameters was published on February 1, 1984 in the journal Zeitschrift für Physikalische Chemie (volume 141, issue 2).

Theoretical study of photoabsorption for the palladium 4d subshell

Photoabsorption by electrons in the 4d10 subshell of palladium atoms is studied theoretically below, above, and between the two 4d thresholds using the relativistic random-phase approximation. In the energy regions above and between the 4d threshold cross sections, angular distributions, and spin polarisation parameters are determined. Between the thresholds resonances in the photoionisation parameters caused by autoionisation are analysed using the multichannel quantum defect theory (MQDT). Below the lower 4d threshold the dipole allowed excitation spectrum is studied using MQDT, and oscillator strengths of the high Rydberg states converging to the 4d thresholds are determined.