Angular Distribution Parameters Research Articles

Angle-resolved photoelectron measurements on the 2p orbitals of Si in SiF 4 and Si(CH 3) 4 in the gas phase

Angle-resolved photoelectron measurements have been carried out on the 2p orbital of Si in the gas-phase molecules SiF 4 and Si(CH 3) 4 as a function of energy from 3 to 45 eV above the ionization threshold. From these data the angular distribution parameter, β, has been obtained. Below a photoelectron energy of 15 eV the angular distribution parameter for these two molecules differ by as much as 0.4 units. The differences in the behavior of β near threshold for the two molecules is attributed to the different molecular environment of the silicon atom. To test this idea, calculations have been made on β for neutral and charged atomic silicon.

Angle-resolved photoelectron spectroscopy of CCl4: The Cooper minimum in molecules

Angle-resolved photoelectron spectra have been taken for the first five orbitals in CCl4 (2t1, 7t2, 2e, 6t2, and 6a1) using a variable photon source extracted from synchrotron radiation. From these data, the partial cross sections and angular distribution parameters β have been determined for photon energies from 16 to 80 eV. In the case of the lone pair orbitals (2t1, 7t2, and 2e) minima in both the cross sections and β values were noted experimentally in the photon energy range of 40 to 50 eV. The behavior is similar in appearance to that observed with the 3p subshell of argon and is believed to be the molecular counterpart of the Cooper minimum in atoms. Calculations of the cross sections and β values have been made for each of the different orbitals of CCl4 measured experimentally using the multiple scattering Xα theory. Agreement between theory and experiment for the lone-pair orbitals is qualitatively good and in the case of photoionization in the 2t1 orbital it has been possible to identify which continuum channels correspond to the atomic 3s and 3d counterparts. It was also observed that the nonlone-pair orbitals (6t2 and 6a1) show both experimentally and theoretically shallow minima in the vicinity of photon energies where the Cooper minimum is found. Finally, experimentally determined β values for the first three valence orbitals in CH3Br were obtained from 20 to 50 eV. The behavior of the lone-pair orbital of CH3 Br could be correlated with the Cooper minimum observed for the 4p orbital of Kr. The general nature of the Cooper minimum in molecules is discussed.

Importance of relativistic interactions in photoemission of high angular momentum electrons in mercury

The authors have studied the interplay between potential barrier effects, exchange terms and relativistic interactions in photoemission processes involving high angular momentum subshells (nd5/2, nd3/2 with n=4 and 5, 4f7/2 and 4f5/2) of mercury. Ab initio calculations of various photoemission cross sections, angular distribution parameters and phaseshifts of the corresponding continuum wavefunctions are performed in jj coupling, using the Dirac-Slater approximation. The physical origin and the importance of spin-orbit effects are established in the framework of the angular momentum transfer theory which shows that, in these cases, the spin-orbit effects introduce extra values of the transferred angular momentum and manifest themselves as anisotropic interactions as the photoelectron escapes from the core. The authors show that they are greatest in the channels nl4l+1l-1, because of the existence of an intense repulsive potential barrier in the channels nl4l+1l+1. In the latter, the excited orbitals may be not penetrating enough to mix both singlets and triplets before the photoelectron energy has gained enough energy so that the influence of relativistic interactions may be delayed.

Angle resolved photoelectron spectroscopy of CS2 and COS measured as a function of photon energy from 21 to 70 eV

Data have been taken on both the partial cross sections and angular distribution parameters for the first five bands in CS2 with a photon energy from 21 to 70 eV and for the first four bands of COS from 21 to 40 eV. The results are compared with calculations based on the multiple scattering method. In the case of photoionization of the 2πg orbital of CS2 and the 3π orbital of COS, the experimental results and calculations have been successfully explained in terms of the Cooper minimum. The behavior of the fifth band of CS2 is accounted for by assigning it to a satellite peak arising from photoionization of the 2πu orbital by way of configuration interaction. Comparison between the experimental results and calculations showed some problem areas, particularly with regard to the prediction of shape resonances, and suggestions are made for future improvement of the calculations.

Partial cross sections for Rb− photodetachment in the region of the Rb(5p 2 P 1/2 3/2) thresholds and their analysis by multichannel quantum defect theory

A crossed ion-laser beam apparatus has been used to measure accurate relative total and partial cross sections for photodetachment from Rb− ions with high photon energy resolution (0.1–0.6 cm−1) in the region of the Rb(5p2P1/2,3/2) thresholds (photon energy range 16,350–16,820 cm−1). Satisfactory fits to these data by multichannel quantum defect theory (MQDT) have been obtained, resulting in a reliable set of seven MQDT parameters. The electron angular distribution parameter for the Rb(5s) channel was found to beβ(5s)=2, independent of photon energy. MQDT predicts a sharp, window-type variation of⨿(5s) around the minimum of the 5s-cross section below the Rb(5p2P1/2) threshold (where an accurate experimental measurement ofβ(5s) was not possible) and a similar behaviour ofβ(6s) in the case of Cs−photodetachment below the Cs(6p2P1/2) threshold.

Molecular effects on the angular distribution parameter from the photoelectron spectra of the 3d orbitals of Kr, HBr, Br 2 and CH 3Br using synchrotron radiation

The angular distribution parameter, β, has been measured as a function of photon energy from 3 to 40 cV above the ionization threshold for the 3d orbital in Kr, HBr, Br 2 and CH 3Br. A chemical effect was observed over the range of photoelectron energies from ≈ 5 to 15 cV.

The angular distribution parameters of argon, krypton and xenon for use in calibration of electron spectometers

Measurements are presented of the angular distribution parameter for the photo ejected valence electrons of argon, krypton and xenon, from threshold to hv≈25 eV. The experimental arrangement at the NBS (SURF II) storage ring is described and the method of data analysis discussed. The results are compared with other experimental data and theoretical predictions.

On the reactions [formula omitted

The total cross section for π +d → pp and the angular distribution and asymmetry parameters for the inverse reaction p p → π + d have been calculated with different models for the pion absorption (and production) operator and several sets of nuclear wave functions. The absorption operator includes both single-nucleon and two-nucleon operators. Fair agreement can be achieved with all empirical parameters at low energies, but significant discrepancies occur at high energies. The results are very sensitive to the model for the nucleon-nucleon interaction used to generate the wave functions.

Manifestation of Dynamically Unfavored Transitions in the Angular Distribution of Photogragments

A class of parity-favored electric dipole transitions are classed as "dynamically unfavored" with a photoparticle angular distribution parameter $\ensuremath{\beta}\ensuremath{\sim}\ensuremath{-}1$. This deviation from the elementary-model value $\ensuremath{\beta}=2$ results when the squared pseudoscalar operator ${({\stackrel{\ensuremath{\rightarrow}}{j}}_{t}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{^}{r})}^{2}$ is nonzero. Herrick's SO(4) classification singles out doubly excited $^{1}P^{\ensuremath{\circ}}$. continuum eigenchannels of ${\mathrm{H}}^{\ensuremath{-}}$ and He with ${({\stackrel{\ensuremath{\rightarrow}}{j}}_{t}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{^}{r})}^{2}\ensuremath{\sim}0 or \ensuremath{\sim}1$. Most of the photoelectrons should have ${({\stackrel{\ensuremath{\rightarrow}}{j}}_{t}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{^}{r})}^{2}\ensuremath{\sim}1$, i.e., $\ensuremath{\beta}\ensuremath{\sim}\ensuremath{-}1$.

Photoionisation of Hg in the soft X-ray energy range

The photoionisation cross sections relative to the 5d, 5p and 4f subshells of Hg have been calculated with two models: the Hartree-Slater and Hartree-Fock models. The influence of intrachannel interactions on the cross sections and the photoelectron angular distribution parameter for the 4f subshell is discussed.

The photoionisation of krypton atoms: a comparison of pseudopotential calculations with experimental data for the 4p asymmetry parameter and cross section as a function of the energy of the ejected photoelectrons

New measurements of the angular distribution parameter beta 4p(E) for photoelectrons emitted from the 4p shell of krypton by synchrotron radiation are reported. Analyses of these data produce an empirical pseudopotential together with predictions of beta 4p(E) and the total cross sections sigma 4p(E) for photoelectron energies from threshold to greater than 100 eV. The predicted cross sections are compared with recent experimental data obtained at the Synchrotron Radiation Facility on the Daresbury Laboratory 5 GeV electron synchrotron NINA. Both beta 4p(E) and sigma 4p(E) are well described by both RPAE and pseudopotential theories, suggesting that the latter aptly mimics the exchange and correlation effects throughout the range of observation.

μeproduction ine+e−annihilation

We calculate the observed cross section, the horizontal-vertical asymmetry, the angular-distribution parameter $\ensuremath{\alpha}$ ($\frac{d\ensuremath{\sigma}}{dcos\ensuremath{\theta}}\ensuremath{\propto}1+\ensuremath{\alpha}{cos}^{2}\ensuremath{\theta}$), and the distribution of the decay-lepton momentum over a wide range of energy under the hypothesis that heavy leptons are produced in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation. The heavy-lepton decay coupling is assumed to be vector and axial-vector in character. The use of the narrow-width approximation allows the distributions of interest to be expressed analytically as functions of $s$.

Angular distribution and photoionization measurements on the 2p and 2s electrons in neon

The angular distribution parameter beta has been measured for the neon 2p electrons in the energy range 0-80 eV above threshold using a synchrotron light source. The absolute photoionization cross section of neon 2s electrons has also been determined in the 0-130 eV region above threshold. Both sets of data are compared with recent theoretical calculations and with experimental data using conventional light sources.

The angular distribution of the 3p electrons and the partial cross section of the 3s electrons of argon from threshold to 70 eV

The angular distribution parameter β has been measured for the argon 3p electrons in the energy range 0–70 eV above threshold using a synchrotron light source. The absolute photoionization cross section of argon 3s electrons has also been determined in the 0–60 eV region above threshold. Both sets of data are compared with recent theoretical calculations which include electron correlation effects.

"Photoelectron" Spectroscopy by Electron Impact: Coincidence Studies of Scattered and Ejected Electrons

The quantitative relation between fast electron impact and photoabsorption is discussed with reference to simulation of the technique of photoelectron spectroscopy. An apparatus is described that employs coincidence detection of scattered and ejected electrons resulting from ionization over a range of energy losses up to 70 eV. Absolute oscillator strengths are reported for total absorption and ionization to electronic states of water and ammonia. Relative state populations are in good agreement with photoelectron spectroscopy at 584 A. Angular distribution parameters are measured for neon, argon, and krypton. (auth)

Angular distribution and photoionization cross section measurements on the 3p and 3s subshells of argon

The photoelectron angular distribution parameter has been measured in the energy region 0-34 eV above threshold for argon 3p electrons, using a synchrotron light source. The cross section of the argon 3s subshell has also been measured in the 0-20 eV region above its threshold. Both sets of data are compared with recent theoretical calculations.

Measurement of the energy dependences of the photoelectron angular distribution parameters for Ar 3p and Kr 4p electrons using an electron-electron coincidence experiment

The energy dependence of the photoelectron angular distribution parameter (β) has been measured for Ar 3p and Kr 4p electrons in the energy ranges 4–54 eV and 4–40 eV above threshold respectively, using 3.5 keV electron impact with coincidence detection of the scattered and ejected electrons. This energy range is considerably greater than that covered in previous experiments. The data over the whole energy range are compared with the Hartree-Fock calculations of Kennedy and Manson and with those of Amusia et al., using the random phase approximation with exchange method. For Ar the calculations of Amusia et al., which take into account many-electron correlations, are shown to agree more closely with the present data. The data are also shown to be in very good agreement with earlier experimental data obtained over a more limited energy range using electron synchrotron radiation.

Theory of atomic photoionization measurements

The theory of photoionization measurements for a general atomic system is developed in terms of a density matrix which determines the ejected electron and residual ion polarizations as a function of the target atom and incident photon polarization states. Expressions are derived which relate the photoelectron angular distribution and spin polarization parameters to the reduced matrix elements for the photoelectric transition. These expressions incorporate the fine structure of the atomic levels and the complete interaction between the residual ion and the ejected electron. The polarization of the residual ions which are formed in excited states is treated in terms of the subsequently emitted decay radiation.

Energy dependence of the photoelectron angular distribution parameter for Ne 2p electrons, measured in an electron—electron coincidence experiment

Abstract The photoelectron angular distribution parameter β for the 2p electrons of Ne has been measured in the 4–35 eV region above threshold, using 3.5 keV electron impact and coincidence detection of scattered and ejected electrons. The data are shown to be in good agreement with Hartree—Fock calculations by Kennedy and Manson.

The angular distribution of neon 2p shell photoelectrons in the 0–20 eV region above threshold

The photoelectron angular distribution parameter β has been measured in the 0–20 eV region above threshold for the neon 2p electrons using a synchrotron light source. Measurements are compared with the Hartree-Fock calculations of Manson and Kennedy.