Angular Distribution Parameters Research Articles

Dynamics of the C1s→π*excitation and decay inCO2probed by vibrationally and angularly resolved Auger spectroscopy

Participator resonant Auger decay spectra populating the $X, A, B$, and $C$ states of ${\mathrm{CO}}_{2}{}^{+}$ are recorded with angular and vibrational resolution for selected photon energies in the vicinity of the C $1s\ensuremath{\rightarrow}{\ensuremath{\pi}}^{*}$ resonance of ${\mathrm{CO}}_{2}$ using a narrow photon bandwidth and a high-resolution electron spectrometer. The measured electron spectra and the corresponding angular distribution parameters exhibit significant changes as functions of the photon energy across the resonance and with respect to the vibrational sublevels of a final ionic state. The measured spectra are interpreted by ab initio electronic structure and nuclear dynamics calculations which attribute observed variations to the effects of lifetime vibrational interference and of electronic state interference between the direct ionization amplitude and the resonant amplitudes for the excitation and decay of two overlapping resonant states of different symmetry. The present results provide deeper insight into the femtosecond relaxation dynamics of the core-excited ${\mathrm{CO}}_{2}$, which is not achievable with lower resolution, angle-averaged measurements.

Dichroism in the photoionisation of atoms at XUV free-electron lasers

Two-color photoionization of atomic He has been investigated by angle-integrated and angle-resolved electron spectroscopy. The combined action of intense radiation pulses from the XUV free-electron laser (FEL), FERMI or FLASH, and a synchronized optical laser on the target atom gives rise to a rich sideband structure in the photoemission spectrum. Measurements of the angular distribution parameters and the determination of the circular and linear dichroism for the two-color photoionization enable a detailed analysis of the symmetry of the outgoing electron waves and of the dynamics underlying the multi-photon processes. The experimental results are in excellent agreement with theoretical results obtained using perturbation theory (low intensity regime) and the strong field approximation. For the particular case of two-photon ionization the measurements represent an ideal tool for characterizing certain FEL parameters, here for example the degree and the sign of circular polarization. Finally, new features of the dichroism are theoretically predicted originating from the non-dipole contribution into the photoionization amplitudes.

Nondipole Effects in Chiral Molecules Measured with Linearly Polarized Light

SynopsisWe present the first-ever measurement of nondipole chiral angular distribution parameters for C 1s photoemission from each enantiomer of camphor in the photon energy range 296-343eV using linearly polarized light. The angular distribution parameters are determined to be enantiomer-specific, suggesting a new form of linear dichroism.

Dipole and nondipole photoionization of molecular hydrogen

We describe a theoretical approach to molecular photoionization that includes first-order corrections to the dipole approximation. The theoretical formalism is presented and applied to photoionization of ${\mathrm{H}}_{2}$ over the 20- to 180-eV photon energy range. The angle-integrated cross section $\ensuremath{\sigma}$, the electric dipole anisotropy parameter ${\ensuremath{\beta}}_{e}$, the molecular alignment anisotropy parameter ${\ensuremath{\beta}}_{m}$, and the first-order nondipole asymmetry parameters $\ensuremath{\gamma}$ and $\ensuremath{\delta}$ were calculated within the single-channel, static-exchange approximation. The calculated parameters are compared with previous measurements of $\ensuremath{\sigma}$ and ${\ensuremath{\beta}}_{m}$ and the present measurements of ${\ensuremath{\beta}}_{e}$ and $\ensuremath{\gamma}+3\ensuremath{\delta}$. The dipole and nondipole angular distribution parameters were determined simultaneously using an efficient, multiangle measurement technique. Good overall agreement is observed between the magnitudes and spectral variations of the calculated and measured parameters. The nondipole asymmetries of He $1s$ and Ne $2p$ photoelectrons were also measured in the course of this work.

Photoelectric fields in lithium niobate crystals

The angular-distribution parameters of the photoinduced scattering of light at a wavelength of 476.5 nm are used to determine the photovoltaic and diffusion field in nominally pure single crystals of stoichiometric composition (R=Li/Nb=1), grown from the melt with 58.6 mol% LiO2 (LiNbO3 stoich.), in nominally pure single crystals of congruent composition (LiNbO3) in congruent single crystals doped with Cu2+, Zn2+, Gd3+, Y3+, Er3+, B3+, (Cu2++Gd3+), and (Ta5++Mg2+). The photoinduced variations of the refractive index of the crystals are determined.

Hartree-Fock calculation of the differential photoionization cross sections of small Li clusters.

Cross sections and angular distribution parameters for the single-photon ionization of all electron orbitals of Li2-8 are systematically computed in a broad interval of the photoelectron kinetic energies for the energetically most stable geometry of each cluster. Calculations of the partial photoelectron continuum waves in clusters are carried out by the single center method within the Hartree-Fock approximation. We study photoionization cross sections per one electron and analyze in some details general trends in the photoionization of inner and outer shells with respect to the size and geometry of a cluster. The present differential cross sections computed for Li2 are in a good agreement with the available theoretical data, whereas those computed for Li3-8 clusters can be considered as theoretical predictions.

Fluorescence cascades after excitation of XeII 5p46p satellite states by synchrotron radiation

Dispersed fluorescence excitation functions and the relative total ion yield as a function of the exciting-photon energy in the range between 26.150 eV and 26.400 eV have been measured for Xe after excitation with monochromatized synchrotron radiation with the very narrow bandwidth of 2.5 meV. Fluorescence excitation functions have been simultaneously measured in the VUV and in the visible spectral range to track and identify radiative decay cascades after photoionization into excited XeII states of 5p46p electron configuration. Additionally the angular fluorescence distribution parameter βfl-parameter was experimentally determined for some of the observed fluorescence lines.

Angle-resolved study of resonant Auger decay and fluorescence emission processes after core excitations of the terminal and central nitrogen atoms inN2O

Angular distributions of the ${\mathrm{N}}_{2}$${\mathrm{O}}^{+}(X)$ and ${\mathrm{N}}_{2}$${\mathrm{O}}^{+}(A)$ photoelectrons were measured as functions of the exciting-photon energy with small bandwidth in the vicinity of the resonant ${\mathrm{N}}_{t}(1s\ensuremath{\rightarrow}{\ensuremath{\pi}}^{*})$, ${\mathrm{N}}_{t}(1s\ensuremath{\rightarrow}{\ensuremath{\sigma}}^{*})$, and ${\mathrm{N}}_{c}(1s\ensuremath{\rightarrow}{\ensuremath{\pi}}^{*})$ core excitations of ${\mathrm{N}}_{2}\mathrm{O}$. For selected exciting-photon energies in this range, angular distribution parameters of the ${\mathrm{N}}_{2}$${\mathrm{O}}^{+}(A\ensuremath{\rightarrow}X)$ fluorescence were also determined. These data are interpreted by ab initio calculations. Long-range exciting-photon energy dependencies of the photoelectron angular distribution parameters ${\ensuremath{\beta}}_{X}^{e}(\ensuremath{\omega})$ and ${\ensuremath{\beta}}_{A}^{e}(\ensuremath{\omega})$, recorded vibrationally unresolved, are attributed to an electronic state interference between the direct and the different resonant amplitudes for the population of the final ionic states. In addition to that, strong influence of lifetime vibrational interference is identified in the observed dispersion of the vibrationally resolved fluorescence angular distribution parameter $\ensuremath{\beta}{2}_{A}^{X}(\ensuremath{\omega})$ across the electronic resonances.

Spin correlations in polarizations ofP-wave charmoniaχcJand impact onJ/ψpolarization

Based on a general form of the effective vertex functions for the decays of P-wave charmonia $\chicj$, angular distribution formulas for the subsequent decays $\chicj\rightarrow \jpsi \gamma$ and $\jpsi \to \mu^+\mu^-$ are derived. The formulas are the same as those obtained in a different approach in the literature. Our formulas are expressed in a more general form, including parity violation effects and the full angular dependence of $\jpsi$ and muon in the cascade decay $\chicj\to\jpsi\gamma\to\mu^+\mu^-\gamma$. The $\chicj$ polarization observables are expressed in terms of rational functions of the spin density matrix elements of $\chicj$ production. Generalized rotation-invariant relations for arbitrary integer-spin particles are also derived and their expressions in terms of observable angular distribution parameters are given in the $\chi_{c1}$ and $\chi_{c2}$. To complement our previous direct-$\jpsi$ polarization result, we also discuss the impact on the observable prompt-$\jpsi$ polarization. As an illustrative application of our angular distribution formulas, we present the angular distributions in terms of the tree-level spin density matrix elements of $\chi_{c1}$ and $\chi_{c2}$ production in several different frames at the Large Hadron Collider. Moreover, a reweighting method is also proposed to determine the entire set of the production spin density matrix elements of the $\chi_{c2}$, some of which disappear or are suppressed for vanishing higher-order multipole effects making the complete extraction difficult experimentally.

Strong impact of the giant resonance on the radiationless decay of the 4d-vacancy in Xe: II. N4, 5OO Auger effect

The radiationless decay of the Xe N4, 5 levels is investigated theoretically. The strong influence of the giant resonance in the 5s5p5(1P)εf channel on the partial and total Auger widths via the interchannel mixing is revealed. The computed widths of the N4 and N5 levels, equal to 105.9 and 109.6 meV, respectively, are in excellent agreement with the measured values 104(3) and 111(3) meV (Jurvansuu et al 2001 Phys. Rev. A 64 012502). The shape of the computed N4, 5OO Auger spectrum is in good agreement with the measured one. Interchannel interaction reduces the probability of the 5p5p − 4dεg Auger decay by more than an order of magnitude. This conclusion is supported by the good agreement between computed and measured Auger electron angular distribution parameters.

The photoelectron angular distribution of water clusters

The angular distribution of photoelectrons emitted from water clusters has been measured by linearly polarized synchrotron radiation of 40 and 60 eV photon energy. Results are given for the three outermost valence orbitals. The emission patterns are found more isotropic than for isolated molecules. While a simple scattering model is able to explain most of the deviation from molecular behavior, some of our data also suggest an intrinsic change of the angular distribution parameter. The angular distribution function was mapped by rotating the axis of linear polarization of the synchrotron radiation.

Photoelectron angular distribution studies of the outer valence states of N2

We present angle resolved photoelectron data for the ionization of all N2 outer valence shells namely the 3σg, 1πu and 2σu states in the photon energy region from 19 to 50 eV with a photon energy step width down to 20 meV. Signatures due to the autoionization of doubly excited Rydberg states and the corresponding vibrational progression are observed in the dipole electron angular distribution parameter β. They are compared with recent calculations. We also find evidence for theoretically predicted sharp resonance effects due to channel coupling in the electron angular distribution of 1 π−1u. Shape resonance and channel coupling effects are discussed for all outer valence orbitals with respect to recent theoretical findings.

Angular distribution of photoelectrons in small molecules: A molecular quantum defect calculation

The molecular quantum defect orbital (MQDO) method, previously used in the determination of molecular photoionization cross sections, is applied here to calculate the angular distribution of photoelectrons arising from the molecular photoionization. Calculations are performed for the ionization from outer valence orbitals of HF, H(2)O, NH(3), N(2)O, and H(2)CO molecules. The results are compared with previous measurements and with theoretical curves found in the literature. Profiles of the angular distribution parameter as a function of photoelectron energy covering a range from the photoionization threshold to 120 eV are presented for the above molecules. The energy dependence of the angular distributions predicted by the MQDO calculations agrees fairly well with predictions from more sophisticated theories and with observed results.

Theoretical study of angular-resolved two-photon ionization of H2

Cross sections and angular distribution parameters of electrons ejected via two-photon ionization of the hydrogen molecule by linearly and circularly polarized light are computed in the exciting-photon energy range of 8--14 eV, which covers the first four optical resonant states of the molecule. Photoelectron partial waves in the continuous spectrum are obtained within the single center method in precise numerical potential of the molecular ion field. The correlation function technique is used to calculate the two-photon transition matrix element. The presently computed angular-resolved spectra are in good agreement with the theoretical results available for the photon energy of 8.854 eV and can be considered as reliable predictions in the respective energy range.

Ba 5s photoionization in the region of the second Cooper minimum

We investigate the 5s angular distribution parameter and partial photoionization cross section of atomic Ba in the region of the second Cooper minimum covering a photon energy region from 120 to 260 eV. We observe a strong drop in the Ba 5s β value from 2.0, reaching a minimum of 1.57 ± 0.07 at a photon energy of 150 eV. The β value then slowly rises back towards its nominal value of 2.0 at photon energies beyond the minimum. Our measured 5s partial cross section also shows a pronounced dip around 170 eV due to interchannel coupling with the Ba 4d photoelectrons. After combining our measurements with previous experimental values at lower photon energies, we obtain a consistent data set spanning the photon energy range prior to the onset of the partial cross section maximum and through the cross section minimum. We also calculate the 5s partial cross section under several different levels of approximation. We find that the generalized random-phase approximation with exchange calculation models the shape and position of the combined experimental cross section data set rather well after incorporating experimental ionization energies and a shift in the photon energy scale.

Photoionization Processes of the Single-Ionized Boron

The relativistic calculations of the cross-section σ, the angular-distribution parameter β, and spin-polarization parameters {ξ,η,ζ} of photoelectrons using the multiconfiguration relativistic random-phase approximation theory for the photoionization of the B+ ion are presented. Precise energies and widths of all five Rydberg series of doublyexcited states (2pns)1P1o, (2pns)3P1o, (2pnd)1P1o, (2pnd)3P1o, and (2pnd)3D1o are determined. Our predictions are in very close agreement with experiments and are consistent with other calculations.

Effects of dimerization on the photoelectron angular distribution parameters from chiral camphor enantiomers obtained with circularly polarized vacuum-ultraviolet radiation

As an intermediate state of matter between the free monomeric gas phase and the solid state, clusters may exhibit a specific electronic structure and photoionization dynamics that can be unraveled by different types of electron spectroscopies. From mass-selected ion yield scans measured for photoionization of ($R$)-camphor, the ionization potentials (IPs) of the monomer ($8.66\ifmmode\pm\else\textpm\fi{}0.01$ eV), and of the homochiral dimer ($\ensuremath{\leqslant}8.37\ifmmode\pm\else\textpm\fi{}0.01$ eV) and trimer ($\ensuremath{\leqslant}8.30\ifmmode\pm\else\textpm\fi{}0.01$ eV) were obtained. These spectra, combined with threshold photoelectron spectroscopy and velocity map ion imaging, allow us to show that the camphor monomer and dimer photoionization channels are decoupled, i.e., that the highest occupied molecular orbital (HOMO) of the dimer does not undergo a dissociative ionization process that would lead to a spurious contribution to the monomer ion channel. Therefore mass selection, as achieved in our imaging photoelectron-photoion coincidence experiments, leads to size selection of the nascent monomer or dimer species. Since both the monomer and dimer are chiral, their photoelectron angular distribution (PAD) not only involves the usual $\ensuremath{\beta}$ anisotropy parameter but also a chiral asymmetry parameter $b$${}_{1}$ that can generate a forward-backward asymmetry in the PAD. This has been investigated using circularly polarized light (CPL) to record the photoelectron circular dichroism (PECD) in the near-threshold vacuum-ultraviolet (VUV) photoionization region. Analysis of size-selected electron images recorded with left- and right-handed CPL shows that over the first $1.5$ eV above the HOMO orbital ionization potentials (IPs), the $\ensuremath{\beta}$ parameter is not affected by the dimerization process, while the chiral $b$${}_{1}$ parameter shows clear differences between the monomer and the dimer, confirming that PECD is a subtle long-range probe of the molecular potential.

Photoionization of iodine atoms: Angular distributions and relative partial photoionization cross-sections in the energy region 11.0–23.0 eV

Relative partial photoionization cross-sections and angular distribution parameters, beta, have been measured for the first, I(+)((3)P(2))<--I((2)P(3/2)), and fourth, I(+)((1)D(2))<--I((2)P(3/2)), (5p)(-1) photoelectron (PE) bands of atomic iodine, by performing angle-resolved constant-ionic-state (CIS) measurements on these PE bands in the photon energy range 11.0-23.0 eV. Three Rydberg series, two ns and one nd series, which converge to the I(+) (3)P(1) limit at 11.33 eV and four Rydberg series, two ns and two nd series, which converge to the I(+) (1)D(2) limit at 12.15 eV were observed in the first PE band CIS spectra. The fourth band CIS spectrum showed structure in the 12.9-14.1 eV photon energy range, which is also seen in the first band CIS spectra. This structure arises from excitation to ns and nd Rydberg states that are parts of series converging to the I(+) (1)S(0) limit we reported on earlier, as well as 5s-->5p excitations in the photon energy range 17.5-22.5 eV. These atomic iodine CIS spectra show reasonably good agreement with the equivalent spectra obtained for atomic bromine. The beta-plots for the first PE band recorded up to the I(+) (3)P(1) and I(+) (1)D(2) limits only show resonances corresponding to some of the 5p-->nd excitations observed in the first band CIS spectra scanned to the I(+) (1)D(2) limit (12.15 eV). These plots are interpreted in terms of an angular momentum transfer model with the positive values of beta obtained on resonances corresponding to parity allowed j(t)=1 and 3 channels and the off-resonance negative beta values corresponding to parity unfavored channels, where j(t) is the quantum number for angular momentum transfer between the molecule, and the ion and photoelectron. The beta-plots recorded for iodine are significantly different from those obtained for atomic bromine. Comparison of the experimental CIS spectra and beta-plots with available theoretical results highlights the need for higher level calculations which include factors such as configuration interaction in the initial and final states, relativistic effects including spin-orbit interaction, and autoionization via resonant Rydberg states.

Strong interference effects in the angularly resolved Auger decay and fluorescence emission spectra of the core-excited NO molecule

Angular distributions of Auger electrons and subsequent fluorescence photons are studied theoretically and experimentally in the vicinity of the core excitations of NO. In the calculations, lifetime vibrational interference and electronic state interference were taken into account ab initio. The interference between excitation and deexcitation amplitudes for transitions via symmetry-different intermediate resonances 1s−12π2(2Δ, 2Σ±), which is forbidden in the solid-angle-averaged or magic-angle-recorded decay spectra, plays a crucial role in the formation of the angularly resolved decay spectra. Experimentally, angular distribution parameters for the NO+(A1Π → X1Σ+) fluorescence induced by linearly polarized synchrotron radiation are determined in the vicinity of the N*O resonance in the Raman regime for core excitation. Theoretical results are in good agreement with the present experimental fluorescence spectra and with the available vibrationally and angularly resolved resonant Auger electron spectra.

Photoionization of iodine atoms: Rydberg series which converge to the I+(S1)←I(P23/2) threshold

Relative partial photoionization cross sections and angular distribution parameters beta have been measured for the first and fourth (5p)(-1) photoelectron (PE) bands of atomic iodine by performing angle-resolved constant-ionic-state (CIS) measurements on these PE bands between the (1)D(2) and (1)S(0) (5p)(-1) ionic thresholds in the photon energy region of 12.9-14.1 eV. Rydberg series arising from the 5p-->ns and 5p-->nd excitations are observed in both the first PE band, I(+)((3)P(2))<--I((2)P(3/2)), and the fourth PE band, I(+)((1)D(2))<--I((2)P(3/2)), CIS spectra. For each Rydberg state, the resonance energy, quantum defect, linewidth, line shape, and photoelectron angular distribution parameter beta have been determined. For the beta-plots for each PE band, only resonances corresponding to 5p-->nd excitations are observed; no resonances were seen at photon energies corresponding to the 5p-->ns resonances in the CIS spectra. The beta-plots are interpreted in terms of the parity unfavored channel with j(t)=4 being the major contributor at the 5p-->nd resonance positions, where j(t) is the quantum number for angular momentum transferred between the molecule, and the ion and photoelectron. Comparison of the results obtained with those published for bromine shows reasonably good agreement for the CIS spectra but poor agreement for the beta-plots. It appears that parity unfavored channels are playing a greater role in the valence (np)(-1) ionization of atomic iodine than in the corresponding ionization of atomic bromine.