Rydberg Resonances Research Articles

Theory and ab initio calculations of 2p photoabsorption spectra: The lowest Rydberg resonances in HCl

We present a theory for 2p core excitation spectra of linear molecules that explicitly includes the spin-orbit splitting of the 2p core orbitals as well as all nonrelativistic effects. This is applied to the absorption spectrum of HCl at the 2p→6σ*, 4s, 4p, 3d, and 5s resonance energies. All input data for the spectrum are obtained from ab initio calculations. These are (i) the nonrelativistic energies and transition probabilities of the contributing states, (ii) the spin-orbit coupling parameter, and (iii) the total Auger transition rates of the core excited states. The prior theoretical finding that the total Auger decay rate depends substantially on the core hole orientation is supported by a comparison of the theoretical and experimental absorption spectra. Furthermore, the preferred orientation of the core excited HCl molecule with respect to the molecular bond axis is discussed. General considerations about intensity ratios between corresponding states with 2p3/2 and 2p1/2 holes are given on the basis of the theoretical framework.

Rydberg transitions in X-ray absorption spectroscopy of alkanes: The importance of matrix effects

Precise ab initio electronic structure calculations on isolated alkanes (propane, butane) and on propane embedded in a matrix of several propane molecules were used in order to characterize the near-edge x-ray absorption fine structure (NEXAFS) resonances of condensed saturated hydrocarbons. The results demonstrate that upon condensation the dominating NEXAFS spectral features, i.e., the Rydberg resonances located between 287.4 and 288.1 eV, have a significant blue shift from the corresponding transition energies of an isolated alkane molecule. Furthermore, the theoretical results confirm the excitonic character of the final state. Additional calculations carried out for different conformations (trans/gauche) of isolated butane demonstrate that the transition energies of the corresponding NEXAFS resonances do not differ significantly. Previously observed changes in the electronic structure of disordered thin organic films of calciumarachidate are thus attributed to changes in the intermolecular spacing of the molecules rather than to changes in the electronic structure of the different, trans and gauche, conformations of the alkane chain.

Relativistic effects in the photoionization of atomic beryllium

Calculations of the cross section, angular distribution asymmetry parameter and photoelectron spin-polarization parameters for valence photoionization of neutral beryllium using the relativistic-random-phase approximation plus relativistic-multichannel quantum defect theory are performed in the region of Rydberg resonances just below the 1s ionization threshold. A new autoionizing series, 1s2s2np 3P, which occurs solely due to relativistic effects, is found. A quantitative study of the character of resonances has been carried out and the implications of these relativistic resonances for angular distributions and spin polarization are investigated in detail.

Field Enhanced Dielectronic Recombination of Si11+ and Cl14+ Ions

The enhancement of dielectronic recombination of multiply charged ions by external electric fields has been studied under controlled conditions. The heavy ion storage rings CRYRING at Stockholm University and the heavy ion storage ring TSR at the Max-Planck-Institut in Heidelberg were used to store beams of Si11+ (ion energy 280 MeV) and Cl14+ (ion energies 250 MeV and 110 MeV), respectively. Recombination in the electron cooler has been measured over energy ranges covering all resonances due to 2s → 2p core exitation. External electric fields up to 183 V/cm at CRYRING and up to 379 V/cm at the TSR have been applied. In the TSR experiment the influence of different magnetic guiding fields as well as the influence of different electron densities in the electron cooler on the recombination rate was investigated. A significant rate enhancement was found for 1s22pnl Rydberg resonances with n > 25 for Si11+ ions and n > 20 for Cl14+ ions.

Spin-polarization in HBr: Comparison between theory and experiment

Measurements of the electron spin polarization parameter A have been performed for HBr in the energy region between the two ionization thresholds, Π3/22 and Π1/22. Using the multichannel quantum defect theory and formulas derived for the spin parameters in intermediate coupling between Hund’s cases (a) and (e), calculations for both the cross section and the A parameter have been performed. It is shown that the values of A for each Rydberg resonance change with n, following the change from Hund’s case (a) to case (e). In the approximations used in this paper, no simple relation between the sign of A and the value of J+, the rotational angular momentum of the ion core, was found. Values for the calculated angular asymmetry parameter β and the spin polarization parameter ξ are also presented. Since our calculations reproduced only part of the observed resonances, and since the measurements of the A parameter have been performed in relatively narrow energy regions, one could not perform an extensive comparison between theory and experiment. However, some of the peculiarities of the behavior of the A parameter observed experimentally have been qualitatively reproduced by our calculations.

Angle-resolved electronic decay of the π*, σ* and Rydberg resonances below the OK-edge in O2

Angle-resolved electronic decay spectra of the O 2 molecule have been measured at photon energies corresponding to the excitation of core electrons into the π*, σ* and Rydberg levels. Asymmetry parameters have been determined for resonant Auger transitions and compared with previous data where available. The π* spectrum has also been studied with a narrow photon bandwidth in different regions of the vibrationally unresolved absorption feature.

Core to valence transitions in methane

We have identified and characterized 1a 1 core electron transitions to states involving the anti-bonding 2t 2 σ * virtual orbital in methane. The 1t 2 autoionization branching ratio indicates that the excitations lie at the same energies as the Rydberg resonances observed in total absorption. The corresponding 1t 2 angular distribution parameter reflects coupling of electron and nuclear coordinates. Changes in the 1t 2 kinetic energy distribution are explained by nuclear motion during the core-hole lifetime due to repulsive potential energy surfaces. The data indicate that 1a 1 core-excited states involving the valence 2t 2 σ * molecular orbital are split by the Jahn–Teller effect into bands which are much broader than any Rydberg features. These results illustrate the value of valence emission as a probe of resonant molecular core-excited states.

Angle-resolved two-dimensional mapping of electron emission following Cl2pexcitations in the HCl molecule

Angle-resolved Auger and valence photoelectron spectra of HCl were measured over a 14-eV-wide photon-energy range across the Cl $2p$ ionization thresholds. Auger decay spectra of dissociative core-excited states were observed to change with photon energy, reflecting a change in the rate of dissociation. Auger electron spectra at the first Rydberg states were analyzed and the evolution of the resonant Auger to the normal Auger decay distorted by postcollision interaction was examined. Valence photoionization channels were shown to resonate strongly at the photon energies of the core-to-Rydberg excitations. Angular distributions of the photo- and Auger electron lines were derived; strong fluctuations of the \ensuremath{\beta} values of the 2\ensuremath{\pi} photoline were observed at some Rydberg resonances. Anisotropy of the Auger decay at the ${\ensuremath{\sigma}}^{*}$ and Rydberg excitations was found to be different, with the latter showing uniformly negative \ensuremath{\beta} values.

Inner-shell photoionization of ground-state lithium: Theoretical calculation in the photon energy region below 130 eV including1snln′l′Rydberg resonances series

Calculations of 1s electron inner-shell photoionization from the 1s(2)2s S-2(e) Li ground state have been performed using recent developments of the R-matrix code with a 19-term target representation for incident photon energies up to 130 eV. This photon energy range allows important resonances in the partial cross sections due to 1 snln'l' autoionizing states to be obtained. Theoretical resonant results are compared with recent experimental measurements of Kiernan et al, [J. Phys. B 29, L181 (1996)] in the 1s2l threshold region. Partial cross sections, branching ratios, and asymmetry parameters are also compared outside the resonant energy range with previous theoretical results of Lisini, Burke, and Hibbert [J. Phys. B 23, 3767 (1990)], who used the R-matrix code with an 11-term target representation, as well as the corresponding experimental result; of Ferret et al. [Phys. Rev. A 36, 3172 (1987)], Langer et al. [Phys. Rev. A 43, 1652 (1991)], and Cubaynes et al. (private communication). [S1050-2947(98)05702-3].

Angle-resolved Auger spectra of the molecule

Auger decay spectra of the ethyne (acetylene) molecule have been measured at photon energies below as well as above the C 1s ionization threshold. Angular anisotropy has been observed at the resonance and in the region of a continuum feature previously assigned to a resonance, but disappears far above threshold. Because of strong configuration interaction in the final state only high kinetic energy Auger transitions can be assigned to individual electronic states. In the case of resonant Auger decay, this mixing of states also blurs the division of the spectrum into participator and spectator features. Decay spectra resonances assist in the assignment of Rydberg resonances. The decay of the double excitations above the C 1s threshold has also been studied.

Field Enhanced Dielectronic Recombination ofSi11+Ions

The enhancement of dielectronic recombination by applied electric fields has been observed and measured for the first time in a wide range of controlled and measurable fields using multiply charged ions. The heavy ion storage ring CRYRING at Stockholm University was used to store a beam of ${\mathrm{Si}}^{11+}$ and collide it with a cold electron target. Rydberg resonances up to $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}25$ are resolved for both the ${2p}_{3/2}$ and ${2p}_{1/2}$ series. The observation of a substantial monotonic increase of the rate coefficient for the group of higher Rydberg states is in puzzling disagreement with theoretical calculations of electric field enhanced dielectronic recombination.

Observation of New Rydberg Series and Resonances in Doubly Excited Helium at Ultrahigh Resolution

We report on a striking improvement in spectral resolution in the soft x-ray range to 1.0 meV at 64.1 eV, measured via the $\ensuremath{\mu}\mathrm{eV}$-wide 2, ${\ensuremath{-}1}_{3}$ double-excitation resonance of helium. This ultrahigh resolution combined with the high photon flux at undulator beam line 9.0.1 of the Advanced Light Source have allowed observation of new Rydberg series and resonances below the $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$ threshold of doubly excited He. The obtained resonance parameters (energies, lifetime widths, and Fano-q parameters) are in excellent agreement with the results of state-of-the-art calculations.

High-resolution study of 1Po double-excitation states in helium.

We describe extensive results on the $^{1}$${\mathit{P}}^{\mathit{o}}$ double-excitation resonances of He below the N=2--9 ionization thresholds obtained recently by high-resolution photoionization measurements using synchrotron radiation from the SX700/II monochromator at the Berliner Elektronenspeicherring f\"ur Synchrotronstrahlung (BESSY). The resonance energies, linewidths, Fano-q parameters, and quantum defects of the various Rydberg resonances, derived from the experimental data, are compared in detail with the results of ab initio calculations employing the complex-rotation method. All three optically allowed Rydberg series below the N=2 ionization threshold were identified. For 3\ensuremath{\le}N\ensuremath{\le}8, the two most intense Rydberg series were resolved below each threshold, and for N=3, one state of a third series could be identified. For the higher Rydberg series (N\ensuremath{\ge}5), the two neighboring series, N and N+1, generally interfere, which has a strong influence on the transition intensities, linewidths, and quantum defects of the principal series. All together, states of 18 different Rydberg series in the $^{1}$${\mathit{P}}^{\mathit{o}}$ double-excitation resonance region of He were observed. \textcopyright{} 1996 The American Physical Society.

Energy distributions of emitted ion fragments following C(1s) excitations in CO.

Ion-branching ratios following the relaxation of C (1${\mathit{s}}^{\mathrm{\ensuremath{-}}1}$${\mathrm{\ensuremath{\pi}}}^{\mathrm{*}}$,nl\ensuremath{\lambda},${\mathit{v}}^{\ensuremath{'}}$) synchrotron light-excited, vibrationally resolved resonances in CO have been measured using a time-of-flight spectrometer at high extraction voltages. Additional measurements at low extraction voltages (higher kinetic-energy resolution) have enabled an estimate of the kinetic-energy distributions (KED's) of the emitted ${\mathrm{C}}^{+}$, ${\mathrm{O}}^{+}$, ${\mathrm{C}}^{2+}$, and ${\mathrm{O}}^{2+}$ ions. Large differences in these distributions are observed at various resonances and, for instance, a doorway-state dependence of the KED has been found for the 3s\ensuremath{\sigma} and 3p\ensuremath{\pi} Rydberg resonances. While the results give some different information concerning the involved relaxation processes, more theoretical calculations are needed to get a more quantitative understanding. \textcopyright{} 1996 The American Physical Society.

High-resolution measurement of the dielectronic recombination of fluorinelike selenium ions.

We have measured the dielectronic recombination cross section of Se{sup 25+} ions at center-of-mass energies from 1 to 1800 eV using merged electron and ion beams in the Heidelberg heavy-ion Test Storage Ring (TSR). All dielectronic resonances involving changes of {Delta}{ital N}=0 and {Delta}{ital N}=1 of the core principal quantum number {ital N} are covered with high-energy resolution (ranging from {lt}0.6 eV at {lt}90 eV to {approx_equal}6 eV at 1600 eV). A strong contribution of {Delta}{ital N}=1 Rydberg resonances at 1200{endash}1700 eV is observed. The results are compared with isolated-resonance intermediate-coupling calculations of the cross section. Good agreement is found for the {Delta}{ital N}=0 and the low-lying {Delta}{ital N}=1 resonances. For the {Delta}{ital N}=1 Rydberg series the resonant pattern continues to be well reproduced by theory, whereas the total energy-integrated cross section significantly exceeds the theoretical prediction. From experimental and theoretical results rate coefficients for isotropic plasma temperatures between 100 and 2000 eV are also derived. {copyright} {ital 1996 The American Physical Society.}

Vibrationally resolved Si 2p photoabsorption spectrum of SiCl4.

We report on a high-resolution study of the Si 2p photoabsorption spectrum of ${\mathrm{SiCl}}_{4}$ in the gas phase. Characteristic differences in the intrinsic widths of the resonance lines allow a distinction of excitations to valence and Rydberg orbitals, respectively. The Rydberg resonances are found to be narrow and split into vibrational substrates from symmetric-stretching vibrations, providing information---on the basis of a Franck-Condon analysis---on vibrational energies and equilibrium internuclear distances of the core-excited molecule. Thermal population of excited vibrational levels in the molecular ground state has to be taken into account for a proper description of the spectrum.

Pulsed field ionization threshold photoelectron spectroscopy with coherent vacuum ultraviolet: NO+(a 3Σ+ v=0,1,2)←NO(X 2Π1/2)

We report pulsed field ionization spectra of an ionic electronically excited state, specifically, the NO+(a 3Σ+ v+=0,1,2)←NO(X 2Π1/2) transition. A coherent vacuum ultraviolet light source provides single photon excitation, which enables a direct measurement of the ionization potentials for the three vibrational levels — I.P.(v+=0)=126 392±1.5 cm−1, I.P.(v+=1)=127 653±1.5 cm−1, and I.P.(v+=2)=128 884±1.5 cm−1. The rotational structure of these spectra has been simulated using a standard model for rotational line strengths in a photoelectron spectrum, and this simulation shows the strong atomic p orbital character of the initial NO orbital from which the electron is photoionized. However, our data show that the rotational line strengths are strongly dependent on the final vibrational state of NO+, in disagreement with the theoretical model. Also, the spectrum for the v+=1 state of NO+ is strongly affected by the presence of a strong autoionizing Rydberg resonance at the same photon energy, which leads to a complex resonance.

Electron spectra of HCl at core to Rydberg resonances

Electron spectra of 2p to Rydberg excited states of HCl have been measured. The dominating decay channel of these Rydberg resonances is confirmed to be the molecular resonance Auger process. The electron spectrum recorded at the first Rydberg resonance (2p3/2 to , 4s sigma ) is analysed in some detail. In addition to the non-shake spectator resonance Auger decay, also 4s sigma to 5s sigma shake-up processes are suggested to play a minor role in the decay. The share of shake processes probably increases at higher resonances. Results are compared with those of photoion experiments.

Asymmetry in the ionic fragmentation of N2O photoexcited around the N and O K edges

Asymmetry parameters (β) for the fragment ions of N2O following excitation or ionization of the N and O K shell electrons have been determined from photoelectron–photoion coincidence (PEPICO) and photoion–photoion coincidence (PIPICO) spectra measured using monochromatized synchrotron radiation and a rotatable time-of-flight mass spectrometer. Profiles of the β parameters from the N+ ions with low kinetic energies (K.E. <4.5 eV) in the PEPICO spectra were found to be very isotropic (close to 0) around both the N and O K edges. β parameter profiles for the O+ ions with contributions from N+ ions with K.E. ≳4.5 eV and N2+ ions overlapped with NO+ ions show structure with negative values at the π* resonances below the N K-edges and positive values at the unresolved Rydberg resonances below the terminal N K edge and O K edge and at the shape resonance above the N K edges. β parameters from the N+–NO+ and N2+–O+ PIPICO signals were found to be considerably more anisotropic than the corresponding values from the PEPICO signals at the π* resonances below the N K edges and the shape resonance above the ionization edges. β parameters from both the PEPICO and PIPICO signals were close to zero at the π* resonance below the O K edge. The higher degree of anisotropy of ionic fragmentation observed in the PIPICO signals highlights the importance of measuring the fragmentation spectra of polyatomic molecules in coincidence in order to obtain accurate β parameters.

Observation of the (2p,nd)1Po double-excitation Rydberg series of helium.

Double-excitation Rydberg resonances of He below the {ital N}=2 threshold of He{sup +} were studied with an energy resolution of {congruent}4 meV by photoionization using synchrotron radiation. All three Rydberg series of {sup 1}{ital P{ital o}} resonances accessible by photoabsorption, including the hitherto missing'' (2{ital p},{ital nd}){sup 1}{ital P{ital o}} series, were resolved. This settles a long-standing discrepancy between experiment and theoretical predictions and establishes a firm basis for testing the accuracy of atomic multiconfiguration calculations.