Table of contents

A generalized expression for the second hypervirial of an arbitrary hydrogenic radial function is obtained. We illustrate the power of this result showing that a general recurrence relation among hydrogenic matrix elements becomes a simple consequence of it. We also exhibit that a particular case of such a recurrence relation can be rederived employing the hypervirial theorem and the well known mapping between the Morse and the Coulomb problems.

By performing first-order perturbation theory about the mod m mod to infinity limit, we obtain a highly accurate analytical expression for circular Rydberg ( mod m mod =n-1>>1) wavefunctions of the hydrogen atom in a uniform magnetic field. In the mod m mod to infinity limit, the electron executes a circular orbit about the magnetic field axis; the first-order wavefunction simply corresponds to Gaussian fluctuations about this orbit. To demonstrate the utility of the results derived here. We compare our simple expression for the lifetimes of mod m mod =25 and 35 circular states with accurate ab initio results.

We report on experiments in which we have been able to actively cancel the motional Stark effect and observe pure diamagnetic spectra for the barium atom. These differ from those previously reported in that they contain no intruding structure. In addition, the sigma ⁺ and sigma ^- spectra have been found to be identical.

We have searched for evidence of electron circular dichroism, the preferential transmission of longitudinally polarized electrons through a chiral medium, using stereoisomers of camphor. Such an effect was seen by Campbell and Farago in 1987 for 5 eV electrons. Within our detection limit ( approximately 0.02%) we have not observed asymmetric transmission at either an incident electron energy of 1 eV or 5 eV. In preparation for this inquiry, we also measured the total scattering cross section for camphor in the energy range 0.5-5 eV.

A new efficient method of representing electron scattering polarization data is derived based on the stereographic projection of the polarization vector on the Poincare sphere. To illustrate this method we present polarization trajectories for electrons elastically scattered from cadmium atoms.

The superelastic scattering of electrons from a positive ion has been experimentally observed for the first time. A cross section of 12.0*10^-17 cm² was determined for the collisional quenching of the 1s²2s2p²⁴P state of C⁺ at an energy of 3.5 eV. The principle of detailed balancing is used to compare with an R-matrix calculation for the excitation collision strength to this state.

A novel experimental technique is used to determine accurate relative values of ionization cross sections as a function of electron impact for Na. The ionization efficiency curves are then compared with the recent convergent close-coupling (CCC) calculations of Bray (1994) which have been very successful in predicting ionization cross sections of atomic hydrogen. The present results are also compared with the plane-wave Born approximation calculations of McGuire (1971) which are expected to be accurate at high electron-impact energies (>500 eV). These comparisons show that at electron-impact energies greater than about 60 eV, inner-shell ionization plays an important role in Na.

A spectral holography experiment is performed in a hole-burning material. A shaping device is used to tailor the spectrum of the pulses which engrave the hologram. The resolution of the spectral shaping technique is investigated both theoretically and experimentally.

We report on the first isotope shift measurements in the spark spectrum of tungsten. Eight lines have been investigated by means of a classical Fabry-Perot spectrometer with digital data output. The light sources were liquid-nitrogen-cooled hollow cathodes, filled with highly enriched samples of ¹⁸⁴W and ¹⁸⁶W. In order to interpret the experimental results, the mixing of the lower levels of the W II spectrum has been determined by means of a fine structure analysis of the (5d+6s)⁵ configurations. The specific mass shifts of the transitions to 5d⁴6p and 5d³6s6p have been estimated. Electron densities at the nucleus and screening ratios have been calculated with a non-relativistic Hartree-Fock computer code. Semi-empirical field shifts have been derived from these densities. A comparison with the experimental field shifts yields S_II*(W)=0.88(7) as the scaling factor for the electron densities. The semi-empirical field shifts can be used to determine the configuration mixing in the upper levels and to calculate crossed-second-order effects.

A theory for excitons in X-ray spectra of conjugated molecules is presented. Due to the interaction with the core hole the lowest unoccupied pi level splits from other empty levels. The energy position of this state is defined by the renormalized Coulomb interaction with the core hole and by the width of the unoccupied pi band. The ratio of these two quantities determine whether the X-ray state is excitonic or not. It is shown that the conditions for excitonic character are qualitatively different between occupied levels (X-ray emission) and unoccupied levels (X-ray absorption). From the specified normalization we find that only half an electron density of the unoccupied molecular orbital can be localized to the atom with the core hole, while in the X-ray emission case the electron density of the lowest occupied pi orbital can be totally localized. The degree of localization of the lowest unoccupied pi level decreases when the length of the molecule increases. Contrary to lowest occupied and unoccupied molecular orbitals the electron density of higher occupied (emission) and higher unoccupied (absorption) pi orbitals is pushed out from the core excited atom for sufficiently large Coulomb interactions between core hole and valence shell. Strong site and size dependences of the intensity and frequency of excitonic peaks in X-ray absorption spectra are predicted, the site dependency being alternant for conjugated molecules. The model predicts strong depression of the absorption intensity for the pi * levels along the polyene series in good accord with ab initio data.

The second-order alpha corrections in QED, in particular the two-photon exchange corrections, are investigated by the line profile approach. The expressions for equal-energy 'reference state' corrections and for the unequal-energy Coulomb-transverse corrections are given. The numerical calculations for the latter corrections of 'box' and 'cross' type in the case of (1s_1/2)²2s_1/2 and (1s_1/2)²2p_1/2 states of Li-like heavy ions are presented.

A new isotope shift program, part of the MCHF atomic structure package, has recently been written. The program calculates the isotope shift of an atomic level from multiconfiguration Hartree-Fock (MCHF) or configuration interaction (CI) wavefunctions and is specially designed to be used with very large CI expansions, for which angular data cannot be stored on disk. To explore the capacity of the program, large-scale isotope shift calculations have been performed for the 1s²2s ²S and 1s²2p ²P levels in C IV and for the 1s²2s²2p²¹S, 1s²2s²2p3s ¹p, 1s²2s²2p²³P and 1s²2s2p³⁵S levels in C I. From the isotope shifts of these levels the ¹⁴C-¹²C isotope shifts were calculated for the 1s²2s ²S-1s²2p ²P transition in C IV and for the 1s²2s²2p²¹S-1s²2s²2p3s ¹P and 1s²2s²2p²³P-1s²2s2p³⁵S transitions in C I. The calculated transition isotope shifts are in very good agreement with experimental values, available for the C I transitions. As a check on the overall quality of the wavefunctions, the hyperfine structure interaction constants were calculated for the levels in C IV.

High resolution profiles of neutral vanadium lines have been recorded in the infrared region (1800-9000 cm^-1) by Fourier transform spectroscopy. 106 transitions showing resolved or partially resolved hyperfine profiles have been analysed. An investigation of these structures has allowed the deduction of magnetic dipole constants for 101 levels. For 69 levels the results obtained are new. The results of the present work have been compared with the few data previously published in the literature and they are generally in good agreement.

The fifth spectrum of barium was photographed in the 400-1220 AA region on a 3-metre normal incidence spectrograph using a triggered spark source. The earlier analysis of 5s²5p⁴-5s5p⁵ transition array of Ba V has been confirmed. 42 out of 48 levels of the 5s5p⁵, 5s²5p³5d and 5s²5p³6s odd parity configurations have been established. The six unknown levels have J>or=4 which do not give any electric dipole transitions to the levels of the ground configuration. One hundred and thirteen new lines have been classified in Ba V spectrum. The least-squares-fitted (LSF) parametric and Hartree-Fock calculations were carried out and they interpret the level structure satisfactorily.

For atomic media with resonant Doppler-broadened transitions of J=0 to J'=1 or J=1 to J'=0 type and taking into account the relaxation due to depolarizing collisions, a theory of non-linear optical polarization phenomena in the presence of a DC electric field is developed. The theory is valid in the case of both arbitrary resonance radiation intensity and arbitrary external DC electric field spatial orientation. The intensity-dependent contributions to variation of radiation polarization are analysed in detail in the Doppler limit. Special attention is paid to the case of linear polarization of incident radiation; in this case as well as in the presence of a DC electric field, the Doppler-enhanced non-linear optical contributions determining the emerging ellipticity and the rotation angle of polarization, respectively, are of the same order of magnitude (unlike the case of external magnetic field, in which the key effect is the rotation of polarization). It is shown, however, that in the case of the strictly transverse geometry and if the angle between the electric field direction and the initial polarization vector is equal to 45 degrees , the Doppler-enhanced non-linear optical contribution to the rotation angle becomes anomalously small. The effect of the presence of a longitudinal component of electric field on the non-linear optical polarization phenomena is investigated. In addition, although in the case of a purely longitudinal geometry for the considered transitions the electric field effect on radiation polarization modification is absent, some analytic results concerning self-rotation and deformation of a polarization ellipse in the Doppler limit for an intense initially elliptically polarized radiation are also presented.

An analytical expression is derived for the Faraday rotation occurring in a dilute atomic vapour for monochromatic light of any intensity tuned near an absorption transition between two levels, each with total angular momentum J= 1/2 . Collisional effects are included within the framework of the impact approximation. The result is discussed in terms of simple physical mechanisms; it is shown that optical pumping effects play an important role.

The single-hole Green function with the lowest-order self-energy part has been used to calculate energies and spectroscopic factors of the neon ion ground and excited states which originate from the removal of the 2s and 2p valence electrons. The simplest two-hole-one-electron ion states are included explicitly to the self-energy. More complex (m+1)-hole-m-electron states are treated implicitly by using the experimental energy of the two holes in the simplest ion states. The results of the calculation are found to be consistent with experimental satellite line positions and intensities obtained from recent photoionization and electron-impact ionization measurements.

The medium of the three-level Yb atom corresponding to the three-colour, three-step, three-photon scheme of 6¹S₀ (0 cm^-1) to 6³P₁ (17992008 cm^-1) to (7/2, 3/2)₂4f¹³6s²6p (35196.98 cm^-1) to autoionization state (52353 cm^-1) is chosen to examine the selective photoionization of ¹⁶⁸Yb. The Maxwell-Bloch equation is numerically solved, where the interacting laser pulses are supposed to be collinear and resonant with the transition lines of ¹⁶⁸Yb, and the effects of Doppler broadening and laser bandwidth are incorporated. Firstly, the thin medium dynamics are examined to determine the optimal energy of laser pulses for the selective photoionization of ¹⁶⁸Yb, and to determine Yb isotopes which have a large influence on the excitation of ¹⁶⁸Yb. Secondly, the thick medium dynamics are investigated, resulting in the fact that the laser pulse for the first transition is prominently deformed due to the near-resonant interaction with ¹⁷¹Yb and ¹⁷³Yb, and the ion yield along the propagation of the laser beam is strongly dependent on the initial energy of pulse for the first transition and the time-delay between input pulses.

The population inversion in a three-level atomic system, interacting with two coherent laser pulses, occurs from the first level to the third level at the optimal detunings of the laser frequencies near the two-photon resonance. An examination is performed to see whether the energy density and time-delay of the photoionizing laser can significantly influence the ion yield for the case where the atom interacts with two coherent pulses and one photoionizing pulse incoherently coupled. The well-known three-colour, three-step, three-photon ionization scheme, which is available for the selective photoionization of ¹⁶⁸Yb, is chosen for use in this research with the Bloch equation. It is revealed that the proper time-delay and energy density enable us to achieve higher efficiency for the selective photoionization of ¹⁶⁸Yb, regardless of the Doppler-broadening, though the efficiency and selectivity of coherent excitation are prominently enhanced by applying the optimal detunings.

Correlation satellite lines originating from the strong mixing between 5s¹5p⁵, 5s²5p³nd (n=5, 6, 7, ...) and 5s²5p³ms (m=6, 7, 8, ...) configurations in the final state of the N_4,5-O₁O_2,3 Auger decay of Xe and between 4s¹4p⁵, 4s²4p³nd (n=4, 5, 6, ...) and 4s²4p³ms (m=5, 6, 7, ...) final-state configurations in the M_4,5-N₁N_2,3 Auger decay of Kr have been studied by means of synchrotron-radiation excited electron spectroscopy and relativistic multiconfigurational Dirac-Fock calculations. Improvements in experimental and computational methods have made it possible, for the first time, to resolve and to assign most of the satellite lines with high accuracy.

Multiphoton excitation with elliptically polarized light brings out more information in the photodetachment or photoionization processes than linearly polarized light. This information can only be reached, however, by recording photoelectron angular distributions for several values of the ellipticity angle, and fitting the data with a common formula. But the analytic dependence of photoelectron angular distributions on the ellipticity has been unknown up to now, except for the one- and two-photon excitation cases. Here we give a demonstration of a general formula, valid for any number N of exciting photons, with the assumptions of (i) an initially even and momentumless (J=0) atom or ion and (ii) that after excitation of an electron, the residual core is left in an odd state. Slight modifications in the demonstration would make it possible to extend the general formula to any J=0 initial atomic state.

For pt.I see ibid., vol.28, p.3845-59 (1995). The negative ions F^-, Cl^- and I^- have been submitted to multiphoton excitation by elliptically polarized light from a Nd:YAG laser at lambda =1054 nm. Photoelectron angular distributions measured in the polarization plane with various ellipticities are fitted by the analytic formula that was established in the previous paper. Elliptic asymmetry parameters are obtained for three-photon detachment of I^- and four-photon detachment of Cl^- and F^-. Ordinary 'linear' asymmetry parameters can be deduced from these elliptic asymmetry parameters, which makes it possible to compare the present results with those of previous measurements and calculations.

We introduce simple methods for the approximate calculation of the compound two-photon dipole free-free matrix element in a Coulomb field which characterizes the amplitude of the two-photon bremsstrahlung process. Methods are based on the accurate treatment of the diagonal singularity in the one-photon dipole matrix elements, which appear in the compound-matrix element. We demonstrate that the exact results presented by Florescu and Djamo, Veniard and co-workers and Dondera and Florescu, where the two-photon free-free matrix element in the Coulomb field was obtained using the explicit form of the Coulomb Green function, can be reproduced quite accurately (error <3%) with the use of the formulae given in this paper.

A crossed-beam technique, where the collision products have been selected by time-of-flight (TOF) spectroscopy with either a pulsed beam or coincidence counting, has been used to study pure ionization of Fe and Cu by 70-1440 keV amu^-1 H⁺ and 35-425 keV amu^-1 He²⁺ ions. Cross sections for the formation of q times ionized Fe and Cu products by pure ionization have been determined for q=1-4. A comparison with the corresponding (previously measured) cross sections for transfer ionization shows that, in the energy range considered, Fe⁺ and Cu⁺ ions arise predominantly through pure ionization. However, for q>or=2, contributions from both transfer ionization and pure ionization are important. Pure ionization becomes dominant at energies which increase as q increases. Measured cross sections for pure ionization have been successfully fitted to values based on an independent electron model approximation.

A novel classical overbarrier model for the charge exchange is formulated for low and medium collision velocities. The charge-exchange probability is expressed in analytical form. The results are compared with the classical Monte Carlo trajectory calculations for various partners (ground-state atom+multicharged ion, high Rydberg atom+ion with unit charge). The model reproduces well the experimental data for the collisions Na⁺+Na(29s).

Cusp-electron emission in proton on argon collisions has been investigated at impact energies 33, 50 and 75 keV. By detecting the electrons in coincidence with the charge-state analysed outgoing H^+,0 projectiles, the process of electron capture to the continuum (ECC), as well as the process of simultaneous ECC and bound-state capture (transfer ionization, TI) were identified. The ratios of the yields for cusp-electron production by TI and ECC are found to decrease with increasing projectile energies. At the lowest proton energy (33 keV) the measured TI/ECC ratio is about four times smaller than the corresponding ratio for incident He⁺ measured in earlier work. Significant is the finding that there exists a cusp associated with TI events, and, moreover, that this cusp is present for neutral outgoing projectiles.

First calculations of the polarization-correlation Stokes parameters P_i (i=1,2,3,4) for the quadrupole excitations by electron impact in heavy inert gases are carried out taking the 2p⁵3p J=2 states of neon as an example. The distorted-wave Born approximation and the multichannel diffraction approximation are used and the sensitivity of the P_i parameters to different couplings is studied. The indirect dipole couplings via the resonance 2p⁵3s J=1 levels cause a drastic rotation of the excitation amplitudes in the complex plane and strongly affect the Stokes parameters. The results are compared with recent measurements. The excitation cross sections are briefly discussed.

Electron spectra from the Li⁺-Ne and Na⁺-Ne collisions have been measured for collision energies from 3.5 to 60 keV, ejection angles of 20-160 degrees , and electron energies in the 5-150 eV range. In both systems the electron spectrum consists of a relatively large continuum superimposed by discrete lines arising from doubly-excited atomic states. For the Li⁺-Ne system the continuum part decreases exponentially with electron energy, with a slope inversely proportional to the collision velocity. The angular distribution is approximately symmetric in the centre-of-mass system. For the Na⁺-Ne system the behaviour is more complicated, in particular, the continuum part cannot be fitted with a single exponential. The results are discussed in terms of recent models developed for one-electron systems by Solov'ev, Ovchinnikov and collaborators, describing the ionization process in terms of superpromotions, with the electron continuum being parametrized in terms of characteristic properties related to avoided and so-called hidden crossings of the quasimolecule.

Absolute differential cross sections for the electron-impact rotational excitation of N₂ Cl₂, CO and HCl have been measured in a crossed-beam experiment. Results on rotational state-to-state transitions are obtained by a deconvolution procedure from the energy-loss peaks at primary energies between 10 eV and 200 eV and in the angular range from 10 degrees to 160 degrees . Details are given of an apparatus which allows absolute measurements with high-energy resolution and excellent statistics. At intermediate impact energies and scattering angles, unexpected large angular-momentum transfer was found. The results are very different for various energies and for different molecules. Four excitation mechanisms can clearly be distinguished. The experimental endings are compared with theoretical results using the semiclassical spectator model and a close-coupling calculation with an effective interaction potential.

The split-propagation method is applied to the study of the dissociative attachment of slow electrons to the carbon dioxide molecule in the two modes (symmetrical and asymmetrical stretch modes) approximation. This approach implies keeping track of the time evolution of the initial wavepacket, which is fixed by the vibrational state of the molecule before the collision. It is shown that the tardy ebbing of the wavepacket in the active zone principally refutes the conventional assumption of the irrelevance of the bending motion for the DA process. The influence of the averaging procedure on the oscillating structure in the cross sections dependence on the incident electron energy, which may appear to deviate in different experiments, is discussed.