Table of contents

Calculated values of the lifetime of the 3s3p³⁵S₂⁰ state of P II differ within a factor of more than three. A recent experimental determination gives a lifetime of 167+or-12 mu s, confirming the author's earlier calculated value of 163 mu s. The author discusses the reasons for the discrepancies between the theoretical values determined in each case from quite sophisticated calculations and make recommendations on the essential stages of a calculation of transition probabilities of intercombination lines.

A new type of many-electron radiative transitions involving three electrons is predicted. The results of the authors' investigation by many-body perturbation theory are presented. Spectral lines observed in the wavelength range of 37.5 to 54.0 nm by means of photon-induced fluorescence spectroscopy (PIFS) following the excitation of the Kr I 3d^-1np resonances are reported and compared with the predictions.

The authors have measured the population in each of the 5d_3/2(m_j) ion states following autoionization of the (6p_3/2nd)_J=MJ=3 state by using a circularly polarized laser to excite the Ba⁺ 5d_3/2 to 6p₁2/ transition, and observing the polarized fluorescence of the Ba⁺ 6p_1/2 to 6s_1/2 transition. The branching ratios for autoionization into each of the 5d_3/2 in l_j channels can be related to these ion populations by using angular momentum algebra. The fractions of ions found in the m_j=+3/2, +1/2, -1/2 and -3.2 state of the 5d_3/2 ion states were 5.9(+or-2.6)%, 4.5(+or-1.9)%, 3.2(+or-1.3)% and 1.9(+or-0.6)% respectively. This method can easily be generalized to measure the branching ratio for autoonization into other ion states.

The discrepancy between previous R-matrix calculations using fixed boundary conditions and the eigenchannel method for the photoionization spectrum of barium is resolved. In particular, it is shown that the position of the (6p²)¹S₀ resonance that results in a maximum of the experimental photoionization cross section near 44800 cm^-1 relative to the (6s²)¹S₀ ground state of barium cannot be obtained by a standard close-coupling expansion involving only physical bound states; instead, the correct representation of short-range correlation effects and the relaxation of the 6p orbital requires the inclusion of doubly excited configurations of the continuum-continuum type.

With the development of high power, subpicosecond lasers, it has become possible to study the process of multielectron dissociative ionization of small molecules at intensities in excess of 10¹⁴ W cm^-2. At such intensities the conventional multiphoton approach is too complex and the field ionization model becomes more attractive. This article reviews the experimental results obtained to date and indicates how certain aspects of the process, namely the mode of multiple ionization, the thresholds for multiple ionization, the charge symmetry of the fragment ion production and their peaked angular distributions, can be explained in terms of a field ionization, Coulomb explosion model. However, a more sophisticated approach is undoubtedly required to explain the lack of variation of fragment ion kinetic energies with laser risetime, the variation of kinetic energies with laser wavelength and the molecule specificity of the process.

The authors propose a regularization technique which allows Lagrange-mesh calculations to retain their accuracy, efficiency and simplicity when the Hamiltonian is singular at finite distance. Compact analytical expressions of kinetic-energy matrix elements are an essential ingredient of the method. The authors present general procedures for deriving them. Their approach is tested on the hydrogen atom and the squared orbital-momentum operator. They demonstrate its accuracy on the non-separable problem of the hydrogen atom in a magnetic field. This method opens the way to numerous new applications of Lagrange-mesh calculations in atomic and molecular physics.

The authors use the first-order reduced density operator formalism to derive the statistical population analysis for ROHF wavefunctions, along the same lines as they have done before for other types of wavefunctions. In this way they find a partition of the electron density and a partition of the uncoupled spin density. The formalism is completely general and can be applied to any molecular wavefunction, whether ab initio in any level of accuracy, or semi-empirical. Numerical examples are given for systems described by an ROHF wavefunction obtained at the semi-empirical AM1 level. The comparison with UHF results is also reported.

Lanczos' tau method provides a powerful and accurate tool for the resolution of the one-dimensional Schrodinger equation where the potential energy is given in rational form or can be brought into such a form after an appropriate change of variable. The eigenfunction is constructed on two intervals where the different boundary conditions are taken into account by searching, in each case, for a local solution as a product of a polynomial by a function describing the corresponding asymptotic behaviour. The matching of the eigenfunction and its first derivative at the common boundary of the intervals leads to a quantization condition from which the complex poles of the scattering amplitude (i.e. bound states, resonances, growing and virtual states) are obtained. A complete implementation of the method is provided together with a few checks on the bound states of the Coulomb potential and the resonances and virtual states of the exponential potential.

MCHF n-expansion procedures are applied to the Be and Li^- 1s²2s²¹S ground state. Up to n=5 all configuration states are included. From n=6 results, a pattern was observed for triple and quadruple excitations and this pattern was then applied to the higher n. Calculations were performed up to n=10. For Be, the extrapolated total energy of -14.667314 Hartree and the double ionization energy of 1.011796 Hartree agree well with the predicted exact non-relativistic energies. An ab initio value of the quantity related to the Be 2s²-Be⁺ 2s specific mass shift is reported for the first time. The electron affinity for Li is predicted to be 0.6176 eV. Both of these values are in excellent agreement with experiment.

In the calculation of atomic structure using the configuration interaction (CI) approach, very large numbers of terms may be present in important mixing configurations. This causes computational difficulties in, for example, the non-relativistic calculation of low-lying terms in the transition elements which may be serious enough to prohibit or seriously limit investigation of these ions. A method is presented which allows one to proceed in a sequence of progressively more complicated CI calculations while retaining only a relatively small number of terms with little attendant loss in accuracy. The method is demonstrated in a calculation on the simpler ion, P II. Values for the lifetime for the 3s3p³⁵S₂⁰ level are obtained both in a full relativistic calculation and in a relativistic calculation based on a 'progressive reduction of terms' in preliminary non-relativistic calculations. Sources and magnitudes of errors in the calculation are discussed. The full calculation result of 178 mu s for the lifetime of this level is in good agreement with a recent experimental value of 167+or-12 mu s.

Dirac-Hartree-Fock theory (DHF), and density functional theory Hartree-Fock system (DFT-HF) calculations predict that Lu^- (Z=71) is stable in the (Xe)4f¹⁴5d¹6s²6p¹ odd-parity electron configuration and is not bound in the commonly assumed (Xe)4f¹⁴5d²6s² even-parity configuration of Hf⁰ (Z=72). Combining the results of these methods gives an electron affinity approximately=7+or-4 Hartree. The Hartree-Fock energy dominates the crossover from even to odd parity ground state as Z is lowered from 72 to 71 in this 72 electron system. The relativistic effects, which are inherent to the DHF method, are important in unbinding the even-parity state and have been included perturbatively in the DFT-HF calculations. The very large experimental sd interconfiguration energy of Lu⁰ is used to support the conclusion that the even-parity configuration is unstable. A comparison of the electron configuration of singly charged (+or-) and neutral Lu with those of the group IIIB elements indicates that Lu is most similar to Y.

High-resolution silicon K-shell spectra from a short-scalelength, laser-produced plasma have been obtained in temporally and spatially integrated measurements. Density-sensitive line-intensity ratios of the helium-like satellites and that of the lithium-like satellites are employed simultaneously with temperature-sensitive line-intensity ratios between the helium- and lithium-like satellites to assess their diagnostic value. It appears that the emission of dielectronic satellites is dominated by a region with relatively well defined density and temperature in the ablation zone.

Analyses of C IV lines in laboratory measurements and astrophysical high resolution spectroscopy indicate that present Stark broadening data for multielectron atoms fail due to the neglect of or an insufficient description of ion broadening. A new method for the computation of complete Stark profiles is developed using the impact approximation and close-coupling theory for electron broadening. The ion broadening is included by the use of the model microfield method. For the 4d-5f and 4f-5g lines, a comparison with experimental measurements shows good agreement.

Electronic spectra of dicationic molecules comprise a high density of singlet and triplet states. By virtue of simple propensity rules only the singlet states are selected by core-valence (CVV) Auger spectroscopy. The authors use second-order response theory to explore the role of spin-orbit interaction in the manifold of low-lying dicationic states and its implications on the intensity analysis of the Auger spectrum of water.

Two-photon dissociation of HD⁺ from the 1s sigma _g ( nu =0, J=0) state has been theoretically investigated when two intense monochromatic radiation fields at two different frequencies omega and omega ₂ act simultaneously on the molecule. These fields cause resonance with two intermediate excited vibrational levels ( nu =6,J=1) and ( nu =14,J=1) of the 1s sigma _g state. Dissociation at two different energies ( omega ₁+ omega ₂ and 2 omega ₂ above the initial energy) and in two different electronic states, each with two orbital angular momenta has been considered. Situations in which the dissociative decay is describable by a single rate have been specified. Also intensity combinations for which two photon coupling between the two resonant states dominate are found and the regimes of the two approximate treatments compared. Time-dependent dissociation probabilities are demonstrated for situations where single exponential decay does not occur.

A semiclassical theory is applied to describe collisions between sodium atoms which are independently excited to a specific magnetic sublevel of the 3p state. Cross sections for energy transfer are calculated for different combinations of the initial magnetic quantum numbers (m_a,m_b) of the atoms, and as a function of the thermal collision velocity. The motion of the cores is described either by curved trajectories, based on non-averaged adiabatic potential curves, or by straight trajectories. The largest basis set used for the electronic wavefunction contains the 4p, 5s, 4d and 4f exit channels. The electronic interaction Hamiltonian is approximated by a multipole expansion, for which all non-vanishing contributions are evaluated.

The radiative and Auger decay rates of high-lying doubly excited states of multiply charged ions are calculated using wavefunctions obtained from the configuration interaction method. The fluorescence yields of all the states within the intrashell and intershell manifolds are examined and ordered in terms of the correlation quantum numbers. It is shown that the fluorescence yields of certain classes of intershell doubly excited states are quite large which are used to interpret the recent experimental observation of large average fluorescence yield of doubly excited states formed in collisions of multiply charged ions with atoms.

A general theory of elastic spin-dependent collisions between electrons and spinless molecules is developed. The main emphasis is on scattering from oriented, chiral and achiral molecules, although results for isotropic target systems are also derived. Spin-dependent phenomena are predicted and illustrated with several examples. In particular, chiral effects are discussed in detail and classified according to their behaviour under spatial inversion and time reversal. The authors identify two types of chiral phenomena associated with systems exhibiting 'time-even' and 'time-odd' chirality. The corresponding observables are calculated for a chiral model molecule. It is concluded from the numerical results that the predicted new spin-dependent effects could be measured experimentally.

Superelastic electron scattering by laser-excited sodium atoms has been measured to determine alignment and orientation parameters for total energies of 12.1 and 22.1 eV, at scattering angles from 5 to 110'. The results allow critical comparison with previous experimental data obtained using both coincidence and superelastic methods, including spin-resolved measurements, and with available theoretical models. Close coupling methods are found particularly promising, although further development is required.

Relative differential electron impact cross sections sigma ( theta ) for elastic and inelastic scattering in mercury have been measured. The sigma ( theta ) are normalized to the optical oscillator strength for the 6¹S₀-6¹P₁ transition and put on an absolute scale. Results are presented at 15, 25, 35, 40, 50, 60 and 100 eV for elastic scattering and the 6¹P₁ excitation. In addition the 6³P₁, 7¹S₀ and 7¹P₁ excitation sigma ( theta ) are presented at 60 eV. The angular ranges are from 2' for inelastic and from 10' for elastic scattering, up to 150'. Results are compared with the other experimental and theoretical data. Comparison with the relativistic calculations is given by Srivastava et al. in the following paper (ibid., vol.26, no.5, p.1025-30 (1993)).

The authors present results of a completely relativistic distorted-wave calculation for the differential cross sections of mercury excited to the 6¹P₁ state by electron impact at energies from 15 to 100 eV. Cross sections are also presented for the excitation of the 6³P_J and 7¹P₁ states at 15 and 60 eV. Comparisons are made to recent absolute experimental measurements of these cross sections and other theoretical calculations. In general, the theoretical and experimental cross sections for the excitation of the singlet states agree well in shape but are in less good agreement in magnitude. On the other hand, there is significantly better agreement between theory and experiment for the excitation of the triplet states.

The expectation values of the various geometric parameters were determined for the ground state of the Ps^- ion. The evaluated (e⁺,e^-) pair annihilation rate in Ps^- is approximately 2.086121*10⁹ s^-1. The mass dependence of a number of geometric parameters for symmetric negative ions such as X^-X^-Z⁺ where mX<or=m_Z was also studied. It is shown that all presented geometrical parameters have a smooth form of the mass dependence.