Table of contents

Two-body potentials dependent only on inter-particle separation are shown to have a simple expansion in S-state hyperspherical harmonics. This expansion is helpful when solving the N-particle Schrodinger equation in hyperspherical coordinates.

The radiative corrections of order alpha ( alpha Z)⁵mc² to the transition energies 2³S-2³P₀ in the helium isoelectronic sequence are made and the results are compared with high precision experiments. It has been found that the theory is consistent with the experiments up to the alpha ( alpha Z)⁵mc² correction terms.

Fully relativistic calculations (MCDF-EAL) are reported for hydrogen and for first- and second-row atoms. The computed fine-structure intervals are separated according to powers of the fine-structure constant so as to investigate the accuracy of the Breit-Pauli approximation. The results are discussed in terms of their relevance to molecular calculations; the authors identify and examine significant contributions normally neglected in such calculations.

An ab initio configuration interaction calculation for the collinear potential energy surface for the reaction O⁺(⁴S_u)+H₂ to OH⁺(³ Sigma ^-)+H shows that there is no activation barrier on the surface and that there is a well whose depth is at least 13 kcal mol^-1.

The resonance fluorescence of a two-level atom irradiated by a smooth pulse of hyperbolic secant shape is investigated. The authors calculate explicitly the energy spectrum of photons at t to infinity in the limit of spontaneous linewidth much smaller than the Fourier width of the pulse. The spectrum is completely different from the Mollow spectrum. It is multi-peaked and the number of peaks increases with the area of the pulse.

Recently it was found that when Xe was irradiated by a high-intensity laser the photoelectron spectrum contained peaks which corresponded to absorption of more than the minimum number of photons required to ionise the atom. The authors have used a model approximation involving a single bound state and m continua to calculate excitation probabilities and the effective orders of non-linearity of these higher peaks. Simple analytic expressions are obtained for these quantities which agree qualitatively with experiment.

Energy-gain spectroscopy is used to investigate the various electron capture channels in N⁶⁺-He collisions. It is found that, in addition to the dominant one-electron capture into the N⁵⁺ (n=3) states, the two-electron processes and especially transfer ionisation make a large contribution to the production of N⁵⁺ ions for the highest energies investigated.

Numerical results for the Stokes' parameters of the light emitted in the decay 6p²P_1/2,3/2 to 6s²S_1/2 in atomic caesium after electron impact excitation are presented.

A formula for the probability of dielectronic recombination derived recently by Hickman (1984) using a complex-potential model is compared with that derived by Bell and Seaton (1984) from ab initio theory.

The reconstruction of the scattering amplitude (S matrix) from its complex energy poles is investigated. The canonical product expansion and its extension to long-range potentials is discussed and its convergence properties are studied both analytically and numerically for a number of simple potentials which allow almost closed-form solutions.

In a central field description the use of hydrogen wavefunctions for computation of exchange and overlap integrals can be justified as long as relative potential changes are small. The simple procedure leads to linear and quadratic forms, respectively, in the relative potential changes Delta Z/Z from the initial to the final state of the orbitals. Bahcall factors B_n are derived which only contain potential ratios of the nth orbital to the 1s orbital in first order and the relative potential alteration of the nth orbital during the electron capture (EC) process. Their contribution to the variation of the EC decay constant lambda _epsilon leads to mod ( Delta lambda _epsilon / lambda _epsilon )_{Delta B} mod approximately=0.2/Z² for a single charge ionisation of an element (or ion) of atomic number Z. As far as it is justified to model chemical variations in a single-centre consideration by statistical occupation number changes in the valence shell, this allows an estimate of possible disturbances in the interpretation of lambda _epsilon variations in terms of electron density variations near the nucleus and thus of contributions to Mossbauer isomer shift calibration from this method.

The adiabatic polarisation potential experienced by a single valence electron in the field of an N-electron atomic core is derived variationally from the polarised orbitals of the core electrons. The resulting valence electron energies are in excellent agreement with observed ionisation energies of a large number of levels of the ions Si IV, P V and S VI, and electric dipole oscillator strengths computed with the valence orbital wavefunctions and energies are expected to be highly accurate.

For pt.II see ibid., vol.15, p.4315 (1982). Relativistic and non-relativistic g-Hartree calculations of correlation energies for first-row atoms are presented. A discussion of the connection of various mean-field approaches is given.

The Compton profiles and the electron momentum densities of atomic neon and argon have been calculated using the self-interaction-corrected version of the density functional theory (SIC-LDF). The Compton profiles thus obtained have been compared with the local-density (LD) profiles. It is seen that the SIC-LDF profiles show an overall improved agreement with the experimental profiles. A comparison of the two momentum densities (SIC-LDF and LD) shows that the self-interaction correction reduces the momentum density in the low-momentum region. The Lam and Platzman correction to the momentum density within SIC-LDF formalism is derived and the results indicate that the correction is negligible for the self-interaction free local-density theory.

The possibility of using multiple orbitals with the same quantum numbers has been added to a multiconfiguration Dirac-Fock program. This is used to describe the relaxations when several states are computed simultaneously. As an application, the calculation of ns²-nsnp radiative transition rates in neutral atoms is presented.

The authors have measured the Stokes' parameters for the foil-excited 3p ¹P and 4d ¹D levels of He I as a function of foil tilt angle and beam energy. The previously observed tilt angle invariance of one of the alignment parameters has also been observed here. The results have been compared with the surface electric field model.

The authors calculate the fluorescent spectrum of an atom driven by a standing-wave laser field which is exactly resonant with the atomic transition when the atom is at rest. The motion of the atom causes Doppler shifts which destroy the exact resonance and produces a spectrum which can have peaks at omega _k= omega _L+k.V+k_L.vn where omega _L is the laser frequency, k_L.v is the Doppler shift and n is any integer.

The ground state energy of a hydrogen atom in a uniform magnetic field has been computed by means of low-order variational-perturbation theory. High accuracy is obtained for arbitrary strengths up to 10¹² G by the simple expedient of including the leading effect of the field in the zero-order model.

The authors describe a collisional-radiative calculation for hydrogen-like ions of nuclear charge less than about 15. Separate account is taken of the (n,l,j) sublevels up to and including n=4 so that the results of the calculation may be used to predict the intensities of the fine-structure components of the corresponding transitions. In particular the authors present calculated intensity ratios for the Lyman-alpha components (1S₁2/-2P_1/2 and 1S_1/2-2P_3/2) for comparison with the recent observations of these resolved components seen from solar flares and tokamak plasmas. The calculation also gave numerous values of various excitation, recombination and ionisation rate coefficients and some of these are presented by comparing the new results with values derived previously and already published. The differences are shown to arise partly from the new (and the authors believe better) choice of basic atomic data and partly because they have treated the (n,l,j) levels separately.

The broadening and shift of the indium line (5p ²P₁2/-6s²S₁2/, lambda =410.2 nm) caused by the noble gases He, Ne, Ar, Kr, and Xe, and the molecular gases H₂ and N₂ have been measured by laser fluorescence with a single-mode dye laser. The measurements were carried out at a temperature of 748K and the foreign-gas pressure was varied from 0 to 450 mbar. The collision broadening and shift parameters have been determined. Both the linewidth and the lineshift are found to increase linearly with perturbing gas density and are interpreted in terms of the impact theory of collision broadening, assuming a van der Waals and Lennard-Jones potential interaction between radiating and perturbing atoms.

The authors consider the resonant excitation of the 3868 cm^-1 J=3 to 26558 cm^-1 J=2 transition in uranium. An experiment has already been done by Scarl et al. (1981) which measures the upper-state population as a function of laser intensity. The authors re-analyse these data taking proper account of the laser's temporal pulse shape. The effect of the laser bandwidth is also included in a novel way. They find a fit to the data which gives different values for the physical parameters from those found by Scarl et al. and draw some general conclusions for experiments of this type.

The energy spectrum of electrons resulting from multiphoton ionisation is analysed with the help of a simple, exactly soluble model. The weakening of lower energy lines with the increase in laser intensity, observed in experiments, occurs as a strong-field effect. The dependence of the light shift and the light broadening on the laser intensity and on the virtual-bound transitions in the atom are also analysed.

Orbital reorganisation energies in the photoelectron spectra of 15 transitional metal complexes with Ti, V, Cr, Mn, Fe, Co, Ni and Zn as 3d centres have been determined by means of the Green's function formalism. Computational background for the present investigation is an improved semi-empirical INDO Hamiltonian. Detailed results and comparisons with experimental data are given for four representative 3d complexes with V, Mn, Fe and Ni atoms. A self-energy approximation has been employed in the second order of perturbation that allows the decomposition of the net reorganisation energies into orbital relaxation, the loss of ground-state correlation and the variation of the electronic correlation in the cationic hole state as the many-body response to the relaxation energy. The magnitude of these corrections is studied as a function of the localisation properties of the corresponding orbital wavefunctions. Outer valence ionisation energies for delocalised ligand electrons can be assigned on the basis of the canonical molecular orbital energies of the electronic ground state (Koopmans' theorem). Relaxational procedures (e.g. Delta SCF formalism) are a suitable approximation in the case of MO with 40-60% metal character where correlation effects are negligibly small.

The strong-coupling correspondence principle approximation to the S matrix for rotational excitation in atom-rotor collisions is expressed in terms on an infinite series, each term of which corresponds to a well defined angular momentum transfer to the rotor. In this way, numerical averaging over rotor orientations may be avoided and the transition amplitude given as an analytic function of the trajectory integrals. It is shown that the infinite series may be drastically truncated with little loss of accuracy in the important range of impact parameters. The method is applied with success to anisotropic potentials of P₁ and P₂ types, comparison being made in the latter case with close-coupling results for Ar-TlF. The approximation could be useful for other semiclassical theories.

An approximate theory is presented which allows cross sections for rotational transitions in collisions between polar molecules to be estimated. The theory converges to the time-dependent sudden approximation and to the first-order perturbation theory in the appropriate limits; it can be regarded as an approximate form of strong-coupling correspondence principle approximation. Unlike previous theories which have attempted to correct the sudden approximation for adiabatic effects, it treats rotational transitions of 'resonant' and 'non-resonant' type consistently. Its predictions are compared with close-coupling results for the system HF-HF.

Elastic scattering cross sections for electron scattering by N₂ have been calculated in the static-plus-local-exchange model using two different target wavefunctions: Hartree-Fock (HF) and multi-configuration self-consistent-field first-order configuration interaction (MCSCF-FOCI). The range of impact energy considered is 1.5-30 eV. Inclusion of electron correlation in the target wavefunction changes the position of the Pi _g low-energy resonance by about 0.5 eV. Non-resonant partial cross sections typically change by 2% at the equilibrium internuclear separation but sometimes more (up to 26% at the equilibrium internuclear distance and even more at stretched geometries).

Absolute triple differential cross sections (TDCS) for the ionisation of helium by 8 keV electron impact are measured in an asymmetric coplanar electron-electron coincidence experiment (e, 2e method). The angular distributions are made absolute by assuming a cylindrical symmetry about the momentum transfer direction, K, then integrating over all ejection angles and comparing with the corresponding double differential cross section. The latter is independently measured on an absolute scale in a separate experiment. The overall accuracy of the absolute TDCS is about 12%. Systematics in the behaviour of the binary and the recoil intensities as a function of scattering angle and ejection energy are shown. At small K values, the data are discussed in detail in relation to the optical limit (K to 0), and a new qualitative explanation is given for the shift of the recoil lobe axis from the -K direction.

The electron-photon delayed coincidence technique has been used to measure the lifetimes of excited states in He, Ne, Ar and CO that decay with the emission of VUV photons. The states with their measured lifetimes are: He, 5¹P 7.4+or-0.4 ns, 6¹P 14.0+or-0.3 ns, 7¹P 21.6+or-1.2 ns; Ne, 3s(3/2)₁ 20.5+or-0.7 ns; Ar, 4s(3/2)₁ 7.9+or-0.6 ns; CO,C ¹ Sigma ⁺v=0<or=1.5+or-0.3 ns.

The contributions of the excitation-autoionisation transitions 3p⁶4s to 3p⁵3d4s in Ca⁺ and 5p⁶6s to 5p⁵5d6s in Ba⁺ to the total electron impact ionisation cross sections of these ions have been calculated in the distorted-wave approximation. Partial cross sections originating from transitions to three of the nine terms in the configuration 3p⁵3d4s of Ca⁺ are compared with the recent R-matrix close-coupling calculations for these transitions by Burke et al. (1983) in order to determine the effect of continuum coupling between autoionising channels. Both the R-matrix and distorted-wave calculations predict a series of large peaks near threshold in Ca⁺ that are not observed in the measurements of Peart and Dolder (1968). Total cross sections with estimates for the contributions of direct ionisation are calculated and compared with the ionisation measurements of Peart and Dolder for Ca⁺ and of Peart et al. (1973) for Ba⁺. Both LS term dependence in the nd radial wavefunctions and unitarisation are found to have a pronounced effect on these cross sections. The implications of the discrepancies between theory and experiment are discussed.

The absolute scale of the Hg 6¹P₁ direct electron impact excitation cross section has been determined in the positive column of low-pressure mercury discharge. The discharge was studied spectroscopically in a regime where direct excitation and radiative decay are the dominant population and depopulation mechanisms of levels. Using a dye-laser absorption method the author determined the number density of the Hg 6¹P₁ level in the steady state as well as its decay rate in the afterglow under various discharge conditions. From the data the author deduces the excitation rates of the 6¹P₁ level. The electron densities and temperatures in the tail of the energy distribution were obtained from measurements of the radiances at optically thin lines with known excitation functions. With the shape of the excitation function of the 184.9 nm line given in the literature, its absolute scale is obtained from the data. The cascade contribution to this excitation function is less than 15% for 6.7<or=E_e<or=15 eV. The initial slope of the 6¹P₁ direct excitation cross section is (0.35+or-0.1)*10^-20 m² eV^-1, the cross section at 15 eV is (2.1+or-0.6)*10^-20 m².