Table of contents

High-resolution EUV spectra of doubly excited (nln'l') resonances in He I with n and n'>or=2 have been studied by 2 and 5 MeV C⁴⁺ impact on He. Radiation from narrow and supernarrow He I resonances have been observed for the first time.

Detailed analysis of profiles of the calcium 422.7 nm resonance line obtained by laser-induced fluorescence show departures from the usual reduced Voigt form. These discrepancies are shown to be consistent with a fit of the profiles to a Voigt profile with corrected velocity averaging together with an asymmetric component due to the radiation emitted during the collision. An expression for the complete profile in the low pressure limit is given.

Recently calculated collision cross sections for potassium-argon collisions are modified to allow for the presence of nuclear spin and are compared with experimental cross sections for the relaxation of orientation in the resonance levels. The experimental precision is found to be sufficient to decide between the proposed potentials.

Two neglected aspects of rainbow scattering are discussed: (i) monotonously decreasing (repulsive) potentials can sometimes show rainbow effects; (ii) relatively deep potential minima do not necessarily lead to larger rainbow angles mod theta ^R mod than slightly shallower ones. Thus there exist potentials with one minimum and a repulsive core for which the relationship V₁(r)<V₂(r) is fulfilled for all r>0 (i.e. mod V_1min mod > mod V_2min mod ) but which produce rainbow angles with mod theta ₁^R mod < mod theta ₂^R mod .

The authors have computed the cross section for charge transfer from atomic hydrogen to the excited 3s level of doubly charged nitrogen, triply charged nitrogen and atomic hydrogen at very low relative collision energies (mcV). A rich resonance structure is found and interpreted in terms of quasi-bound states associated with the classical phenomenon of orbiting. Possible experimental verification of the resonance structure is discussed.

Expressions for quantities such as reactance and scattering matrices, in terms of the R matrix, appear to become indeterminate at energies E equal to energies E_k at which the R matrix has poles. It is shown that determinate expressions are obtained using a diagonalisation procedure. Use of the procedure can give improved accuracy and stability in making numerical calculations at energies E such that mod E-E_k mod is small. Use of the method for bound-state calculations is also discussed.

New relativistic equations are presented for atoms composed of two particles of spins <1 and arbitrary mass ratios. The equation for one spin-¹/₂ particle has exact solutions for the point Coulomb potential. The equation for two spin-¹/₂ particles contains no tensor force and predicts a new value for the hyperfine quadrupole moment.

For pt.III see ibid., vol.17, p.1699 (1984). An adiabatic generator coordinate method (GCM) is derived and applied to calculations of vibrational states in the Henon-Heiles potential system. It seems that the adiabatic GCM is preferable to the standard adiabatic approach.

A semiclassical self-consistent field method for specification of the structure of a complex atom is developed. The procedure utilises classical position probability densities and a modern version of the Bohr-Sommerfeld-Wilson quantisation condition. The semiclassical results are compared with non-relativistic quantum mechanical Hartree-Fock calculations, and energy eigenvalues and average values are found to be in remarkably close agreement. A relativistic extension of the semiclassical method is used to investigate the fine structure of highly ionised members of the Cu isoelectronic sequence. The calculations suggest two ways in which the observed break near Z=60 in the screening parametrisation of this system could occur.

For pt.I see ibid., vol.17, p.23-75 (1984). As an illustration of the theory developed in the first paper in this series, a set of five orthogonal parameters is used to describe all electrostatic two-particle excitations in the 3d^N configurations completely to second order. These parameters represent the term energies of d² and, consequently, the 3d^N configurations are perceived as a collection of ¹/₂N(N-1)d² pairs, the total energy of the configuration being the sum of the corresponding pair energies. As regards their effects, the parameters are partitioned into a structural and an additive part; the structural part is found to behave as a linear function of N, whereas the additive part is proportional to the average energy of the configuration. In order to take into account all electrostatic one-particle effects as well, two orthogonalised three-body parameters T₁ and T₂ are used, the first corresponding to the well known Trees parameter and the second covering the remaining class of one-electron excitations. With a least-squares fitting procedure, both the d² energies and the three-electron parameters are determined for the d^N ground configuration in the III, IV, V and VI spectra of the iron group elements. Surprisingly, the effects of T₂ turn out to be important, especially for the lower ionisation stages. Amongst other things, old problems concerning the far-off position with respect to calculations of the ¹₂D term in the 3d⁶, and parameter irregularities in the 3d⁷ configurations, seem to be solved with the introduction of T₂. As a result, the mean error of the fit in some of these cases is reduced by factors of three to four. Using the above set of parameters, a prediction of the 3d⁴ ground configuration of Mn IV is made.

A many-electron theory of autoionising states in terms of complex coordinates has been applied to the case of Be⁺ 1s2s²²S. The authors show how the magnitude of the problem can be reduced systematically, by emphasising separate calculations on the real axis and the complex plane. The width is obtained from repeated diagonalisations of small (2*2 or 3*3) complex matrices which optimise nonlinear parameters of the Gamow orbitals. The results are E=123.77 eV, Gamma =0.027 eV. The experimental value for E_exp=123.6+or-0.1 eV. Recently published results from the second-order dilated electron propagator method are E=125.02 eV, Gamma =0.050 eV. (The theoretical energies include a contribution of 0.027 eV from relativistic effects).

A new analytical treatment is developed for resonant multiphonon ionisation which takes into account the physical properties of the exciting laser such as the spatial intensity distribution of a focused Gaussian beam and light statistics effects in the narrow bandwidth limit. The ion number as a function of laser intensity and wavelength follows a 'displacement law', which means that it may be expressed as a single variable function and provides a more reliable way to determine light-induced level shifts than previous methods. Three-photon resonant five-photon ionisation of mercury in a chaotic field serves as an experimental test and agrees excellently with the displacement law. However, the derived dynamical Stark shift differs by about a factor of three from that calculated from currently known oscillator strengths.

For pt.I see ibid., vol.17, p.4135 (1984). Using a previously described new method to evaluate light-induced level shifts, it is experimentally demonstrated that the two possible intermediate 6D₂ states in four-photon resonant five-photon ionisation of mercury are mixed at high laser intensities. Due to this mixing, the AC Stark shifts of these levels are no longer quadratic in field amplitude. This is in good agreement with a simple theoretical model. This makes a direct determination of the oscillator strengths for two mercury lines possible.

The secular approximation is used to calculate an analytic expression for the absorption spectra for one- and two-atom systems. The analysis is valid for high field strengths and arbitrary frequency detuning.

The authors have considered the problem of adiabatic rapid passage (ARP) in a dressed atom formalism. They find that the conditions for ARP can be understood as conditions for minimising the probability of dressed atomic state transitions, and that these probabilities can be used to obtain an estimate of the degree of population reversal. Furthermore, by considering ARP in the dressed atom formalism the similarity between ARP and the Landau-Zener non-adiabatic transition problem is made quite apparent.

Experimental studies of inner-shell alignment investigate the anisotropy or polarisation of emitted X-rays or electrons. In the case of a single vacancy the alignment can be derived from the measured anisotropy by well known formulae. In case of multiple vacancies the observed alignment may be different from the collisionally-induced alignment: post-collision interaction of the vacancies within their lifetimes may perturb the alignment. Examples are discussed and numerical values of the depolarisation caused by coupling with an isotropic spectator are given.

A crossed-beam apparatus with photon detectors is used for the determination of absolute photon emission cross sections for inelastic H⁺-Li(2s) collisions. The authors present details of experimentation and Li(2p) excitation cross sections for proton impact energies of 2-20 keV. The latter data compare well with available theory and are also discussed in context with active neutral Li beam diagnostics of magnetically confined plasma.

For pt.I see ibid., vol.17, p.4185 (1984). Absolute cross sections for L_alpha , L_beta and H_alpha emission resulting from H⁺-Li(2s) collisions at 2-20 keV impact energy have been measured. From these data electron capture cross sections were obtained for the H(2p), H(3s), H(3p) and H(3d) subshells, respectively. The results are presented and compared with available theory.

A simple one-electron potential with a dipole tail is used to study the tracks of poles of the scattering amplitude in the complex momentum plane, close to the origin, and for states with a large s-wave component. Several Riemann sheets have to be considered, because the dipole tail leads to a branch point at the origin. On the 'physical' sheet, there is a single track in the upper half-plane; it follows the positive imaginary axis down to the origin and stops there. On other Riemann sheets, there are two distinct tracks in the lower half-plane, which are mirror images of one another in the negative imaginary axis. They meet the track on the physical sheet at the origin. The tracks in the lower half-plane exist only if the dipole moment is less than 1.19 D, and collapse to the negative imaginary axis if the dipole moment vanishes.

Effective-range theory for electron scattering by non-polar molecules is considered. Low-energy expansions for total and diffusion cross sections are obtained, including terms of the order of k and k² ln k which depend on both the polarisability and quadrupole moment. A comparison with the theory of Chang (1978, 1981) is presented. The results are used for the description of experimental data for e-H₂, N₂ and CO₂ scattering. Comparison with ab initio theoretical results is also given. For the e-CO₂ scattering length in the fixed-nuclei approximation the estimate -7.2<A<-6.8 is obtained.

The absolute experimental (e,2e) cross sections for electron impact single ionisation of helium atoms at an incident electron energy of about 8 keV were measured by Lahmam-Bennani et al. (1983) using an asymmetric geometry. These results are utilised to test various wavefunctions describing the ejected electron when employed in the factorised plane-wave first Born approximation. The results indicate that the use of a Coulomb wavefunction, constructed to be orthogonal to the wavefunction describing the ejecting orbital and assuming an effective charge of +1.05 for the ion formed by the collision, is adequate to describe quantitatively all the important features of the absolute experimental results.

The effect of plasma on the electron impact excitation of He⁺ is investigated. The collision strengths for 1s-2s, 1s-2p and 2s-2p transitions are calculated in the framework of a two-potential approach along with the Debye-Huckel model for plasma screening. Comparison is made with the other calculation.