Table of contents

A numerical method based on the solution of the Schrodinger equation with the inclusion of an external field in a confined region is presented. Polarisability values computed here for zero field are shown to agree with existing results. The applicability of the method in calculating polarisabilities for high fields is demonstrated.

The relative intensities of weak K Auger transitions, including M and higher shells, have been investigated. It is shown that the results of RHFS calculations made by Chen et al (1979) are underestimated by 15-25% for Sigma KMX/ Sigma KMM and do not agree with the experimental data for Sigma KXY/ Sigma KMM. Apparently the discrepancy is caused by the low accuracy, in the region of formation of the K Auger transition amplitudes, of the calculation of the wavefunctions of the electrons which are involved in transitions.

The authors report electron energy spectra resulting from MPL of Xe due to two radiation fields of different wavelengths (1064 and 307.5 nm). In addition to the well known 'above-threshold ionisation' (ATI), the authors observed the more general effect of redistribution of final states. In particular, the stimulated emission of photons-an effect which cannot be measured in a one-colour experiment-turns out to play an important role. The consequences of the observed redistribution for the interpretation of ATI are given. In addition, the authors were able to extract rather accurate information about the average intensity of the applied strong radiation field by interpreting the observed spectrum in terms of sidebands.

A procedure for analytically interpolating numerical adiabatic potentials near an avoided crossing is suggested. The procedure is particularly suitable for semiclassical theories of the Stueckelberg type, since they derive non-adiabatic transitions from the analytic properties of the adiabatic potentials in the complex-coordinate space.

Comparison is made between close-coupling calculations of cross sections for the rotational excitation of OH by H₂ and crossed-beam measurements. Good agreement is obtained for transitions within the ² Pi _3/2 ladder, although discrepancies remain for inter-ladder (² Pi _3/2-² Pi _1/2) transitions. Differences with earlier coupled-states calculations by Schinke and Andresen (1984) are found and discussed.

The L₃-subshell alignment parameter for nitrogen and neon impact ionisation of gold has been calculated in the energy range 0.17-1.5 MeV amu^-1. The strong distortion of the L shell caused by the relatively slow heavy ions has been taken into account through a truncated set of coupled equations including couplings between the L substrates only. Considerable improvement has been obtained over first- and second-order Born theories in the description of the experimental data.

An exact analytic evaluation of the second Born contribution of the long-range potentials, which fall off as r^-n as r to infinity , to the phaseshifts of higher partial waves (2l>2n-5) is presented. This expression agrees, for n = 4, with the second term in the energy expansion of the phaseshifts obtained previously by Ali and Fraser (1977). The expression can be used for predicting higher partial-wave phaseshifts as well as for determining the phaseshifts from experimental scattering data.

An empirically fitted Rydberg-like formula for two-electron systems is described. The resultant revised Rydberg formula (RRF) contains two parameters: the screening constant sigma and the correction to the effective quantum number mu . They can concisely correlate a large number of (core)n/sub /il² binding energies. Both are simple functions of the core charge Z, the core configuration and l. The accuracy of the RRF in calculating the two-electron binding energies of over 50 (core)n/sub /is² species is demonstrated and the physical interpretations of sigma _s and mu _s are discussed.

The method of shifted large-N expansion, where N is the number of spatial dimensions, is applied to the study of energy levels and oscillator strengths for the exponential-cosine screened Coulomb potential, V(r)=-exp(- delta r) cos delta r/r. The analytic expressions for the energy eigenvalues. E/sub /n_,l yield very accurate results in general for a wide range of n, l even when the screening parameter delta is large and quite close to its critical value delta _c for which the quantum state becomes just bound. However, for the 1s state, accuracy of the results falls off rapidly at delta approximately=0.8 delta _c. This is because the effective large-N potential becomes quite shallow in comparison with the true potential and the expansion parameter is not sufficiently small to guarantee the convergence of the expansion series for the energy levels. The normalised wavefunctions are used to calculate the oscillator strengths for the 1s to 2p transition for some values of the screening parameter. In spite of the simplicity of this approach, the predicted oscillator strengths compare fairly well with those obtained numerically. The success of the calculation prompts us to make further applications of the shifted large-N technique to other areas of atomic physics.

The authors have calculated the excitation energies and oscillator strengths for electric-dipole-allowed and intercombination transitions between 3s²¹S, 3s3p^1,3P^o, 3p²³P, ¹D, ¹S and 3s3d^1,3D states in Ar VII, Ca IX and Fe XV ions of the magnesium sequence. These states are represented by the fairly large configuration-interaction expansions. The calculations have been carried out in both LS- and intermediate-coupling schemes. The relativistic corrections have been included through the Breit-Pauli Hamiltonian. The results are compared with previous theoretical calculations and with measurements.

For pt.I see ibid., vol.19, p.149 (1986). The effect of the approximate character of the non-relativistic wavefunction on the second-order relativistic energy correction for the ground state of hydrogen-like atoms is illustrated by means of prototype calculations using Gaussian-type basis functions. Generalisation of the concept of even-tempered basis sets for use in relativistic calculations is proposed. Applications using Gaussian-type and exponential-type functions are presented and the convergence of the second-order relativistic correction with increasing size of basis set is examined. Some attention is paid to the possibility of computation of the third-order energy correction using the first-order correction to the wavefunction.

For pt.II see ibid., vol.19, p.3431 (1986). Using the methods described by A. Rutkowski in pt.I (ibid., vol.19, p.149, 1986). A new perturbation approach is extended to two-electron problems. In this approach the Dirac-Coulomb equation is partitioned into an equivalent of the Schrodinger equation and a perturbation. The two perturbations involved each include a different negative power of the velocity of light. The relevant perturbation equations and formulae for the corrections to energy are derived. The method preserves some of the advantages of the Rayleigh-Schrodinger perturbation theory. A relativistic version of the variational perturbation method is formulated. In order to demonstrate the correctness of our two-electron relativistic perturbation theory, particular attention has been given to the exposition that the two-electron approach is consistent with the one-electron approach. It is shown that for the exact non-relativistic wavefunction the author's first-order energy correction is equal to the sum of appropriate quasirelativistic corrections. Numerical results are presented for the ground-state of helium-like atoms.

Generalised master equations in two equivalent forms, namely differential master equations (DME) and integro-differential master equations (IDME), are obtained. Both differ from the Bloch ones in that they take into account the density matrix dynamics during the correlation time tau _C of the relaxational perturbations. On the basis of these equations, the non-linear optical problems of high-power radiation absorption, the resonance fluorescence spectrum and the free induction decay signal are discussed.

Laser-induced Zeeman coherences and non-linear processes in the neon 2p₅(J = 1) to 1s₅(J = 2) transition have been studied experimentally and theoretically. By varying the observation geometry and choice of polarisation, the fluorescence observed in the 2p₅ to 1s₃ (J = 0) transition becomes sensitive to different processes within the atom. A detailed theoretical treatment enables profiles to be matched to the experiment using an appropriate choice of parameters. Moreover, analysis of the equations of motion for the system allows the origins of the various features of the fluorescence profiles to be precisely identified in terms of the generation of higher-order Zeeman coherences in the 1s₅ level and coherent trapping of part of the atomic population there. The population trapping can be interpreted and analysed, for a particular choice of geometry, in terms of simpler subsystems of the full transition.

The detailed rotational analyses for the E bands of the dihydrides and deuterides of Se and Te recorded in a high-resolution photoabsorption experiment, using synchrotron radiation are presented. This provides the symmetry species and effective rotational constants of the excited states. Discrepancies in the intensities of the lines between the observed and theoretical spectra, reveal effects due to homogeneous and heterogeneous predissociation and l uncoupling.

For pt.I see ibid., vol.19, p.3493 (1986). New high- and low-resolution observations of the photoabsorption spectra of H₂Se and D₂Se in the 2600-1200 AA range are presented. The observed Rydberg series are identified from their rotational fine structure, oscillator strengths, definition of possible Rydberg complexes for low n (for which the effects of strong l uncoupling are obvious) and quantum defects. Accurate values for the first ionisation potentials of H₂Se and D₂Se are given.

The spin polarisation of electrons elastically scattered from xenon is calculated via a relativistic form of the Schrodinger equation for energies from near threshold to 300 eV. The static and relativistic potentials used are calculated from relativistic Hartree-Fock wavefunctions while the polarisation potential is derived from a non-relativistic polarised-orbital calculation. Exchange is included exactly for the large component of the scattered wavefunction. Very good agreement with recent experimental measurements is obtained over the whole energy range.

Polarised electrons have been scattered elastically from mercury and xenon. The angular distribution of the parameters that describe the change in the electron polarisation caused by the scattering process has been measured in the energy range from 25 to 150 eV for mercury and from 40 to 350 eV for xenon. With these parameters, in conjunction with the absolute differential cross section, a complete analysis of the scattering amplitudes with respect to their magnitudes and their relative phase is performed for xenon.

The previously developed two-potential approach for electron-molecule scattering is applied to the scattering of electrons by the hydrogen molecule. Differential cross sections for both elastic collisions and vibrational excitation are calculated at electron impact energies of 50-700 eV. Comparisons with the available experimental data are made.

The virial theorem is used as a supplementary constraint, in conjunction with a normal variational principal, in order to obtain wavefunctions for the (2s²)¹S, (2p²)¹S, (2p²)¹D, (2s, 2p)¹P and (2s,2p)³P autoionising states of helium. Good energies are obtained, except for the ¹D state. The angular-correlation properties of the wavefunctions are compared with those of Lipsky-Conneely type functions (1977) and the effect of the mixing of the s² and p² configurations in investigated for the ¹S states. A comparison is made of the resonance widths calculated using various approximations for the degenerate continua and matrix elements of either the Hamiltonian H or the operator (PHQ+QHP). A compact and relatively simple expansion basis is used in order to simplify subsequent collision calculations. This does not allow mixing with higher autoionising states to be taken into account; this affects the correlation properties of the ¹P and ³P states and the width of the (2p²)¹S state.

A first-order model for the autoionisation of helium by electron impact is proposed in which full account is taken of exchange and in which the principal resonances are each described by two angle-dependent parameters. It is also shown how second-order terms may be incorporated into the model. The wavefunctions for the incident, scattered and ejected electrons are calculated using the polarised-orbital approximation. Results are presented for the triple differential (e-2e) cross section for the (2s²)¹S, (2s,2p)³P and (2s,2p)¹P resonances at incident energies of 70 and 80 eV for a scattering angle of 15 degrees and also for the double differential cross section corresponding to an integral over the scattering angle. The limits on the validity of this type of model are discussed together with the possible errors introduced by the use of a simplified representation of the autoionising states.

The absolute triple differential cross sections for the ionisation of helium measured recently by Jung et al (1985) in coplanar asymmetric geometry at 600 eV incident electron energy are analysed using the second Born (B2) and the modified Glauber (MG) approximations. Our MG results show better agreement with the data, both in the binary and the recoil peak regions, compared with the B2 results.

The authors present collision strengths in the LS-coupling scheme for transitions between the ground state 3d⁶4s⁶D and the first three excited states 3d⁷⁴F, 3d⁶4s⁴D and 3d⁷⁴P of Fe II using the R-matrix method. The authors include these four target states and all the appropriate short-range correlation terms in the expansion of the total wavefunction of the system. The target states are described by configuration interaction wavefunctions. Since the cross sections are dominated by resonances, the authors tabulate effective collision strengths for a wide range of electron temperatures assuming a Maxwellian distribution.

Angular dependences of the elastic scattering of electrons from CH₄ for impact energies between 0.2 and 5 eV in the angular range between 15 degrees and 138 degrees are presented. Absolute differential cross sections have been obtained. With the help of a phaseshift analysis, integrated cross sections are calculated. The Ramsauer minimum is found to be at a collision energy close to 0.45 eV. The sum of the integrated vibrationally elastic cross sections and the vibrational excitation cross sections yields the total cross sections. These data are compared with the recent data for sigma _T of Ferch et al. (1985).