Table of contents

Three-dimensional non-separable problems of wave mechanics are solved in terms of generalised power series solutions. Non-central interactions are shown to produce, in general, logarithmic terms in regular wavefunctions. A necessary and sufficient criterion for the appearance of logarithmic terms is derived.

Using a two-step two-photon laser excitation, 9dn'd doubly excited states of neutral barium atoms have been observed for n'=18 to 31. Corresponding quantum defects and autoionisation rates are reported. The interpretation of spectroscopic data (resonances, asymmetric line profiles) is discussed in terms of quantum defect characterisation of the involved wavefunctions.

The K-shell photoionisation cross section of argon has been calculated in the length and velocity gauge using the Dirac-Fock method. The relaxation is taken into account completely by constructing separate solutions for the ground state and the final 1s^-1 hole state and by including all the resulting overlap matrix elements between the initial- and final-state one-electron four spinors in the transition amplitude. The post-collision interaction has been taken into account quantum mechanically by incorporating the lowest-order scattering theory amplitude into the cross section. The authors' results reveal dramatic relaxation effects in the threshold region bringing the theoretical cross section into close agreement with experiment. The cross section is nearly gauge independent with only the E1 multipole contributing significantly. The post-collision interaction is found to lower the cross section by 15% at threshold. This result is attributed to inadequacies in the lowest-order treatment of the influence of the residual ionic field on the photoelectron.

The authors propose a candidate mechanism for the lambda =564.6 nm resonance in multiphoton ionisation of calcium observed by Agostini and Petite (1984).

The authors have studied the five-photon ionisation of H₂ via the four-photon resonance on the E, F¹ Sigma _g⁺, v_E=2 from X¹ Sigma _g⁺, v=0 transition. A dye laser delivering up to 5*10¹¹ W cm^-2 around 3860 AA is focused into an H₂ cell at room temperature and at a pressure of 5*10^-4 Torr. The time-of-flight mass spectrum exhibits comparable signals of H⁺ and H₂⁺ thus demonstrating the existence of an important dissociative mechanism superimposed on the ionisation channel. Different processes are considered to tentatively explain this unexpectedly high probability of the multiphoton dissociation of H₂.

Sulphur ions of energy 125 MeV with initial charge states q=10+ to 16+ have been passed through 4-200 mu g cm^-2 carbon foils. The generated convoy electrons which emerge from the foils in the forward direction with approximate beam velocity, have been measured. The authors find a strong dependence of the convoy electron yield on the initial charge state of the ions, suggesting that (i) convoy electrons are produced primarily by electron loss to the continuum (ELC) and (ii) the mean free path of convoy electrons is larger than that for electrons moving freely in solids.

A merging-beams technique is used to obtain absolute and relative cross sections for the ion pair production process Na+Cl to Na⁺+Cl^- in which the reactants and products are in the ground state. The relative kinetic energy of the reactants is varied from near threshold at 1.52 eV to 10 eV. The data are compared with the theoretical calculations of Faist and Levine (1976).

High-quality measurements of differential cross sections (DCS) for He-N₂ and He-O₂ collisions at a centre-of-mass energy of 27 meV have recently produced angular distributions for the total DCS and for various individual, rotationally inelastic processes. A previous multiproperty analysis carried out by the authors on the above systems had yielded very accurate forms for the corresponding potential energy surfaces (PES) that describe the anisotropy of the interactions. In the present work fully converged, close-coupling (CC) calculations and approximate IOS results are analysed and compared with the experimental data. The acceptable agreement found between the two computational methods and the very good accord of the calculated points with the measured DCS indicate the validity of multiproperty studies based on the IOS treatment of the available dynamical observables from beam experiments.

Calculations of the s-wave scattering of electrons by positronium with energy less than 7.35 eV are reported in a simple static exchange model based on the for e^--H, the full static exchange model, and an accurate variational model. The pattern of the results is similar to that for scattering by atomic hydrogen. The lowest ¹S resonance is seen at E_r=4.768 eV with a width of 1.6 meV. The zero-energy limit of the elastic cross section is close to 228 pi a₀².

By appeal to a Thomson-style treatment of recombination, it is shown that the rate for recombination of ions generated with uniform frequency within a reaction volume is a factor of ⁹/₄ times greater than the rate for recombination of ions which approach each other from infinite separation. A valuable relationship connecting the two problems is uncovered. The analysis is pertinent to recombination involving dilute and high degrees of ionisation.

It is shown that the application of the partitioning technique to the Dirac equation in the algebraic approximation has a number of advantages: (i) a correct matrix representation of the Schrodinger equation is obtained in the limit c to infinity ; (ii) the positive and negative energy solutions are separated; (iii) it has variational properties which are independent of the choice of basis sets for parametrisation of the large and small components of the relativistic wavefunction; (iv) a relativistic generalisation of the bracketing function can be obtained, (v) it leads to improved numerical accuracy. These advantages of the partitioned Dirac equation are illustrated by means of prototype calculations.

Neutral-atom binding energies, computed using the Slater transition-state concept in the relativistic Xi method, are reported for various atoms. It is shown that the relaxation and relativistic effects are well accounted for by the present relativistic transition-state calculations. The reported values are generally in good agreement with the experimental values and the agreement is particularly satisfactory in the case of valence levels. Slight discrepancies in the 1s level of heavier atoms may be due to the Breit interaction corrections and because finite-nuclear-size effects are not accounted for fully in the present calculations.

A series of increasingly accurate wavefunctions for H^-, and He built from Gaussian geminals is presented. Such wavefunctions are found to be much more compact than configuration interaction wavefunctions of similar accuracy. Moreover, comparison with nearly exact values shows that they predict one- and two-electron moments in position space quite well but perform less satisfactorily with respect to point properties. The wavefunctions can be Fourier-Dirac transformed in closed form and are used to predict values of one- and two-electron momentum space properties including Compton profiles. Most of these momentum properties are expected to be of benchmark quality.

A new proposal for determining CI quasi-diabatic states, potential energy surfaces and electronic couplings is introduced using the quasi-degenerate perturbation theory (QDPT); zeroth-order CI adiabatic states, resulting from a partial diagonalisation, are submitted to a unitary transformation in order to yield quasi-diabatic states presenting the maximum overlap with an external set of independent diabatic reference functions. An effective Hamiltonian in the quasi-diabatic representation is then obtained by applying the QDPT in the model space spanned by the quasi-diabatic states. This algorithm is exemplified by the HeNe²⁺¹ Sigma ⁺ states for which the dynamical couplings are computed using finite difference techniques combined with first-order transition density matrices.

A model-potential method including core polarisation effects is used to obtain the Sigma , Pi , Delta states of Na₂⁺ and K₂⁺, up to the states dissociating to the 6s atomic state. Dipole moments and radial coupling matrix elements are calculated. The structure of the energy curves is analysed in terms of molecular quantum defects.

Discontinuities attributed to multielectron excitations were observed in the X-ray absorption spectra of thulium (₆₉Tm). They were identified as being the results of 2s^-2, 2s^-1+2p₁2/^-1, 2p₁2/^-2, 2p₁2/^-1+2p₃2/^-1 and 2p₃2/^-2 excitations. Their measured energies and the results of a non-relativistic Hartree-Fock calculation are in general agreement. The observed splitting of the (2s^-1+2p₁2/^-1) discontinuity was explained on the basis of intermediate coupling calculations. The cross sections of these discontinuities were found to be between 1.6+or-0.4 and 1.9+or-0.4 per cent of the L₃-absorption cross section of the element.

The polarisation of the Ll X-ray line of ₂₇Co, ₂₈Ni, ₂₉Cu and ₃₀Zn targets induced by proton impact has been measured at ion energies ranging from 60 keV to 2.4 MeV. The polarisation is attributed to the collisionally induced alignment of the 2p_3/2 vacancy. Measured polarisation values show strong dependence on the target nuclear charge. The small values found particularly in Co and Ni are attributed to a dealignment after the collision caused by angular momentum recoupling between the 2p_3/2 vacancy and the partially filled 3d shell. For Cu and Zn the dealignment is expected to be small, and the collisionally induced alignment has been derived from the measured polarisation values. The experimental alignment data agree with the theory only qualitatively.

The ejected-electron spectrum of tin vapour atoms has been observed at 75 degrees to an incident electron beam of 20-1000 eV kinetic energy. A total to 71 lines are reported in the ejected-electron energy range 0-20 eV corresponding to autoionisation processes in Sn I and Sn II. Calculations have been used to make new assignments to the sp²np, d⁹s²p³ and d⁹s²p² configurations. The results are compared with data from photoabsorption measurements, arc spectra and theoretical calculations.

The long-range diamagnetic interaction arising from the Earth's magnetic field produces a striking change in the photoionisation Stark spectra. The profiles of the supplementary resonances observed for the excited sodium atoms are typical of continuum-continuum state mixing.

Using recent measurements of multiphoton free-free transitions in e-Ar scattering in the presence of a CO₂ laser as reference data, an analysis is made of the role different properties of realistic lasers may play in affecting the cross sections of multiphoton transitions. Single-mode and N-mode fields are considered with and without given statistics, emphasis being placed on few-mode cases. Spatial and temporal inhomogeneities, accounting respectively for the focusing and pulsed regimes, are also taken into account. While a complete and detailed agreement is probably out of the question at the present due to incomplete knowledge of all the experimental conditions, the basic and most important features are reproduced with satisfactory agreement. To achieve this agreement a decisive role is played by spatial and temporal inhomogeneities irrespective of the particular laser model in which they are considered.

Total photoelectric cross sections were measured for 279 and 661 keV photons in Y, Ce, Dy and Yb by direct measurement of the photoelectron intensity using a well-type plastic scintillation spectrometer in conjunction with a multichannel analyser. The experimental values were found to be more or less in agreement with the interpolated theoretical values of Storm and Israel (1970) and of Scofield (1973) and with the values of Veigele (1973) which were mostly based on previous experimental results.

The range of very low collision energies where shape resonances may occur has been systematically explored by pure quantum mechanical calculations in the case of Lennard-Jones (12-6) systems. Semi-empirical formulae have been established which lead, from the characteristic parameter of the system: b_z=2 mu epsilon r_m²/h(cross)², to the prediction of the number of quasi-bound rovibrational states of the molecule temporarily created during the collision. It is shown that the number and the nature of the shape resonances are periodical functions of B_z¹2/. These results can be used either to predict experimental results or to determine the potential parameters from experimental data.

Photoelectron asymmetry parameters beta have been measured for ionisations from the valence molecular orbitals of the molecules CFCl₃, CF₂Cl₂ using CF₃Cl using photons in the energy range 18-80 eV. Cooper minima are observed in the beta spectra for ionisation from orbitals with substantial chlorine 3p character. For Cf₂Cl₂, three resonances are observed in beta spectra which are tentatively assigned to shape resonances.

Absorption measurements have been made in the near blue wing and over a 75 nm range in the red wing of the 213.8 nm Zn line for nine temperatures between 685 and 1030 degrees C and for Zn pressures between 2.5*10^-3 and 1.3 atm. The data are analysed wit the statistical theory of broadening. At the lowest pressures and near the line centre the line is symmetrical and an oscillator strength of 1.502+or-0.044 is obtained. The red wing is assumed to arise from transitions to a single, non-degenerate excited state with a constant oscillator strength that is one-third the value for the isolated atom. The ground-state and excited-state potentials are then obtained as a function of R³-R_ref³ where R is the interatomic separation and R_ref is not fixed by the authors' experiment. The depth of the minimum in the ground state is 46 meV with a standard deviation of 10 meV. No minimum in the excited-state potential is seen but a lower limit of 1.2 eV for its depth is fixed. Taking one value of R from the calculation of Hay et al. (1976), the authors have constructed the potentials in terms of R between 0.27 and 1.38 nm. The authors' excited state falls below the calculated result at the smallest values of R.

The relaxation of highly excited Rb(7²S₁2/) atoms by collisions with excited K(4²P₃2/) atoms is investigated using the time-resolved spectroscopy technique. An estimation of the effective cross section is (5.6+or-0.6)*10^-13 cm² at a working temperature T=593K. A comparison is made with similar processes involving atoms of the same species.

The triple differential cross section for the ionisation of atomic hydrogen by fast electrons is analysed in the case of the coplanar, asymmetric geometry within the framework of the eikonal-Born series theory. Detailed calculations are performed for an incident electron energy of 250 eV, and ejected-electron energy of 5 eV and several angles of the scattered electron. The authors find that second-order effects are crucial in explaining both the positions and magnitudes of the binary and recoil peaks. Their calculations are in excellent agreement with recent absolute measurements.

Cross sections for the dielectronic recombination (DER) of electrons with Mg⁺(3s) are calculated for electron energies just below the 3s to 3p excitation threshold. Fine structure is explicitly treated by using pair coupling to define the states Mg(3p(J_i); nl), and the autoionisation rates of these states are obtained by extrapolating electron-ion scattering calculations downward across the ionisation threshold using quantum defect theory. The physical effect of fine structure is significant; a manifold of autoionising states split by the spin-orbit interaction makes a greater contribution to the cross section than the same number of degenerate states. The present results, averaged over the experimental conditions of Belic et al. (1983), have a maximum value of 4.2*10^-18 cm².

An electron spectrometer which incorporates a position-sensitive detector and differential pumping has been used to obtain spectra of molecular chlorine up to the second ionisation potential A ² Pi _u. This is the first experimental work to reveal transitions above 11.3 eV and the first using electron impact to produce spectra with a scattering angle as high as 90 degrees . The best energy resolution displayed in the present spectra is 18 meV (FWHM) which is significantly better than any previously reported. Features which are forbidden by electric-dipole selection rules are discerned by obtaining spectra using a variety of scattering conditions. Many previously reported transitions are seen plus approximately seventy new ones, some of which combine to form three Rydberg progressions and eight new vibrational series. Five of these series are allowed by electric-dipole selection rules and three are spin forbidden.

Positronium yields and the annihilation rates of free positrons and orthopositronium have been measured as functions of density and electric field in methane gas at room temperature. Positronium yields and Z_eff show complex dependences on density. Positronium yields were measured at three different densities and were found to decrease with increasing electric fields. For the range of electric fields investigated, the annihilation rates are independent of the applied field. These results are discussed in terms of current models.