Table of contents

A method for computing scattering amplitudes and total cross sections is suggested. This is no more difficult than a second Born computation yet it gives results surprisingly good at low and intermediate energies.

Analysis of the numerical range of the atomic Stark Hamiltonian under the dilatation transformation r to re^{i theta} gives sufficient information about the spectrum to justify use of the method for determination of atomic Stark shifting and broadening parameters in DC electric fields.

Lower bounds to the energy levels are obtained from a generalised Brillouin-Wigner equation using the Lippman-Schwinger variational principle. The connection with matrix Pade approximants is discussed and the variational solution to the wavefunctions is given.

An SCF+CI calculation of the potential energy surface of H₂O⁺ in C_{infinity v} symmetry (linear approach) is reported. No energy barrier has been found for the chemical reaction O⁺+H₂ to OH⁺+H. Instead, the energy of the intermediate species (O...H...H)⁺ is found to be 12 kcal/mole below the energy of the input products. This leads to the conclusions that the reaction can actually occur at low temperatures (interstellar clouds) and that the complete potential energy surface is worth computing.

The frozen-orbital (FO) method previously proposed by Gauyacq (1978) to generate diabatic molecular orbitals is improved by the introduction of distortion effects. The basic idea of this 'distorted frozen-orbital' (DFO) method is to calculate variationally the different diabatic orbitals in different orthogonal subspaces defined with the help of the frozen-orbital method. Application to the Ne-Ne collisional system indeed shows that the major defects of the FO method are removed. Cross section calculations are performed in the DFO basis set in order to compare its predictions with those of the previous diabatic basis sets.

The cross sections sigma _i,i+m for the loss of m electrons (m=1, 2, 3) for light ions in helium, nitrogen, neon and argon are measured at ion velocities V=2.7, 4 and 8*10⁸ cm s^-1. The values of sigma _i,i+m are used to obtain the cross sections sigma _i(nl) for outer 1s, 2s and 2p electron loss. It has been shown that in the range of V<or approximately=4*10⁸ cm s^-1 the cross sections sigma _i(2p) for 2p electron loss are 1.2-3 times the cross sections sigma _i(1s) and sigma _i(2s) for 1s and 2s electrons at the same electron binding energy. The relations between these cross sections are in qualitative agreement with the variations of the electron binding energy when the electrons are promoted to the quasimolecular states.

The classical-trajectory Monte-Carlo method has been used to calculate the ionisation and charge-transfer cross sections for the H⁺, He²⁺+He⁺ systems in the energy range 100-500 keV amu^-1. For the H⁺+He⁺ system, the sum of the calculated ionisation and charge-transfer cross sections is found to lie uniformly about 40% higher than the measured values of Angel et al. (1978). However, for both systems the classical-trajectory values are in good agreement with calculations based on the Born and binary-encounter approximations at the higher collision energies.

Cross sections for electron capture and loss by Li⁺, Li²⁺ and Li³⁺ ions in H and H₂ have been obtained in the energy range of 65-1500 keV from measurements using a tungsten-tube furnace to provide a target of highly dissociated hydrogen.

An attempt has been made to resolve an apparent disagreement between two very similar calculations, by Thomas et al. (1974) and Madison and Shelton (1973), for the electron impact excitation of He 2¹P at 80 eV impact energy. The present results are in good agreement with those of Thomas et al. Another parameter is calculated which has not been calculated previously in the first-order many-body theory, and the angular rate of the calculation is extended to compare it with newly obtained experimental data.

Measurements of the energy exchange, Delta E between scattered and ejected electrons following autoionisation of the 2s2p⁶3s(¹S) state of Ne reveal that for sufficiently low values of excess energy E₁, Delta E is no longer proportional to E₁^-1.2, in accordance with a quantum-mechanical model of Bottcher and Scheider (1976) which includes dynamical screening of the ion core.

A method is proposed to determine the dependence of the electron-atom cross section on the energy from measured values of the thermal-conductivity coefficient in a plasma. Preliminary results on Cs are reported.

The effects of a high-density interstitial helium gas on the ortho-positronium (o-Ps) decay rate in the metallic-oxide powders, SiO₂ and MgO, have been investigated. Measurements were made at gas densities 0-170 Amagat (at 293K) and 0-530 Amagat (at 77K). A model is presented in which the annihilation probability is expressed in terms of an effective barrier height against o-Ps penetration into the powder. A lower limit of 0.44 eV for the barrier height is obtained from the data. Indications of an energy loss for Ps moderation in helium gas significantly larger than that in evacuated oxide powders are also discussed.

It is shown that the on-energy-shell single-particle scattering amplitudes obtained from the minimal-coupling and the multipolar forms of the Hamiltonian in non-relativistic quantum electrodynamics are equal to order e²; both forms of the Hamiltonian thus lead to the same differential cross section for Kramers-Heisenberg scattering. The proof given is based directly on the relations which hold between the two transition matrices and is simpler than a previous proof which relied on sum rules derived from the canonical commutation relations. The proof is also more general in that the multipolar Hamiltonian is defined in terms of line integrals along paths which are not assumed to be straight lines but which can be chosen from a large class of possible curves.

The analytic behaviour of the ordinary (f) and exchange (g) amplitudes appearing in the dispersion relation for e^--H(1s) scattering is examined via comparatively simple configuration-space arguments. It is found that the quantity f-f_B is everywhere analytic in the energy (E) plane at energies where the total Green's function G(E) is analytic, in agreement with assumptions made by Gerjuoy and Krall (1960, 1962) in deriving dispersion relations for e^--H(1s) scattering; here the subscript B denotes the first Born approximation. However, the amplitude g-g_B is found to be singular at certain negative real energies, in disagreement with Gerjuoy and Krall's assumptions, but consistent with the recent conclusions of several groups.

The authors have calculated the second-order perturbative corrections to the ground-state energy of He, Li and Be with the Hartree-Fock Hamiltonian as H₀. Increasingly large basis sets were used, up to the point where results stabilised. The converged basis-independent second-order corrections are E_he⁽²⁾=-0.0372 au, E_Li⁽²⁾=-0.416 au and E_Be⁽²⁾=-0.757 au, which amount to 88%, 92% and 80% respectively, of the experimental correlation energies.

The relative importance of the direct and indirect relativistic effects on the behaviour of atomic valence electrons in the Dirac-Fock scheme is investigated for the ground configurations of gold, thallium and lutetium which give information on s, p, p, d and d orbitals. The direct effect, which is always found to contract the relativistic orbital, is completely responsible for the relativistic contraction of the 6s orbital in gold, and the effect is found to become progressively smaller in the order s>p>d approximately d; for none of the systems studied is the direct relativistic effect negligible. The indirect effect is always found to expand the orbital and increases according to the order s<p<p<d approximately d. The consequences of the results for calculations on molecules containing heavy atoms are discussed.

The relative oscillator strengths of eleven resonance lines of copper, having excited levels belonging to the configurations 3d⁹4s4p, 3d¹⁰4p and 3d¹⁰5p, have been determined from atomic absorption measurements of the radiation emitted from a copper hollow-cathode lamp. Allowance is made in the analysis for the effect of differences in the hyperfine structures of the lines. The results are interpreted by considering the effects of configuration interaction and departures from LS coupling, using mixing coefficients derived by Landman et al. (1969).

Measurements have been made on the partial photoionisation cross sections of cadmium (19-30 eV) and mercury (15-35 eV), using the technique of photoelectron spectroscopy and synchrotron radiation from the 5 GeV electron synchrotron NINA. The ²D_5/2:²D_3/2 branching ratios for both cadmium and mercury deviate from the statistical ratio as a function of photon energy, in agreement with recent theoretical calculations; the deviation is greater in the case of mercury, demonstrating the increased importance of relativistic effects.

A density-matrix formulation is given of two-photon ionisation of alkali atoms, for two incoming light pulses of arbitrary direction, polarisation, pulse duration and time difference. The frequency of one of the pulses coincides with a resonant transition. The emphasis is on separating out angular momentum factors from the basic physics contained in the radial matrix elements of the atomic electric dipole. The bandwidth of the exciting light is assumed large compared to natural and induced linewidths. The polarisation of the photoelectron is calculated with or without saturation of the excitation for various values of the nuclear spin.

Vibration-rotation interaction coefficients F_vJ were calculated for the e³ Pi _g-a³ Sigma _u⁺ and E¹ Pi _g-A¹ Sigma _u⁺ transitions of He₂ on the basis of a Morse-Pekeris potential and a polynomial expansion of the dipole-moment function M(r)= Sigma _iM_i(r-r_e)ⁱ reduced to the first two terms. Owing to the importance of F_vJ they cannot be neglected when determining the rotational temperature of He₂ by spectroscopic methods involving line-intensity measurements.

Collisions between metastable O(⁵S) atoms and rare-gas atoms were studied in the energy range from 0.1 eV to about 10 eV. The use of a beam-attenuation technique yielded total cross sections for O(⁵S) in Ne, Ar, Kr, and Xe. Sensitised fluorescence was observed near the thresholds for production of excited O(³S), Kr(³P₁), Xe(¹P₁) and Xe(³P₁). No sensitised fluorescence was observed in the lighter rare gases, Ne and Ar. Total cross sections for O(⁵S) attenuation were obtained as functions of velocity by pulsing the metastable source and using appropriate time-of-flight techniques.

The formalism describing low-energy collisions between a linear molecule and an atom with fine-structure levels is set forth. It is shown that the resulting equations are rendered more tractable by making either the fixed-nucleus or averaged-field approximations. These are usually complementary approximations, but it is shown by physical arguments and numerical calculation that they are in good agreement for Na-N₂ collisions. Using the surfaces calculated in an earlier paper, rotational excitation and fine-structure-changing cross sections for Na(²S, ²P)-N₂(j) collisions at energies between 0.004 and 0.05 eV are presented, the molecule being in its ground vibrational state. The results are in agreement with the single available measurement.

Calculations are performed in the first Born approximation for the formation of He⁺(2s or 2p), the formation of H(2s or 2p) and the ionisation of He⁺(1s) in He⁺(1s)+H(1s) collisions. Close-coupling theory is also employed to examine the effect of coupling for the single-transition processes contributing to the formation of the n=2 states of He⁺ and H. For He²(2s or 2p) coupling is important for helium-ion impact energies less than 300 keV. For H(2s or 2p) coupling is important for hydrogen impact energies less than 1000 keV and 600 keV, respectively. Theory and experiment are good agreement for He⁺(2s) formation and for He⁺(1s) ionisation for impact energies greater than 300 keV and 150 keV, respectively.

Cl^--rare-gas collisions are investigated in the laboratory energy range 80-2000 eV. The main processes are identified by the characteristic energy losses undergone by the scattered particles. Relative differential cross sections for various processes have been measured. Basic similarities with other closed-shell systems (rare-gas-rare-gas and alkali-ion-rare-gas collisions) are underlined, and this gives confidence in the application of the molecular-orbital description to the halide negative-ion-rare-gas collisions. In particular, the use of this model suggests a new type of mechanism for the simple detachment process as an alternative to direct coupling between the incident state and a continuum. The simple detachment proceeds via a two-step mechanism: population of a resonant singly excited quasi-molecular state occurs at small internuclear distance; on the way out, this state autodetaches in the continuum associated with the ² Sigma ⁺ ground state.

New data are reported for the two-electron-one-photon K_{alpha alpha} decay mode of double K vacancies in both collision partners for a variety of asymmetric heavy-ion-atom systems. A model is presented for KK-vacancy sharing that predicts a double K-vacancy ratio R_KK=exp(-4X_K)=R_K² where R_K is the familiar single K-vacancy ratio. There is very good agreement between all available experimental results and the theoretical prediction, consistent with independent sharing of each vacancy in the (2p sigma )^-2 configuration between the collision partners, through 2p sigma -1s sigma radial coupling.

The charge-state distributions of heavy ions after passing through carbon foils with an energy per nucleon E/M<or approximately=20 keV amu^-1, and through gases in the energy domain analysed, i.e. 10<or approximately=E/M (keV amu^-1)<or approximately=300, are very well fitted by the authors' recent 'chi-squared model' (1977). Charge-state distributions in carbon foils for E/M>or approximately=20 keV amu^-1 follow the Gaussian law surprisingly well. Charge-state distributions in carbon foils calculated using either the chi-squared model or the Gaussian model are in better agreement with experimental data than those calculated from the independent-electron model (binomial model).

The unitarised distorted-wave polarised-orbital (UDWPO) approximation is used to calculate integral cross sections for electron impact excitation of the resonance transitions of Be⁺, Mg⁺ and Ca⁺ from threshold to 100 eV. Results are also given in a variety of simpler approximations and the cross sections are compared with other calculations and with experiment. The polarisation of the emitted Ca⁺ K-line radiation is also considered and adiabatic dipole polarisabilities are calculated for the ground states of the above ions.

Using as a definition of resonance, a discrete complex eigenvalue of the rotated Hamiltonian H_alpha obtained from H by the transformation r to re^{i alpha} , it is shown that an infinite sequence of S-wave resonances (disregarding relativistic effects), approaching the H(n=2) threshold along a line, will exist. The location of these resonances depends asymptotically on the generalised scattering length b, which is related to the form of the solution of Schrodinger's equation at the threshold energy. With the help of the Kohn variational principle, b is calculated using Pekeris basis functions (1958), which give rise to a sparse matrix. It is found that the resonances have a small width.

The self-consistent-field method is used to calculate optimised s and p pseudo-states for the low-energy (0<or=ka₀<or=1) elastic scattering and annihilation of positrons by hydrogen atoms. The elastic s-wave phaseshifts and the annihilation rates are determined at functions of incident energy and are compared to similar close-coupling and algebraic pseudo-state calculations where available. In addition, the angular correlation of two-photon pair annihilation radiation at zero energy is presented for the various models considered.