Table of contents

Atomic and molecular properties dependent on the valence electrons are sensitive to intra-atomic correlation effects, and these tend to be largest in atoms of high atomic number where accurate ab initio computations are difficult. A simple model potential method is proposed for including correlation effects in Hartree-Fock calculations. Application is made to an electron-gas computation of the Hg₂(X¹ Sigma _g⁺) potential.

A simple connection between the Baylis pseudopotential and the Nikitin-Smirnov-Roueff potential is established. A semi-empirical potential is suggested for excited-state-ground-state atom pairs.

Calculations are presented on the widths and shifts of the following transitions in calcium perturbed by helium and neon using model-potential curves: 4s5s³S to 4s4p³P, 4s4p³P to 4s²¹S and 4s4p¹P to 4s¹²S. A comparison with experimental data is given. Results are also presented for lithium (2p) broadened by helium.

Photon emission between 200 and 800 AA and production of slow ions and slow electrons have been investigated in 25 to 800 keV collisions between singly and multiply charged Ne ions (z=1-4) with He and Ar. When z is increased, electron capture into excited projectile states contributes increasingly to the total single-electron capture process. At z=4 excitation inversion in the fast product ions can be demonstrated. Furthermore, the considerably enlarged slow-electron production for high-z projectiles is ascribed to the onset of capture ionisation processes.

The total cross sections for single electron capture in proton-helium collisions with due allowance for momentum translation effects are calculated in the 3 to 200 keV range. Following Burns and Crothers (1976), the two state impact parameter equations are integrated numerically and the phase integral nonadiabatic theory applied analytically. The computer time compares extremely favourably with previous treatments, due to the adoption of simple one electron symmetrised matrix elements being the leading terms in the asymptotic expansions appropriate to the energy range. The results are remarkably accurate whether in the non-adiabatic range (3 to 20 keV) or the two step Thomas model range (20 to 200 keV).

The relationship of the optical model to the distorted-wave second Born approximation is discussed, in the light of recent comments by Dewangan and Walters (1977).

The elastic scattering and rotational excitation cross sections for e^--H₂ are calculated in the adiabatic nuclei approximation, using the 'semiclassical' and 'free-electron-gas' local exchange approximations. The integrated elastic scattering results are compared to calculations in which exchange was treated 'exactly', over the energy range of 0 to 20 eV. The semiclassical exchange approximation is found to agree best with the 'exact' results for energies above 6 eV. The differential elastic and rotational excitation cross sections, for the various local exchange approximations, are compared with experimental measurements and a similar semiclassical exchange calculation at 10 eV.

The angular correlations of the 'scattered' (186.4 eV) and 'ejected' (50 eV) electrons have been measured for the ionisation of hydrogen atoms by 250 eV incident electrons. The shape of the five-fold differential cross section is in poor agreement with Born, plane-wave Born and the Coulomb-projected Born approximations.

The ejected-electron spectrum of cadmium vapour following autoionisation of two-electron excited states of the type 4d¹⁰5pnl has been observed from 0.7 eV to 5.8 eV. Ejected electrons were energy analysed at 75 degrees to the direction of an incident electron beam of energy 15 to 400 eV. 25 new lines are observed for the first time, in addition to the 39 lines reported for this region in earlier work. Of these, 51 lines are attributed to two-electron excited states. Comparison is made with the ultraviolet observations of Mansfield.

A formulation of the Feshbach projection-operator technique for a three-electron system is presented which renders practicable the calculation of the H₂^- resonance positions, and ultimately their widths, by standard configurational interaction methods. Striking and hitherto unidentified resonances in the 0 to 12 eV region have been discovered and these may lead to a more complete interpretation of the existing experimental results.

Hypervirial relations are used in a method of obtaining recurrence relations for matrix elements of powers of the radial distance for problems with spherically symmetric potentials. The method is generalised to include matrix elements involving radial functions with different values of l. Recurrence relations are obtained for the hydrogen atom, the isotropic harmonic oscillator and the isotropic oscillator with a quartic term. For the hydrogen atom the results obtained agree with recurrence relations previously obtained.

A theoretical treatment of long-living decaying states in resonance phenomena is given from the viewpoint of decaying bound states. The effective Hamiltonian for the Kapur-Peierls resonant state is constructed in this theory by distinct potentials or operators. This theory is based on a method of coupled equations similar to the Faddeev equation, and hence no projection operators are needed to construct the effective Hamiltonian. The 'extended' Hellmann-Feynman theorem applied to the resonant states is developed. Particularly, the energy gradient of the Kapur-Peierls eigenvalue is found in a compact form in terms of the original bound state which decays and the reaction operator. The difference between the Siegert resonant-state energy and the particular solution of the Kapur-Peierls eigenvalue problem at the resonant-state energy is estimated. A simple example of tunnelling problems is given.

Total photon cross sections are determined around the K edges of four elements Cu, Sn, Pb and U using a Ge(Li) detector, argon and krypton proportional counters on a 'good geometry' set-up. The total photoelectric cross sections are extracted by subtracting the small scattering contribution from the total photon cross sections. Total-to-K-shell photoelectric cross section ratios (K-jump ratios) are evaluated by extrapolating the total photon cross section data to the K-edge. An analysis of the data is presented.

The R-matrix theory of atomic photoionisation using the Dirac Hamiltonian is formulated in a similar way to that used in the non-relativistic case. Both the initial atomic bound state and the final atomic continuum state are expanded in terms of R-matrix bases. The method is programmed for a general atomic system and then used to calculate the total photoionisation cross sections of ground-state neon atoms.

New measurements of the angular distribution parameter beta _4p(E) for photoelectrons emitted from the 4p shell of krypton by synchrotron radiation are reported. Analyses of these data produce an empirical pseudopotential together with predictions of beta _4p(E) and the total cross sections sigma _4p(E) for photoelectron energies from threshold to greater than 100 eV. The predicted cross sections are compared with recent experimental data obtained at the Synchrotron Radiation Facility on the Daresbury Laboratory 5 GeV electron synchrotron NINA. Both beta _4p(E) and sigma _4p(E) are well described by both RPAE and pseudopotential theories, suggesting that the latter aptly mimics the exchange and correlation effects throughout the range of observation.

A new band of CuO with head at 6522.1 AA has been analysed and interpreted as a ² Delta _5/2-x² Pi _3/2 transition. The constants derived for the new ² Delta _5/2 state are (in cm^-1): T₀=15317.24, B₀=0.4253₆, D₀=0.84₅*10^-6.

Si K_alpha spectra from Si, SiC, SiO₂ and Si₃N₄ have been measured in fluorescence by using a double crystal spectrometer. The chemical shifts, the linewidths as well as relative intensities have been observed for K_{alpha 12} as well as for K_alpha satellite lines. The measured K_{alpha 1} X-ray width is 0.43 eV. The chemical environment affects all K_alpha lines and this effect is especially strong on the satellite lines. Satellite structure in pure silicon is discussed based on the TOP calculations of Aberg et al. as well as on intermediate coupling.

Elastic and inelastic collisions of metastable He* atoms on He have been investigated experimentally by electrostatic energy analysis of electrons and ions arising from the collisions, and by time-of-flight analysis of the scattered neutrals. Collision energies were between 1000 and 1400 eV in case of He⁺ and He analysis and up to 5000 eV for the electron analysis. Excitation of autoionising He states was observed in all spectra. Contributions to the spectra due to collisions of ground-state atoms, which were also contained in the beam, could be identified and thus relative differential cross sections for pure He*-He scattering were determined for reduced scattering angles tau >or approximately=2.5 keV deg. Scattered ions were only analysed at a scattering angle of Theta =8 degrees and therefore the authors could not investigate ionisation processes leading mainly to small scattering angles, e.g. the direct coupling into the ionisation continuum He⁺+He+e^-, which was investigated earlier by Gillen et al. (1977).

The production of K-shell vacancies in collisions of Neⁿ⁺ to Ne has been studied in the energy range 50-1200 keV for n=1, 2, 3 and 4. For this purpose, cross sections for K X-ray and K Auger-electron production have been measured. The results show no indication of an asymmetry effect which was expected to be seen according to calculations of correlation diagrams for the Neⁿ⁺ to Ne system. On the contrary, the data agree very well with the predictions of the simple one-electron promotion model, i.e. the cross sections scale with the incoming charge state of the projectile. The absolute K-shell ionisation cross sections agree within 20% with cross sections calculated theoretically. From the X-ray and Auger data, fluorescence yields are obtained. These fluorescence yields depend on the projectile's energy as well as on its charge state.

The authors' study is designed to test whether or not existing 'charge transfer to the continuum' theory adequately explains the production of v_i approximately=v_e electrons resulting from 0.2-0.5 MeV H⁺ and H₂⁺ ion bombardment of thin carbon foils; the work suggests that it does not. The differential energy and angular distributions of the emitted electrons are discussed in terms of the vectorial electron-ion velocity differences (v_e-v_i). Although the cusp shaped peaks in both angle and energy are observed, (i) the mod v_e-v_i mod ^-1 dependence predicted by all 'charge transfer into continuum' theories is not found; furthermore, (ii) the predicted increase in cusp width when plotted in terms of (v_e-v_i) and as a function of E_i is not found; finally (iii) it is confirmed that the yield of v_e approximately=v_i electrons from H⁺ bombardment is not the predicted E_i^-5 but rather very nearly an E_i^-3 dependence through the energy range. Furthermore, the cusp widths associated with H⁺ ions are considerably larger than those for equal velocity H₂⁺ ions.

A complete set of data obtained from the collision-induced emission of the Na resonance lines is presented for Na-noble-gas collisions. The data include the emission cross sections and the polarisation fractions of the Na 3²P_3/2 to 3²S_1/2 resonance line, and the ratio of the cross sections for emission of the two resonance lines as a function of the collision energy, measured between the apparent thresholds and about 500 eV collision energy. Cross sections for ultraviolet emission by the noble-gas atoms have been measured in the same energy range. Except for Na-Ne, excitation of the noble-gas atom is relatively unimportant compared to the Na excitation. A qualitative interpretation of the results is attempted on the basis of molecular-orbital energy diagrams.

The angular distribution and polarisation of hydrogenic line radiation excited by electron impact is considered for the case of coincidence experiments. The theory of coherent excitation of hydrogenic states with opposite parity is developed. A set of multipole parameters is defined which characterise the excited states and which enable the formulation of Fano and Macek to be generalised.

The excitation of hydrogen atoms to the n=2 states by electrons is studied for impact energies from 10.9 to 12.1 eV. The effect of resonances below the n=3 threshold on scattering cross sections is studied in detail. The calculations employ the algebraic variational method and a basis of 14 functions, including six atomic eigenstates and eight pseudostates.

Zero-angle energy-loss spectra in sodium are obtained for incident electron energies of 7 to 500 eV using an electron spectrometer and a modulated atom beam. Absolute generalised oscillator strengths for excitation to the 4²S, 3²D, 4²P, 5²S and 5²P states are given. Values of reduced matrix elements, optical oscillator strengths and quadrupole transition probabilities are deduced for S-S, S-P and S-D transitions respectively. Comparison is made with previous experimental work and existing theory.

Relative differential electron-impact cross sections have been measured for elastic scattering for excitation of the 3d¹⁰4p ² P_1/2,3/2, 3d⁹4s²²D_5/2 and 3d⁹4s²²D_3/2 states of Cu at 6, 10, 20, 60 and 100 eV in the 0 degrees to 140 degrees angular range. The relative values were normalised to the absolute scale by utilising He as a secondary standard for determining the correct energy dependence and by accepting the value of the calculated elastic differential cross section at 100 eV, 40 degrees as 1.28*10^-16 cm² sr^-1. Integral and momentum-transfer cross sections have been obtained by extrapolation to 180 degress. The cross section for the excitation of the ²P state is large compared to that for elastic scattering, and population inversion in this state with respect to the ²D state is readily achieved by electron impact. None of the theoretical predictions utilising classical, Born or static-exchange approximations agree with the experimental results at low impact energies.

The R-matrix method for electron-atom scattering using the Dirac Hamiltonian is programmed for a general atomic system and the case of electron scattering by Ne⁺ is considered. Only the results for the electron plus Ne⁺ system in the J=1 and pi =1 state were evaluated in order to compare with the non-relativistic R-matrix calculations. The cross sections for transitions between the fine-structure levels were also obtained.

Utilising a crossed electron-beam-molecular-beam scattering technique, differential electron impact cross sections (DCS) for the excitation of the nu '=2 vibrational band of the B ¹ Sigma _u⁺ state of H₂ have been measured and are presented for the first time. These measurements were made at electron impact energies of 15, 20, 30, 40, 50 and 60 eV. At each energy, DCS between scattering angles of 10 degrees and 135 degrees were determined. They were then extrapolated to 0 degrees and 180 degrees scattering angles to obtain the integral cross sections. These integral cross sections and the Franck-Condon factor for the nu '=2 band were used to calculate the total cross sections for the excitation of the B ¹ Sigma _u⁺ state.

The exact values of the first relativistic corrections to the electric 2^l-pole polarisability alpha _l and the shielding factor beta _l of a hydrogen-like ion are calculated using the Dirac equation. It is shown that the explicit solution of the perturbed Dirac equation is not necessary to calculate the exact values of the corrections. The results for l=1 (dipole) and for l=2 (quadrupole) are: alpha ₁=(a³/Z⁴(⁹/₂-¹⁴/₃( alpha Z)²), beta ₁=1/Z; alpha ₂=(3a⁵/Z⁶)(5-²⁹³/₄₀( alpha Z)²), beta ₂=(1/3Z)(1-²/₅( alpha Z)²). The corrections to the higher-multipole polarisabilities and shielding factors are also calculated.