Table of contents

It is shown that Martin-Schwinger functional differentiation technique can be extended with certain limitations to systems with spin-degenerate ground states. The Hartree-Fock and the time-dependent Hartree-Fock approximations are discussed for these systems.

The range of applicability of non-relativistic K Auger transition probability calculations has been established by comparing experimental data, relativistic Hartree-Fock-Slater calculations (RHFS) and conclusions on non-relativistic theories with jj and intermediate coupling. As is shown, relativistic effects play the most important role in K Auger transitions resulting in the formation of s vacancies, and they should be taken into account when calculating the probabilities of such transitions for atoms with Z>or approximately=30. An error has been observed in the RHFS calculations of the KL₁M_4,5, KM₁M_4,5 transition probabilities made by Bhalla et al. (1970).

A widely applicable technique is described by which atomic hyperfine-structure splittings and optical isotope shifts may be measured to high accuracies by determining the heterodyne beat frequency between two tunable dye lasers locked to different hyperfine-structure or isotope-shifted transitions of atoms in an atomic beam. A measurement of the hyperfine splitting of the 3P_1/2 level in the 589.6 nm line of sodium has been performed, producing a value of 188.93 (+or-0.02) MHz. The quoted accuracy represents +or-4 parts in 10¹¹ of the optical transition frequency.

The polarized frozen-core (PFC) approximation, which describes a negative ion as an electron captured in the field of a neutral polarized core, is applied for the first time to the complex negative ions O^-(²P⁰) and C^-(⁴S⁰). The negative-ion states are represented by variationally determined antisymmetrized expansions over wavefunctions of the atomic core A, including all the terms of its ground configuration and polarized pseudostates accounting for the full polarizability of its ground state. The most important attachment correlations, which are the long-range (LR) polarization of the core and short-range (SR) correlations due to exchange and capture by the open valence shell, are thus included thoroughly at the outset.

It is shown that, in the second-order Faddeev-Watson multiple-scattering approximation to electron-hydrogen collisions, angular momentum tends to be transferred to the atom in a direction normal to that of the scattered particle if the linear momentum transfer is large. This is in contrast to the first Born approximation which predicts the angular momentum transfer to be always normal to the linear momentum transfer. Other theoretical predictions are examined.

The authors use the model of Parlant and Fiquet-Fayard (1976) to analyse the experimental data of Tronc et al. (1975) for vibrational excitation of NO by electron impact. They obtain the following values for the spectroscopic constants: R_e"(³ Sigma ^-)=1.267 AA (+0.004, -0.025), R_e"(¹ Delta )=1.262 AA (+0.008, -0.022) and T_e(¹ Delta )-T_e(³ Sigma ^-) approximately=0.75 eV. The electronic part of the autodetachment width is assumed to be the same for both resonant states; using the energy dependence (in eV), Gamma (E)=CE^1.5(1+ alpha E), the authors find alpha positive ( alpha =2.5 eV^-1 (+1.5, -2.0) and C approximately=0.07 eV^-0.5).

In order to resolve a discrepancy in previously published static e-N₂ phaseshifts, the authors have carried out an independent calculation for scattering energies from 0.01 to 1.0 Ryd. Comments on convergence of the results are also presented.

The expectation values for the three hyperfine-structure operators are calculated with accurate wavefunctions for the helium isoelectronic series from Z=2 to Z=10. For the contact term the relative accuracy of the results is 5*10^-5, for the spin-orbit term it is 5*10^-4 and for the spin-spin term it is 10^-3.

By way of calculations on the 2s-inp transitions of the isoelectronic species O⁴⁺ to Be, it is demonstrated that the transition-operator method can be employed to mimic the trends in excitation energies and transition values of the SCF method.

Fast La⁺ ions are excited selectively from the a³F levels to the y³F⁰ levels by the radiation inside the cavity of a tunable dye laser. The intensity distributions of the cascade-free decays downstream yield the following lifetimes: y³F₄⁰: 455+or-11 ns, y³F₃⁰: 430+or-10 ns and y³F₂⁰: 511+or-13 ns. These lifetimes are in order of magnitude shorter than those inferred from the emission data of Corliss and Bozman (1962). The significance of the new lifetime values for the determination of the La abundance in the solar photosphere is discussed.

The form of the model potential of the valence electron suggested by Simons (1971) is used for the calculation of atomic dynamic characteristics given by second-order perturbation theory for the interaction of the atoms with an electromagnetic field. General formulae are derived and the results of numerical calculations in a wide frequency range for the dynamic polarizabilities of ground and excited state of alkali atoms and inert gases are presented. The efficiency of different calculation methods for various light frequencies and principal quantum numbers of the atomic levels is discussed.

The optical-pumping cycle in the three-level system e,g,f (J_e=1=J_f, J_g=0), irradiated by two monochromatic sigma -polarized laser light waves is analysed theoretically by the successive approximation (iteration) method up to fourth order. The solutions of the density-matrix evolution equations describe (i) in second order, the influence of the Zeeman structure of the e and f states on the saturation resonances in the intermediate level g (second-order population effect) and (ii) in fourth order, the influence of the Hanle effects and the saturation phenomena on the shape of the double-quantum Hanle resonances and on the two-photon transition probabilities.

The spectral distribution of light scattered from sodium atoms present in helium gas at high temperature and density was investigated. The authors compare the spectral distribution of the exciting laser line, the fluorescence spectrum and the absorption lineshape. Agreement is found with the theories that predict that the fluorescence and absorption lineshapes should be equal and independent of the exciting laser lineshape under these experimental conditions. The scattered radiation intensity varied linearly with laser power intensity up to 500 kW cm^-2.

The threshold photoelectron spectrum of Xe in the region of the 4d edge is analysed with the aid of detailed photoion charge ratios. The experimental technique is that of detecting energy losses of 8 keV electrons at zero angle, in coincidence with either ejected threshold (0< epsilon <1 eV) electrons or with ions. Near the 4d edge clear evidence is found for post-collision interaction, i.e. energy exchange between the slow photoelectron and the fast Auger electron. The occurrence of 'capture' of the photoelectron into an excited Xe¹⁺ state is seen as a significant loss of intensity of zero-volt electrons at the actual threshold.

Measurements are reported of the triple-differential cross sections for ionization of helium by electron impact. Experimental conditions were chosen to help clarify the situation in the theory of ionization. Data are presented for primary energies of 100, 105, 125 and 165 eV. Unlike previous measurements in this energy regime, data are included for the circumstance where the three electron trajectories are not in a plane.

Cross sections for the 2³S-n³L(n=2-5, L=S-F) excitations and for single ionization in e-He(2^1,3S) collisions are determined by using the Born approximation. For a given n, the 2³S-n³D transitions dominate at intermediate energies and this trend is continued for transitions to the near continuum. For larger energies epsilon of the ejected electron, higher angular momentum l waves progressively dominate. While up to nine partial waves are in general required for convergence of the bound-free form factor, as many as 30 are needed when momentum changes are in the vicinity of the Bethe ridge for large epsilon . Binary-encounter results for ionization are also obtained and agree with the Born values at intermediate energies.

It is proposed that the interaction V between an incident electron and an atom may be usefully split into two parts, V₁ and V₂, in such a way that couplings which are readily amenable to perturbation theory are contained in V₂, while V₁ corresponds to the remaining couplings which cannot be so effectively handled perturbatively. By making a distorted-wave Born series expansion in powers of V₂ it is possible to calculate the scattering amplitude correct to any order in V₂ while treating V₁ non-perturbatively. Cross sections for the elastic scattering of electrons on helium and neon are calculated in the energy range 100 eV to 2 keV and compared with experiment.

The elastic scattering of positrons from noble gases has been formulated using a polarized-orbital approximation. In principle all multipole moments of the positron-atom interaction are included and the polarized orbital is calculated by a perturbed Hartree-Fock scheme. The scattered wave is readily obtained from a potential scattering problem and is used to calculate Z_eff and the angular correlation as well as the scattering cross sections of interest. Numerical results are presented for positron-helium scattering in the elastic region.

Calculations are performed in the first Born approximation for electron loss from, and total destruction of, He⁺(2s) colliding with helium. For both processes the theoretical cross sections are in excellent agreement with experimental data. First Born approximation and close-coupling theories are also used to study the formation of He⁺(2s) and He⁺(2p) in He⁺(1s)+He collisions. Coupling effects are found to be important for impact energies below 200 keV.

Reports measurements of the metastable fraction of the n=2 population of hydrogen atoms formed by electron capture of protons in caesium in the energy range 2.5 to 10 keV. The experimental method does not involve the detection of photons and is thus free from the related calibration problems. Measurements are also reported of the ratio of the differential cross sections for negative-ion formation in the forward direction when hydrogen atoms in the 2s and 1s states impinge on helium, neons, krypton, xenon and hydrogen at 3 keV.

For pt.I see ibid., p.2693 (1976). Differential cross sections for He(2¹S)+Ar have been measured for six relative kinetic energies between 21 and 180 MeV. At low kinetic energies the small-angle oscillations are clearly resolved. Except for the lowest energy (21 MeV) a well resolved rainbow peak is observed in the differential cross sections. The real and imaginary parts of the interaction potential are obtained from the data. The real part has an intermediate maximum in the potential ( Delta E=25 MeV, r_max=7 au) which causes the rainbow peaks. The imaginary part can be expressed by an exponential plus a Gaussian. The velocity dependence of the total and ionization cross sections is calculated and the possibility of an energy-dependent width of the potential is indicated.

The rate coefficient for the associative ionization was measured during optical excitation of the resonance level 4²P of potassium. The results are compared with the results previously obtained by the same method for other alkali metals.

High-resolution electron energy-loss spectra of the hydrogen afterglow have revealed transitions from the first two vibrationally excited levels of the ground state to the B¹ Sigma _u⁺ state in the energy-loss range 10.5 to 11.2 eV. Franck-Condon factor calculations are used to obtain an estimate of the vibrational concentration in the ground state.

Calculations on low-energy electron scattering from molecular hydrogen have shown the importance of both polarization and exchange in electron-diatomic-molecule collisions. In 1970 Burke and Sin Fai Lam developed within a fixed-body frame a general theory for low-energy electron scattering from closed-shell diatomic molecules and applied it to e^-+N₂. They obtained only qualitative agreement with experiment. The reasons appear to be twofold. Firstly, they omitted polarization, and secondly, they failed to ensure convergence in the single-centred expansions employed in the theory. These inadequacies are corrected and satisfactory agreement with existing experimental data for electron-nitrogen scattering is shown to be possible.

The collision-induced polarization of the angular momentum of a diatomic molecule is discussed within the framework of the quantum-mechanical spectator model. For purely rotational excitation from the molecular ground state to some final angular momentum j, the distribution over the projections m is investigated at different scattering angles and the differential and total cross sections are studied as functions of m. A simple scheme for the calculation of the most probable m transitions is given. Numerical results are presented for a simplified model of the system N₂+Li⁺.

Criteria are given as a function of electron density N_e, temperature T, nuclear charge number Z and principal quantum number n for the validity of the assumption of statistical equilibrium among the sublevels l, j of level n in a hydrogenic atom or ion. Essentially all values of Z and impact ion charge eZ_i are considered, but only small values of n(n<or=5) are considered.