Table of contents

The use of universal basis sets of elliptical functions in molecular electronic structure calculations for diatomic molecules is discussed. It is shown that universal elliptical basis sets have a number of advantages in studies of diatomic molecules over the more frequently used exponential-type and Gaussian-type basis sets.

A recent comparison of theory and experiment by Juncar and co-workers (1983) suggested residual errors in the theory due to non-relativistic correlation energy and to radiative corrections. A careful analysis shows that theory and experiment agree to within the experimental limits, 5*10^-4 cm^-1.

The excitation spectrum for Rydberg states near n=11 of atomic sodium in crossed electric and magnetic fields has been recorded. The theoretical analysis of the spectroscopic data reveals degeneracies among some sublevels even though different sublevels are mixed by the external fields. The degeneracies are traced to a dynamical symmetry that is characteristic of the Coulomb potential.

A manifestly gauge-invariant formulation of the Dirac equation for an electron in the electromagnetic field generated by two heavy ions is given, which used the eigenstates and eigenvalues of the gauge-invariant energy operator. Transitions between the energy eigenstates are induced by the power operator, not the vector potential.

A crossed-beam coincidence counting technique incorporating time-of-flight spectroscopy, previously developed in the authors' laboratory, has been used to determine the cross section for ionisation of H(1s) atoms by C⁶⁺ ions at 400 keV amu^-1. The result is compared with previous measurements for bare nuclei projectiles and with recent theoretical predictions.

The angular distribution of the asymmetry in scattering of spin-polarised electrons by spin-polarised hydrogen atoms has been calculated for the first time, for the 1s-1s and 1s-2s transitions, at impact energies of 35 and 54.4 eV. A full six-state calculation was done at 54.4 eV and ten-state localised exchange calculations at both energies. The predicted behaviour of A_1s,1s( theta ) is smooth with a maximum of about -0.25 near 20 degrees (54.4 eV). However, A_1s,2s( theta ) is always positive and shows a strong narrow 'resonance' near 40 degrees .

Low-energy electron impact total excitation cross sections of the lowest-lying autoionising level generated due to the inner-shell electron excitation 1s²2s²2p⁶3s²S^e to 1s²2s²2p⁵3s²²P⁰ and 1s²2s²2p⁶3s²3p⁶4s²S^e to 1s²2s²2p⁶3s²3p⁵4s²²P⁰ complex transitions in lighter alkali metal atoms i.e. sodium (Na) and potassium (K) atomic systems respectively have been calculated using single configuration Hartree-Fock (HF) wavefunctions for both initial and final states within the R-matrix method in the low bombarding energy region. The present calculated theoretical results differ significantly in nature from all earlier predictions and also disagree with the estimated values of the contribution of the lowest-lying autionising level to direct ionisation on the basis of the classical scaling law reported by McDowell (1969).

New measurements of positronium formation cross sections are reported for the inert gases at energies up to 150 eV. These data show pronounced structure in the cross sections of all gases in the form of secondary peaks and plateaus above the ionisation potentials.

The (non-relativistic) ground-state energies for H^-, He, Li⁺, C⁴⁺ and Ne⁸⁺ are calculated using the 1913 orbit model of Bohr for a two-electron atomic system, modified so that the electrons are able to move away from Bohr's 180 degrees arrangement of them around the orbit. Both classical and non-classical weighting factors (P( phi )) are associated with the energy E( phi ) for angle phi . If phi is restricted so that E( phi ) cannot exceed the energy of He⁺, then the calculated average energies E for He(-2.900 or -2.908 au, with classical and non-classical P( phi )) are much closer to the exact energy (-2.9037 au) than is Bohr's estimate (-3.0625 au). Similar calculations for H^- and the isoelectronic cations give values for E that are respectively rather less than and greater than the exact energies. For H^-, with a classical P( phi ), a simple further modification gives E=-0.52793 au; the exact energy is -0.52775 au. For He, Ne⁸⁺ and Ca¹⁸⁺ the results of approximate calculations are also reported, which allow for the possibility that the two electrons move around separate orbits when phi is small. Relationships are developed between the orbit and orbital models for the ground states of two-electron systems.

The 19 lowest states of CsH and the 11 lowest states of Cs₂ have been calculated using a non-empirical relativistic effective core potential considering the caesium atom as a one-electron system. The core-valence polarisation and correlation energy has been included employing a recently developed perturbation treatment. The experimental atomic spectrum of caesium is well reproduced. The calculated energy curves show the remarkable precision of this procedure for the ground-state characteristics. For CsH, R_e=4.47 Bohr (experimental 4.71 Bohr), D_e=1.80 eV (experimental 1.83 eV), omega _e=871 cm^-1 (experimental 891 cm^-1); for Cs₂, R_e=8.75 Bohr (experimental 8.78 Bohr), D_e=0.40 eV (experimental 0.45 eV), omega _e=41 cm^-1 (experimental 42 cm^-). The well-to-well transition energies are in error by less than 400 cm^-1 for experimentally known transitions.

The author expresses the time-dependent physical spectrum of any signal as a twofold convolution over frequency and time of the Page-Lampard quasi-spectrum and a smoothing function that is determined by the properties of the spectrometer. This result is applied to the collisional redistribution of intense time-dependent radiation. Without resort to the adiabatic approximation the authors derive a differential equation that determines the time-dependent redistributed spectrum for any given time variation of the incident field. In the special case of adiabatic or sudden switch on the incident radiation he evaluates the approach to the steady state of the fluorescence spectrum of a two-state atom.

The multiconfiguration optimised potential model has been applied to the first six elements of the gallium sequence. The structure of the ²P ground state as well as of the two lowest ²S and ²D terms has been calculated along with the gf values for the ²P-²S and ²P-²D transitions. Irregularities in the isoelectronic behaviour of the gf values owing to plunging terms of the 4s4p² configuration are accounted for and comparison is made with recent experiments. Some discrepancies between theory and experiments have been cleared up but some still remain.

Helium triplet metastable densities have been calculated from measured absorption of resonant, CW, UV laser radiation on the 2³S-5³P transition at 294.511 nm. Gas temperatures have also been deduced by measuring the Doppler width of this transition. A 3 mm bore capillary tube filled to pressures in the range 1-8 Torr and run at currents in the range 2.5-80 mA was studied. With constant discharge current (60 mA) at a maximum value for the triplet metastable density of 11*10¹² cm^-3 at about 2 Torr was obtained. The metastable densities show the expected saturation behaviour, saturating at currents above 40 mA. Experimental values are used in conjunction with the rate equation describing the metastable level population in order to estimate the rate coefficient for loss of metastables through electron collisions. Mention is made of the use of the visible laser radiation for measuring the UV laser wavelength in a Kowalski-type wavemeter.

Sub-Doppler width signals have been observed in the optogalvanic current when a magnetic field is altered through regions of Zeeman level crossings. It is shown that the signals can be interpreted as due entirely to population changes in the levels involved.

An optical pumping charge exchange collision experiment for precise measurement of the nuclear g factor of the ³⁹K⁺ ion in a helium buffer gas is reported. ³⁹K⁺ ions are polarised by charge exchange collisions with oriented ³⁹K atoms. The NMR frequencies of ³⁹K⁺ and the ESR frequencies of free electrons polarised by oriented ³⁹K atoms are measured in a magnetic field (3-34 G). This gives the ratio of the nuclear g factor of the ³⁹K⁺ ion to the electronic g factor of free electrons to be: g_I(³⁹K⁺)/g_e=0.07088733 (17)*10^-3. Using this ratio together with the best available measured values of g_e=2.0023193134 (70) and g_I(³⁹K)=1.4193489 (12)*10^-4 the authors obtain: (i) g_I(³⁹K⁺)=-1.4193906 (34)*10^-4 in units of the Bohr magneton; (ii) the diamagnetic shielding constants difference between free atoms and ions is: sigma (³⁹K⁺)- sigma (³⁹K)=-29(6)*10^-6.

Two-photon first ionisation cross sections were computed for Ne and Ar by exploiting the results of a random phase approximation calculation. The final states lying in the continuum were described in a static-exchange-type model. The calculations were performed with the length and velocity form of the perturbation operator for the differential and total cross sections. The results of the calculations are presented for linearly as well as for circularly polarised light.

Differential incoherent scattering cross sections of 661.6 keV gamma rays in the solid compounds NaCl, NaNO₂, KCl, NiO, NaNO₃, CuCl, NaBr, CaCO₃, CaCl₂ and ZnCl₂ and in the liquid compounds H₂O and HCl at 30, 45 and 60 degrees have been measured. Making use of the bonded hydrogen incoherent scattering functions of Hubbell et al. and the mixture rule, the differential incoherent scattering cross sections in C, N, O, Cl, Na, K, Ca, Br, Ni, Cu and Zn are derived, compared with the theoretical values of Hubbell et al. and discussed.

Relaxation parameters of the optically depopulated ( nu ", J")X¹ Sigma _g⁺ level of the K₂ molecule with nu "=1 and J"=72 have been determined for thermal collisions with He, Ne, Ar, Kr and Xe atoms, using the method of laser-induced fluorescence kinetic monitoring. Rate constants of about 10^-9 cm³ s^-1 and effective cross sections between 0.5*10^-14 and 1.6*10^-14 cm² have been obtained. Rectangular modulation of the He-Ne laser 628.8 nm intensity, exciting the transition (1,72)X¹ Sigma _g⁺ to (8,72)B¹ Pi _u, was employed making it change periodically from depopulating to probing. The time dependence of the probe-beam-induced fluorescence directly reflects the transient process restoring the thermally equilibrated populations of the lower level ( nu ", J"). The kinetic equations were solved in the classical-limit J" to infinity approximation, allowing for participation of two relaxation processes, namely collisions and collisionless exchange of molecules inside and outside the laser beam in their thermal motion. It is shown that the assumption of additive rates for both processes can lead to distortion of the concentration dependence of total relaxation rate. A description of the transient process is also given within the framework of irreducible tensor operators, permitting the authors to consider separately the contribution of population relaxation and of alignment. For the rovibronic state (8,72)B¹ Pi _u from measurements of the degree of polarisation of the fluorescence it was found that cross sections for population and alignment relaxation coincide within 3% and would fit into the limits of the experimental error.

Atomic form factors containing the product of the Coulomb wavefunction (r mod k) with either the hydrogenic or Slater-type orbital (r mod nlm), are calculated in a closed form, for an arbitrary triple nlm. By choosing the quantisation axis for mod nlm> along the vector k, it is shown that the present integrals can be reduced to a linear combination of easily calculable hypergeometric polynomials of two and three variables. Results are particularly useful for second-order theories of charge exchange, notably CDW and CIS approximations.

For pt.I see ibid., vol.16, p.2265 (1983). A method for computing the multichannel S matrix at real and complex energies is proposed. This method is a generalization of the one given previously for single-channel problems. It requires a potential matrix of the form V_n,n'(r)= Sigma _j=1^infinity U_n,n'^(j)( alpha )exp(- j alpha r). The algorithm to determine the Jost matrix (and hence the S matrix) is simple and fast. The feasibility and usefulness of the method is demonstrated by applying it to model problems on electronic and vibrational predissociation.

Trajectory calculations are reported in the sudden approximation for the Maxwellian averaged diffusion and viscosity cross sections for He-N₂, Ar-N₂ and He-CO₂ collisions. Comparison is made with classical infinite-order-sudden (IOS) calculations, also known as the Mason-Monchick approximation, and with various quantal IOS calculations. For the N₂ collisions, the energy-sudden and classical IOS results agree within 1% and differ from the quantal results by less than 2%. For the He-CO₂ collisions, the classical IOS results differ by about 5% from the energy-sudden calculations. An energy-corrected sudden approximation is introduced. This correction is significant only for viscosity-type cross sections, making a 6% difference for Ar-N₂ and He-CO₂ collisions at 300K. Criteria for the validity of the classical IOS approximation are suggested.

A Feshbach projection operator technique involving self-consistent field (SCF) calculations in orthogonal subspaces is used to obtain diabatic orbitals of the Na-He collisional system. Analysis of the molecular orbital wavefunctions and their delta / delta R couplings show that the Barat-Lichten correlation rule for the promoted orbital is incompatible with the diabatic smoothness criterion. The previously admitted conjecture that the strong asymmetry of the system would lead to an adiabatic behaviour of the sigma 1s_He- sigma 3s_Na molecular orbital (MO) crossing is not supported by the presently calculated coupling matrix elements. The molecular mechanism for Na(3s to 3p) excitation appears to be induced indirectly (as for Na-Ne collisions) by two successive curve crossings via the core-core K-L shell interaction.

Cross sections for He²⁺ production and charge transfer have been measured for collisions between two unexcited He⁺ ions at centre-of-mass energies between 14 and 58 keV. In this range the cross section for He²⁺ production rose with increasing energy from 5.3*10^-18 cm² to 24*10^-18 cm², whilst the cross section for charge transfer increased from 5.2*10^-18 cm² to about 19*10^-18 cm². The measurements of charge transfer were compared with theoretical and experimental results for He(1s²)+He²⁺ to He⁺(1s)+He⁺(1s). Excellent agreement was found which implies that, for interactions between ⁴He⁺ ions at these energies, charge transfer proceeds almost exclusively into the ground state.

Reports the results of the first calculations of single- and double-electron transfer cross sections in He²⁺+He(1s²) collisions within the time-dependent Hartree-Fock approximation. The energy range studied is 30 to 150 keV. The total cross sections are calculated in the rotating-frame approximation; the final amplitudes are determined by projection of the time-evolved two-electron wavefunction onto atomic states with appropriate translation factors. The authors compare their results with other theoretical calculations and with experiment.

Charge exchange between O⁸⁺ and He(1s²) is studied both theoretically and experimentally. In the energy range where capture cross sections have been measured good agreement is obtained between theory and experiments. Calculations predict that in single-electron capture the electron is transferred dominantly into O⁷⁺ (n=4), which is supported by earlier experimental work.

Differential cross sections (DCS) for the vibrational excitations ( nu _2,4, 170 meV; nu _1,3, 360 meV) of CH₄ by electron impact have been investigated for incident energies of 3 to 20 eV in the range of 30 to 140 degrees using a crossed-beam apparatus. Integral and momentum transfer cross sections are calculated from the DCS. At about 7.5 eV, the angular distribution shows d-wave behaviour, and the integral cross sections are enhanced to about 10^-16 cm². The parameters of angular correlation theory with the irreducible tensor method for the T₂ molecular symmetry of CH₄ were obtained by fitting. It was found that the d wave alone suffices to explain the angular distributions due to the presence of a broad resonant excitation process in the nu _2,4 and nu _1,3 channels. At incident energies of 10 to 20 eV, the angular distributions are isotropic within the experimental error. At lower energies of 3 to 5 eV, the distributions are practically constant within the angular range of 40 to 140 degrees , but the cross sections continuously increase towards smaller angles.