Table of contents

Constancy of the second differences in Hartree-Fock SCF energies within an isoelectronic series is shown to result from the systematic change in the behaviour of (1/r₁). An approximate relationship for the second differences is proposed.

The study of the a ³ Sigma _g⁺ to b ³ Sigma _u⁺ molecular hydrogen transition, excited by an electron beam at pressures between 0.1 and 16 Torr, has revealed a complex temporal evolution which cannot be explained by the radiative and collisional relaxation of only the a ³ Sigma _g⁺ state after its excitation by the electrons. A model based on a cascading process from an upper state, identified as the d ³ Pi _u, can explain all the experimental results. The radiative lifetime and the quenching rate constants of these two states are reported.

The second Born amplitude (with the exact propagator replaced by the free particle propagator) for the electron capture reaction H⁺+H(1s) to H(1s)+H⁺ is reduced to a two-dimensional integral. The integrand has several singularities, which are dealt with. Results of the numerical integration of the cross section for various energies in the 25-200 keV range are presented.

It is found that use of the second Born approximation in the calculation of triple differential ionisation cross sections of hydrogen and helium by fast electrons does not lead to any general improvement over results obtained using the first Born approximation.

The M₃M₄₅N₂₃ Coster-Kronig electron spectra of krypton excited by electron impact at low energies have been investigated. This is the first observation of the Read (PCI) effects in the Coster-Kronig processes. At the lowest impact energy (225 eV) an asymmetric line profile that has a tail towards lower energies has been found, while tails towards higher energies have been observed at moderate impact energies in the same way as in previous works for the ordinary Auger processes. The energy shift ε of the line has been found to obey the power laws ε∝(ΔE)^-0.71 and ε∝(ΔE)^-2.9, where ΔE is the excess energy of primary electrons.

Scattering lengths for positron-helium collisions are obtained from least-squares fits to the experimental low-energy total cross section data of Canter and co-workers (1979) and Stein and co-workers (1978). Previous conclusions regarding the quality of these experimental data based on such fits are challenged. The effect of small-angle forward elastic scattering in experiments at low energies is analysed.

The authors report the first detection of fast muonium atoms formed in the 2S state. Approximately 115 2S muonium atoms per second, with velocities from 0.006 to 0.02 times the speed of light, were produced in a vacuum from gold and aluminium foils bombarded with 5*10⁴ positive muons per second having incident kinetic energy 2.1 MeV. The Lamb shift in the n=2 excited state has been measured to be 930(+570/-640) MHz.

The symmetry inherent in the periodic system of elements is discussed on the basis of the model one-electron potential in atoms. This potential approximates well that of the Thomas-Fermi theory and reproduces the well known n+l building-up rule describing the configurations of the ground-state neutral atoms. The modifications of the model potential accounting for the Coulomb tail allows us to analyse the (n+l) grouping in the Rydberg spectra of atoms. This grouping is shown to be closely connected with the n+l building-up rule for the ground states. The dynamic group of the periodic system (or of the atomic potential) is proposed. The specific doubling of the periods (as compared with the hydrogen type spectrum) is described by means of a group formally analogous to the isospin group. The operator of the 'isospin' projection on the chosen axis in the 'isospace' is found explicitly as an inversion operation in some sphere. The states classification according to the related quantum number allows us to give the group-theoretical interpretation of the 'secondary periodicity' effect in the periodic system.

Binding properties of multiatomic systems are studied on the basis of the McWeeny density matrix method. Exchange and correlation is described by using the local density approximation which causes a non-linear dependence of the total energy on the charge density ρ(r). However, on separating off a suitably chosen background charge density ρ₀(r), the exchange-correlation energy can be expressed in terms of the first and second power of the density difference. Hence the total energy becomes a second-degree function in the density matrix elements D^s_αβ, depending on the spin orientation s. The minimum of the total energy in the space of these elements can be found directly by the steepest descent method, where the condition of charge conservation and a generalised condition of idempotency for the D^s_αβ have to be satisfied. It appears to be an important feature of this method that it avoids explicit calculation of one-particle states.

A modified version of the McWeeny density matrix method as described in I is used to calculate the binding characteristics of a number of first-row diatomic molecules. The exchange energy is approximated by the X_α expression. A similar formula is derived to include correlation. The properties of the deepest multiplet states of the molecules Be₂, Be₂⁺, B₂, B₂⁺, C₂, C₂⁺, C₂^-, O₂, O₂⁺ , CO, CO⁺ and CO^- are studied and compared with other theoretical results obtained by different methods.

It is shown that the fine-structure inversions in highly excited d and f levels of atoms containing a single valence electron can be explained solely as first-order relativistic corrections to the energies of the non-relativistic Hartree-Fock wavefunctions. The variation (with respect to the position of the atom in the periodic table) of the contribution Delta E_K arising from the relativistic correction to the core exchange potential, shown to be responsible for the inversions, is related to changes in the differential overlaps between the valence and the outermost core orbitals and their first-order relativistic corrections. It is further shown that although the magnitude of Delta E_K decreases less rapidly with the principal quantum number n of the valence electron than 1/n³ for intermediate values of n, it varies as 1/n³ in the limit of large n.

Using two-step laser excitation in an atomic beam and time-delayed field ionisation detection, we have measured the lifetimes of the Rydberg levels of Ba I belonging to the perturbed series 6snd ¹D₂ (n = 17-35) and 6snd ³D₂ (n = 17-28) and also the lifetime of the perturbing 5d7d ¹D₂ level. The expected shortening has been observed for the lifetimes of those levels which are strongly mixed with the perturber. The measured values have been satisfactorily interpreted by a parametric method based upon the wavefunctions previously obtained from a multichannel quantum defect analysis of the energies.

RbXe bands are observed using pulsed dye laser excitation of atomic alkali transitions in Rb/Xe mixtures containing 193 and 465 Torr xenon. Bands observed in absorption (A) or emission (E) at 427.0 nm (E), 497.8 nm (A), 501.8 nm (A, E), 509.0 nm (A, E), 520.0 nm (A, E) and 535.0 nm (E) are assigned to molecular potentials associated with the 6²P_1/2 atomic rubidium states for the first, 6²S_1/2 for the next two and 4²D_3/2,5/2 for the remaining three. The time evolution of the emission bands depends on the population mechanism of the parent atomic state which involves superradiant transitions from the pumped excited state. Monitoring of the corresponding infrared emission allows a control over the population mechanisms and an evaluation of the lifetimes, collisional quenching and reaction rates of the excimer and parent states. This in turn allows a determination of the atomic parent states of the bands observed.

The Demkov model is widely used for the calculation of non-adiabatic transition probabilities in various problems of atomic physics. The choice of the Demkov and Nikitin model parameters is discussed. The asymptote of large internuclear distance theory allows us to obtain quasimolecular potential curves and non-adiabatic interaction matrix elements using data on separated atoms only. This information is used in the proposed parametrisation procedure. The parametrisation scheme is employed to calculate the transition probability between lsσ and 2pσ molecular orbitals. First the two-centre Coulomb system is considered and the model probability is compared with the result of a two-state numerical calculation. The model is also applied to the calculation of the muon distribution between the prompt fission fragments where the potentials are non-Coulombic due to the finite size of the nucleus. The results agree with the existing experimental data. The parametrisation scheme is also applicable to vacancy sharing problems in atomic collisions.

The author considers the maximum stopping power for protons, S_m, which occurs at a certain energy E_m. According to the Brandt theory, the product _mE_m is a function of only the relative number of target electrons taking part in the stopping process. This theory is compared to all the fitted values from the tables of Andersen and Ziegler (28 targets) using, in addition to the Thomas-Fermi model, the Lenz-Jensen model for the determination of the effective number of electrons. Both models give good agreement with the data, when the best values for the free parameters in the theories are used.

Stopping power of He, Ne, Ar, Kr, and Xe were measured for He⁺, Ne⁺, Ar⁺, Kr⁺ with energies in the range 40-200 keV using the ion beams from a Cockcroft and Walton type accelerator and a differently pumped gas cell. The result shows asymmetry for Z₁ and Z₂. The author was not able to find oscillating structures for Z₁ and Z₂ because the Z points were so rough.

The autoionisation of the helium atom has been experimentally studied, by electron spectrometry, in collisions between neutral helium atoms in the energy range 5-140 keV. The fast neutral beam is formed by charge exchange of a fast helium ion beam in helium gas, and its composition is discussed. Above 10 keV the shapes and intensities of the 2s²¹S, 2s2p ³P, 2p²¹D, 2s2p ¹P and He^-(1s2s²)²S lines are determined by a numerical fitting procedure. Excitation of these autoionising states at low energy is discussed within the quasimolecular model. The experimental results are analysed in terms of the collisional system symmetry. The comparison of slow and fast atom excitations is used to determine the energy range within which the quasimolecular model holds. The influence of metastable atoms present in the incident beam is shown to explain the 2s2p ³P line excitation below 30 keV, within the quasimolecular model. Discrepancies between shapes and intensities of lines emitted (at given collision energy and emission angle) by the two atoms are interpreted as being due to an excitation by fast metastable atoms, within an atomic model.

Na (ns)-Ar collisions have been investigated for 20<or=n<or=48 using a beam-pulsed cell technique with time-resolved selective field ionisation. The total cross section has a broad maximum of 130 AA² around n=30-35. Preliminary observations indicate that principal quantum number changes are large in such collisions.

Absolute cross sections for the collisional de-excitation of the metastable rare-gas atoms Ar (³P_0.f2), Kr (³P_0.2) and Xe (³P_0.2) by molecular hydrogen and deuterium have been measured. The experiment employs a velocity-selected metastable atom beam and a collision chamber with a variable length. During a collision, transfer of electronic energy from the metastable atom ideas to dissociation of the target molecule. In the case of argon metastable atoms this process may be complicated by other de-excitation mechanisms.

The authors examine the general charge transfer reaction in the first and second Born approximations for arbitrary initial (Z_T,n'l'm') and final (Z_P,nlm) states. The salient features of the first (single scattering) and second (single and double scattering) Born total cross sections are pointed out, with special emphasis on the possible dominance and detection of the double scattering contribution in charge exchange processes. The single scattering contribution is treated exactly and the double scattering contribution approximately as in a previous paper by the authors (1980). Representative distributions of cross sections are presented as a function of impact velocity and the various quantum numbers, thereby illustrating the characteristic trends of the two contributions.

Elastic scattering of electrons by helium atoms has been investigated using a model potential approach. The present model potential contains static, adiabatic polarisation and distortion potentials. A model exchange potential coupled with the orthogonality constraint for l=0 has been employed to take account of the Pauli principle. The scattering parameters have been obtained in the energy range 2-19 eV. The present results are in good agreement with measured values and other theoretical estimates.

The authors have determined the spin polarisation of electrons scattered elastically from argon and krypton at energies between 10 and 50 eV in the angular range 40-110 degrees . For krypton they find reasonable agreement at 50 eV with the measurement of Schackert (1968) and good agreement with the optical-model calculation of McCarthy et al. Between 50 and 20 eV their results on Kr agree with the theoretical results of Walker (1971). In the case of argon the overall agreement with theoretical results and with the few existing measurements of Schackert (1968) and Mehr (1967) is worse. At 10 eV, both in krypton and argon, they observe a broad feature of rather high polarisation, which seems to indicate that the predicted points of complete polarisation appear as broad structures over a much larger angular range than expected from theory.

A semiclassical interpretation of the effect of the Coulomb interaction between three charged particles in the final state of a break-up (ionisation) process is given. The method is developed for the co-planar case. A recipe for calculating triple differential cross sections when both electrons have energies which are large compared with the ionisation energy is also suggested.

The ejected-electron spectrum of lead vapour in the range 0-12.5 eV has been observed at 65 degrees with respect to an incident electron beam of kinetic energy 20-400 eV. A total of 207 lines are reported correspondingly to excitation of both Pb I and Pb II autoionising levels. The results are compared with data from absorption measurements, arc spectra and theoretical calculations.

Resonant scattering of electrons from molecules is discussed in the context of both a non-local complex potential and a local complex potential (boomerang model). Vibrational excitation cross sections are computed for an exactly solvable model and compared with those calculated within the boomerang approach. The range of applicability of the local complex potential approach is analysed in detail. A semi-local approximation to the cross sections is introduced which is only slightly different from the boomerang approximation, but leads to improved results.

The incoherent renormalised multicentre potential model (IRMPM) is extended to calculate the elastic and vibrational excitation cross sections for e^--H₂ collisions at impact energies between 20 and 81.6 eV. The results are compared with the experimental data and other theoretical results.

For pt.I see ibid., vol.14, p.4389 (1981). The adiabatic theory developed in the first paper of this series is now applied to the d³ Pi _u to X¹ Sigma _g⁺ electron impact excitation of the hydrogen molecule. It gives the opportunity to determine semi-empirically all vibro-rotational cross sections for the transitions occurring within the electronic transition studied. The theoretically well founded procedure of extracting information from the intensities of spectral lines excited with the gas-beam technique is proposed and put into practice. In particular, it is established that for the electronic transition in the H₂ molecule considered there are substantial deviations from the Franck-Condon approximation. The principal and applied practical significances of this fact are discussed.

Dissociative recombination of Hg₂⁺ ions with electrons has been studied using microwave afterglow and optical spectrometric techniques. The total rate coefficient is found to be alpha (Hg₂⁺)=(4.2+or-0.5)*10^-7(T_e(K)/340)^-1.1 cm³ s^-1 over the electron temperature range 340K<or=T_e<or=5600K and at T₊=T_gas=340K. The excited states produced by the dissociative recombination have been determined at T_e=340K and 4900K; in both cases the 7s and 6d states are strongly populated.