Table of contents

The first-order Hartree-Fock equations for the 1s2p ³P and ¹P states of two-electron atomic systems are solved exactly. The solutions are used to evaluate the second-order Hartree-Fock energies exactly and the third-order Hartree-Fock energies with great accuracy. New and more accurate expressions for the correlation energies of these states are given. The zero- and first-order terms in the expectation values of δ(r), 1/r, r and r² are also calculated for each orbital. Outlines of the methods involved in the solution of the first-order Hartree-Fock equation for any orbital and in the evaluation of integrals occurring in the second- and third-order energies are given in a series of mathematical appendixes at the end of the paper.

A variational method is used to calculate the effective electric-dipole oscillator strength distributions of the ground and metastable states of helium. Accurate values are obtained of the refractive indices, the long-range interactions and the mean excitation energies controlling the absorption of a beam of fast charged particles.

Values of the van der Waals interaction between the 2 ¹S and 2 ³S metastable states of helium and the systems Ne, Ar, Kr, Xe, H₂, N₂, O₂, CH₄, Li, Na, K, Rb, Cs and O are computed. The values are used to determine Penning ionization probabilities from the experimental data with results differing significantly from an earlier analysis. Estimates are made of Penning ionization cross sections for He (2 ³S) in the alkali metals, in atomic oxygen and in methane, for which no experimental data exist.

The ionization structure of the sodium-like ions is considered. The autoionization effect, due to the excitation of the internal electrons with principal quantum number n = 2 followed by autoionization, is computed using estimated Coulomb-Born excitation cross sections. It is found that this effect is fairly large compared with the usual ionization. Results are given for Mg II, Al III, P V, Ca X and Fe XVI. The autoionization is particularly strong for the highly ionized ions of the sequence and decreases as the ions become less ionized. The limiting case of Na I is discussed.

Scattering lengths for elastic collisions between zero-energy positrons and atoms of hydrogen and helium have been calculated, using Kohn's variational method together with trial functions which make explicit allowance for the correlation between the incident positron and the atomic electrons and which depend upon three exponential parameters as well as a number of linear parameters.

For the case of atomic hydrogen we obtain -1·78 a₀ for the scattering length, employing 21 linear parameters, compared with the accurate value -2·10 a₀ calculated by Schwartz in 1961 also using Kohn's variational method. For helium, using a Hartree ground-state wave function, we find the scattering length to be -0·398 a₀, again employing 21 linear parameters. This is somewhat larger than the value -0·575 a₀ calculated by Kestner et al. in 1965, using a method based on a pseudopotential, and the value -0·546 a₀ calculated by Hashino in 1966, using the method of polarized orbitals.

The annihilation rate of positrons in helium gas is proportional to an effective electron number Z which is calculated using the positron scattering wave function obtained by Houston and Moiseiwitsch in 1967. The value Z = 4·61 is obtained and this may be compared with the experimental value Z similar,equals 3·9 obtained by Falk et al. in 1965.

A simplification of the second Born approximation, in which the terms arising from coupling to the lowest N levels are evaluated exactly and those arising from coupling to all the higher levels with principal quantum numbers n >or= N + 1 and to the continuum states are determined approximately by using the closure relation, is employed to investigate the elastic scattering of electrons by hydrogen atoms and the 1s -> 2s and 1s -> 2p excitations of atomic hydrogen by electron and proton impact.

For the case of elastic scattering the inclusion of coupling to higher states increases the total cross section above the first Born approximation at all electron impact energies. However, for the 1s -> 2s and 1s -> 2p excitations the effect of coupling to states with principal quantum numbers n >or= 3 is opposite to that of coupling to the n = 2 level, and brings the total cross sections closer to the first Born approximation at the highest impact energies (greater,similar 100 ev for incident electrons).

We present calculations of the inelastic contributions to the Stark widths of some S II lines, using Burgess' semi-classical theory of electron-ion collisions. Addition of the inelastic widths to classically calculated elastic widths is found to give good agreement with measured widths.

This approach to calculating ion-broadening parameters is compared with other existing methods.

The profiles of several electron-impact-broadened Ar II lines emitted by a high-density Z-pinch plasma have been recorded using a rapid scanning Fabry-Pérot interferometer. The plasma electron density was determined by Fabry-Pérot interferometry in conjunction with a laser light source. Measurement of the relative intensity of an Ar III line and a nearby Ar II line enabled the plasma temperature to be estimated.

The measured Ar II linewidths are compared with those predicted by the impact approximation using straight-line perturber orbits and neglecting lower-state broadening. In all cases studied the ratio of experimental to theoretical linewidth was at least a factor of 2. The cause of these large discrepancies, and the implications of the results for other emitting species, are to be discussed in a subsequent paper.

Electron collisions with slow CX₂⁺ (CO₂ or CS₂) ions trapped in the electron beam which produces them gave CX₂²⁺, CX⁺, C⁺, and X₂⁺ and X⁺, although this last ion was also produced from X atoms formed by dissociation of the CX₂ molecule on the electron-beam filament. The direct, double ionization potential of CS₂ to CS₂²⁺ was also observed, for the first time in a mass spectrometer, at 25·5 ± 0·3 eV, and the corresponding double ionization potential for CO₂ was confirmed at 36·3 ± 0·5 eV. The production of S₂⁺ from CS₂ was observed, for the first time, at 18·2 ± 0·9 eV in agreement with the value expected from the ionization potential of S₂ at 10·8 ± 0·3 eV. Relative transition probabilities are given for the 19 processes observed.

Absolute cross sections for simultaneous ionization and excitation of CO₂ by electron impact have been measured using a crossed-beam technique. The maximum value of the cross section of the B ²Σ_u⁺ level is 22·4 × 10^-18 cm² and that of the A ²capital Sigma_u⁺ level is 74·4 × 10^-18 cm². Relative cross sections within the vibrational bands are given. The excitation functions are similar in shape to the total ionization function.

Detailed time-resolved measurements of the electron densities and temperatures in a high-density helium plasma generated in a theta-pinch discharge are reported (electron density similar, equals 5 × 10¹⁷ cm^-3, temperature similar, equals 55 000 °K). In the later stages of the discharge the electron temperatures are estimated from both the parent helium radiation and from the radiation emitted by the successive ionization stages of the principal impurity, namely silicon, using a simplified collisional-radiative model. The two estimates of the temperature are in close agreement. The relative collisional-radiative ionization and recombination rates of the Si IV ion are deduced from the experimental data and are compared with theoretical estimates. Finally, the relative absorption oscillator strengths of some of the principal Si III and Si IV transitions in the visible spectrum based on the Coulomb approximation are shown to be consistent with the experimental values except for the Si III 3d ³D-4p ³P transition.

Cancellation effects in Franck-Condon integrals, which lead to the absence of certain (totally symmetric) progression members in electronic spectra, are discussed. In an approximate theory, where the upper- and lower-state vibrational frequencies are assumed to be equal, it is shown that the positions of the vibrational bands of least intensity are closely related to the zeros of the associated Laguerre polynomials. In particular, it is found that: (i) if the ratio of the intensities of the (1, 0) and (0, 0) bands equals m, the band (m, 1) will be absent from the spectrum; (ii) if the ratio of the intensities of the (1, 0) and (0, 0) bands is equal to one of the n zeros of the Laguerre polynomial L_n(x), the sequence member (n, n) will be absent from the spectrum. (Here (m, n) refers to the transition m <- n, where m and n are vibrational quantum numbers.)

These results appear to be approximately valid for many real spectra. The 2500 Angstrom system of PN, the second positive system of nitrogen, and the 2600 Angstrom system of benzene are considered as examples, and the expected effects are found. Corresponding effects in non-totally symmetric vibrations are considered, and shown to be of small importance. A note is included on the abnormal prominence of the (1, 1) sequence band which occurs when the change in geometry accompanying an electronic transition is large.

A very recent scrutiny of the data for the dipole and non-dipole transitions in the K, L and M regions of x-ray emission spectra has revealed the existence of many screening doublets in the K and L regions which have not been reported so far. They are found to fit well into one or other of the five categories of Deodhar et al., thus giving full support to the validity of the basis of such a classification. No additional screening doublets were found in the M region. The greater precision of the classification of Deodhar et al. compared with that of Mande and Damle is discussed.

Using a focusing x-ray spectrograph of Cauchois type, five new forbidden lines L_IN_I λ 1236·80 X.U., L_IIN_VI λ 1240·63 X.U., L_IIN_III λ 1284·43 X.U., L_IIIN_VI,VII λ 1384·80 X.U. and L_IIIN_III λ 1438·75 X.U. have been found for the element ytterbium 70. The transitions L_IIO_I, L_IIIO_I, L_IIIO_IV,V, L_IM_V, L_IO_I, L_IO_IV,V, L_IIM_II and L_IIIO_II,III, reported earlier only by Allais, have been confirmed. However, the transitions L_IM_IV, L_IIO_II,III and L_IIIM_II, reported by Allais, could not be confirmed.

The absorption spectrum of strontium vapour in the quartz ultra-violet and Schumann region has been obtained at good dispersion, leading to extension of the singlet principal series to n = 33 and discovery of 94 lines due to double-electron transitions, most of which are classifiable within six series converging on the Sr II 4 ²D metastable term. Pronounced autoionization resonance effects occur in the Schumann region. We reclassify as 4d6p ³D° a triplet term previously listed as 4d6p ³F°.

A photoelectric spectrometer has been used to measure relative absorption cross sections in the Sr I spectrum, over the region comprising about twenty-two of the autoionization resonances described in the preceding paper. The results are unfolded by a computer programme into Fano-type or dispersion profiles, and values of `line-profile-indices' and autoionization damping constants are derived. One additional resonance, not recognizable from the photographic spectrum, is reported.

The M_V, M_IV and M_III absorption edges of Yb in YbF₃ and in the metal have been detected and the variation in the absorption coefficient of Yb, in these regions, computed. The M_V line absorption of Yb³⁺ has been studied in detail and shown to be absent for Yb metal. This latter has been cited as evidence supporting the conclusion, from magnetic studies, that Yb is a divalent metal, possessing a completely full 4f shell. A shift of the M_V and M_IV edges for Yb in YbF₃ and Yb₂O₃ to positions some 10 ev higher in energy than those for the metal has been observed and discussed.

The apparent detachment rate observed by Hackam and Lennon in O₂-N₂ mixtures is most likely not due solely to collisional detachment by N₂ molecules.

The work of Day et al., Kang and Sucher and Kang and Foland is discussed. It is shown that their expression for the scattering amplitude contains a divergent phase factor, and argued that the term in the Born-Oppenheimer amplitude which they describe as `fictitious' is not so.

The cross-section values for high-energy charge-transfer collisions involving the rare gases, measured recently by Wittkower and Gilbody, are analysed with the use of the adiabatic hypothesis. If polarization effects are included in the change of internal energy of the collision it is indicated that the main maxima in the cross-section values would arise from 10/01 collisions, while the secondary maxima would arise from 1*0/01 or 1*0/01* collisions, in which the excitation energy of 1* is in the vicinity of the second ionization potential of the relevant atom.

For the 2pδ state of the H₂⁺ molecule the function

ψ=(1+pRξ) exp(-αRξ) sinh(βRη)

which is separable in elliptic coordinates, has been studied. The calculated energy is lower than that of any of the existing variational functions for 2 > 2. The integralsX² and Z² as well as the energy values for different nuclear separations have also been calculated.

In atomic scattering calculations it is often required to evaluate integrals of the form

where F and F' are radical functions for a colliding particle. Owing to slow convergence, direct numerical integration may fail to give accurate results. A method employing asymptotic expansions has been developed for the fast, accurate evaluation of such integrals.