Table of contents

The overlap integral R(m, n) of two harmonic-oscillator wave functions ψ_m' and ψ_n'' is considered. It is shown that

where [m, n] is the smaller of the two integers m and n, q = 2 (ν'ν'')^1/2/(ν'' + ν') and ν' and ν'' are the frequencies associated with the wave functions ψ_m' and ψ_n'' respectively. It is also shown that if the quantities R(m, n), where m and n run from 0 to p, are considered as the elements of a square matrix R of order p + 1, then

The reduction of the general expression for R(m, n) to special cases of importance in molecular spectroscopy is indicated.

The scattering matrix for electron collisions with positive ions may be expressed in terms of a matrix R which varies slowly as a function of the energy. In the neighbourhood of resonances the scattering matrix varies rapidly.

Resonances associated with a single closed channel, or with a group of degenerate closed channels, are analysed using a method similar to that published by Gailitis in 1963. It is shown that the poles of the scattering matrix are given by a Rydberg formula containing a complex quantum defect. The case of non-degenerate closed channels is also discussed.

For electron collisions with highly ionized atoms the R matrix may be calculated using perturbation theory. It is shown that, in this limit, the resonant and non-resonant contributions to excitation rates are of comparable order of magnitude.

A separable series representation of the off-shell two-body t matrix with Coulomb potential is introduced and compared with the Sturmian-function expansion.

A particular peaking approximation used by Kang and Foland to evaluate a Coulomb-Born matrix element is shown to badly misrepresent their total and differential cross sections for the 1s -> 2s transition in atomic hydrogen at low impact energies.

The polarization of Lyman α radiation is calculated in the Born and distortion approximation including rotational coupling between the hydrogen magnetic substates. The rare gases helium, neon and argon are represented by their Hartree-Fock potentials. Comparison with recent experiments shows that both rotational coupling and distortion have to be considered to obtain reasonable agreement between theory and experiment.

The relativistic corrections to the eigenvalues of the 1sns ^1,3S states of the helium sequence are determined exactly to O(Z³α²) using perturbation theory. These results, together with the very accurate values obtained by Pekeris for helium, are used to predict relativistic shifts for Li⁺, Be²⁺, etc. for the states n = 2,..., 5.

Accurate first Born approximation cross sections are given for the electron impact excitation of the ground state of helium to the n¹S (n = 2 to 7), n¹P (n = 2 to 6) and n¹D (n = 3 to 6) excited states. Many-parameter correlated wave functions for both the initial and final states have been employed in the length formulation of the Born approximation integrals to obtain cross sections for excitation to the n¹S (n = 2 to 7), n¹P (n = 2, 3, 4) and 3 ¹D states. Calculations have also been performed in both length and velocity formulations using a six-parameter ground-state wave function and unrestricted Hartree-Fock excited-state wave functions. The results are compared with other calculations and with experiment.

The wave function of the e^--He⁺ system is expanded as a sum of close-coupling states together with a number of short-range correlation terms. The scattering matrix is evaluated in the energy range between the n = 2 and n = 3 thresholds. The convergence of the expansion of the wave function is discussed and comparison is made with recent experiments for the 1s-2s excitation cross section.

Absolute excitation cross sections for the emission of the second positive bands of nitrogen under electron impact have been obtained. Peak level cross sections for the νprime = 0, 1, 2 levels of the c ³II_u state were found to be, respectively, 23·5 × 10^-18 cm², 14·4 × 10^-18 cm² and 4·9 × 10^-18 cm². Good agreement is found with the theoretical A coefficients for the relative intensities of the different vibrational bands. The results are compared with those of other workers and various secondary effects which were observed are discussed.

The use of the Coulomb approximation for the calculation of molecular transition integrals is examined. The results for single-electron systems and for molecular hydrogen are very encouraging. Many data on ionization potentials are needed to enable the approximation to be widely applied.

Mean scattering cross sections and drift velocity data for thermal electrons in 34 polar molecules in the pure form and 4 in mixtures with ethylene are presented and discussed. The electric molecular dipole moment μ ranges from 0 to about 4·1 debye. The general conclusion is that the point-dipole Born approximation calculation of Altshuler is in better agreement with experiment than the exact calculation of Mittleman and von Holdt. Further, the experimental cross sections are higher than those predicted by Altshuler for all μ ≲ 2·4 debye and smaller when μ ≳ 2·4 debye, while their behaviour at and around the minimum dipole moment μ_min required to bind an electron is complicated. The overall dependence of the experimental cross sections on μ indicates the possible effect of the binding of an electron to a molecule (when μ > μ_min) and the possible effect of a potential resonance as predicted by Takayanagi and Itikawa.

Expressions have been obtained for the longitudinal diffusion coefficient, the velocity distribution function and velocity averages <νⁿ>, for gaseous ions moving in strong electric fields, taking into account only charge-transfer collisions between the ions and the gas molecules and neglecting thermal energies. No restrictions are imposed on the velocity dependence of the collision cross section σ(ν). Numerical results are quoted for the case of a collision cross section proportional to the square of the logarithm of the velocity, which is considered the appropriate velocity dependence for resonance charge transfer in monoatomic gases.

Measurements, using the drift technique of Kaneko, Megill and Hasted, are reported of rate constants for charge-transfer processes Ar⁺ in N₂, O₂, CO, NO in the energy range 1·0-15 eV, for charge transfer and dissociative charge transfer for He⁺ in N₂ and for the three-body process He⁺ +2He -> He₂⁺ + He in the energy range 0·04-0·25 eV. The two-body rates are not in disagreement with flowing afterglow data. Comparison of the argon ion rates is made with `nearest resonance' calculations of Böhme, Hasted and Ong.

The A ²π-X ²Σ⁺ system of BeF has been photographed in absorption at high resolution, and the rotational analysis of the 1-0, 0-0 and 0-1 bands has been completed. The results confirm earlier work that the A ²π state is inverted, although derived mainly from the configuration... σ²π⁴π. This conclusion is in agreement with recent molecular orbital calculations on BeF, and is to some extent confirmed by other experimental work on this molecule which is briefly discussed.

Absolute cross sections for photoionization and autoionization processes are reported from the ionization threshold at 1320 Angstrom to 750 Angstrom. The value of the photoionization cross section at the ionization threshold is 1·1 ± 0·2 Mbn falling to a near zero minimum in the neighbourhood of 1200 Angstrom. At shorter wavelengths, the spectrum is completely dominated by autoionization transitions. The oscillator strengths and half-widths of the absorption features are reported, and configuration interaction effects discussed, in connection with the observed cross-section profiles of the 4s²¹S₀ -> 3d⁹4s²4p ¹P₁, ³P₁, ³D₁ multiplet.

The band spectrum of BaO has been obtained by spraying barium chloride solution into a flame. The integrated intensities of the bands have been determined by photographic photometry. The experimental results along with the theoretically computed Franck-Condon factors have been used to evaluate a relation betweenR_e, the electronic transition moment, andr, the internuclear separation, in the form

R_e(macronr_{νprimeνPrime}) = constant (1 - 0·536r).

This relation has been used to obtain improved Franck-Condon factors. The theoretically computed Franck-Condon factors, with and without the inclusion of R_e variation, have been compared with the experimental band strengths.

The blue-green and ultra-violet bands of A1O are obtained in emission from a d.c. arc between aluminium electrodes in an atmosphere of oxygen at low pressures. For isotopic studies, oxygen enriched in ¹⁸O to 50% is used. Isotope shifts observed for some of the intense bands of the c²Σ⁺-x²Σ⁺ system confirm the vibrational assignments proposed earlier. Three red-degraded double-headed bands at 2500·1 Angstrom, 2545·9 Angstrom and 2592·9 Angstrom form a ν−or+ progression of a new system. Isotope shift studies show that they arise from a ν&acute; = 0 level of an excited electronic state to ν−or+ = 0, 1 and 2 levels of a lower electronic state. During these studies the blue-green bands of Al¹⁸O are also photographed and their shifts measured with respect to the corresponding bands of Al¹⁶O.

Hyperfine structure measurements have been made by atomic beam magnetic resonance in weak fields on the J = 2, 3, 4, 5 and 6 states of the 4f⁷5d6s²⁹D ground fine-structure multiplets in ¹⁵⁵Gd and ¹⁵⁷Gd. These reveal a 2:1 ratio in the effective radial integrals <(r_5d^-3> associated with the l. I and (sC⁽²⁾)⁽¹⁾. I parts of the magnetic dipole interaction as a result of configuration mixing. Significant relativistic effects are found in the quadrupole interaction, and the ratios ¹⁵⁷A/¹⁵⁵A = 1·311 43(23) and ¹⁵⁷B/¹⁵⁵B = 1·065 34(3) are established.

Further measurements in kilogauss magnetic fields by triple resonance on the state J = 3 give the dipole moment ¹⁵⁵μ_I = -0·2584(5) n.m. (after diamagnetic correction), the electric quadrupole moment ¹⁵⁵Q = 1·59(16) × 10^-24 cm², and show the existence of a measurable octupole interaction. After making second-order hyperfine structure corrections, an unusually large octupole moment ¹⁵⁵Ω = -1·6(6) × 10^-24 n.m. cm^-2 is deduced.

After a critical examination of the available data on x-ray forbidden transitions, it has been found possible to classify the so-called forbidden transitions as electric quadrupole, electric octupole, distinctly magnetic dipole and an admixture of magnetic dipole and electric quadrupole transitions. The necessity for studying the individual contributions in the x-ray field has been pointed out. It is significant that a transition corresponding to Δl = 3 and Δj = 2 or 3 is now definitely known for elements Ta 73, Pb 82, Bi 83 and Th 90.

A new method for the determination of atomic screening parameters is considered. With the aid of this method the values of screening parameters are determined for the ground state and some excited states of He-Ne atoms.

The correction to the Wigner threshold law caused by long-range interaction for the excitation of ns-nprime s transitions in atoms is given.

The effect of the inclusion of an exponential attenuating factor in the electron-polar-molecule interaction potential is briefly examined. The calculated cross sections are, as expected, lower than in the unscreened case. It is suggested that the exponential factors have their origin in a screening effect due to the pressure of the gas.

Advantage has been taken of the high optical gain available under pulsed excitation conditions at 7229 Angstrom in excited lead vapour to enhance this transition and reduce its linewidth. The isotope shifts have been measured between ²⁰⁶Pb and ²⁰⁷Pb, and between ²⁰⁶Pb and ²⁰⁸Pb, as 36 mK and 91 mK respectively. A reason for the discrepancy between these and earlier results is suggested.

In continuation of the classification of forbidden transitions in x-ray spectra made by Padalia and Rao in 1969, some of the reported transitions in x-ray spectra have been classified as an admixture of electric octupole and magnetic quadrupole transitions.

An expression for the cross section for excitation by fast protons of hydrogen atoms to any state ns has been obtained. Numerical values for the cross section as a function of impact energy and n are exhibited in tabular form.

A superradiative transient has been observed following rapid passage of an exciting signal through the absorption resonance of a molecular beam of ammonia.