Table of contents

The elastic scattering of electrons is calculated with a Hylleraas product wave function for the target atom and with neglect of polarization. A narrow resonance is found at an incident kinetic energy of 4.2 eV, provided that the exchange operator is changed slightly, from the value corresponding to the no-polarization approximation, by multiplying by a constant factor differing from unity by plus or minus a few per cent.

The elastic scattering of electrons by helium atoms is calculated with a target wave function containing some correlation. Polarization is simulated by the addition of a small attractive potential. A resonance is found at an energy which is extremely sensitive to the magnitude of the polarization. The resonant wave function has one electron in the 1s level, and the other two in the correlation component (orthogonal to (1s)²) of the helium ground state. The treatment shows that such a resonance should always be found in a one-channel calculation with a target wave function containing some correlation. However, the customary approximations are of such dubious validity at the resonance that it is doubtful whether anything like it exists in the real world.

The theory of configuration interaction is discussed in relation to molecular states which have sufficient energy to decay by electron emission or pre-dissociation. By considering the effects of electron emission a resonant scattering formalism is developed which is useful for electron-molecule collisions at very low energies. The application of the theory to pre-dissociation is demonstrated by an analysis of the recent study by Barrow et al. of the spectrum of selenium.

It is suggested that there are two distinct modes of dissociative recombination, which are called direct and indirect. The direct mechanism, first described by Bates, involves a single radiationless transition, whereas the indirect mode occurs through an intermediate Rydberg state of the molecule. The recombination rate for ground-state ions should decrease with increasing temperature for both processes, but the rate of decrease is faster for the indirect process. Complete calculations of the recombination rate do not seem possible yet, but it is shown that spectroscopic data can be used to give estimates of these rates. The method is illustrated by a partial calculation of the rate of direct recombination in nitric oxide.

A calculation of the position and width of the lowest-lying autoionizing 2p²¹D state of helium is presented using the method of configuration interaction. Good agreement is obtained with recent close-coupling calculations. Results for H^-, Li⁺ and other two-electron systems are also given.

The collision integral occurring in the rate coefficient describing the energy change of ion pairs moving in a gas is made available by determining accurate curve fits throughout the region of most physical interest.

The total, charge-transfer, diffusion and viscosity cross sections for He⁺ in He are calculated using numerically integrated phase shifts and term by term summations. The calculated mobility is in harmony with recent measurements. The corrections to the usual mobility expression are evaluated and found to be negligible. The average behaviour of the total cross section is satisfactorily described by the Schiff-Landau-Lifshitz approximation.

The mobilities of alpha particles in helium at temperatures between 10 °K and 300 °K and of protons in helium at temperatures between 1 °K and 600 °K have been calculated. Both mobilities remain close to the polarization limit at all temperatures considered. A discussion is presented of the behaviour of the total and viscosity cross sections, and, for He²⁺ in He, of the double-charge-transfer cross section. The higher-order corrections to the mobility are evaluated and found to be negligible.

Numerical calculations are made, using the methods discussed in a previous paper by Hibbert and Coulson. The restrictions on the wave function, which are imposed by the `best direction from the saddle-point' criterion, do not greatly affect the value of the minimum open-shell energy. When we leave the open-shell manifold, the Hartree-Fock energy is no longer a saddle-point. The `best direction' is along the negative gradient to the level surfaces, E = constant. The wave function takes the form of the pair-correlated function of Sinanoglu. The correlation function is strongly orthogonal to the Hartree-Fock orbital.

The mercury atom is treated as a two-electron system with the orbitals determined using the Coulomb approximation, and intermediate-coupling wave functions are employed which allow for the spin-orbit interaction of the 6p electron of the 6 ¹P₁ and 6 ³P₁ states of mercury. The oscillator strengths of the 6 ¹P₁ -> 6 ¹S₀ 1850 Angstrom line and the 6 ³P₁ -> 6 ¹S₀ 2537 Angstrom line are calculated to be 1.17 and 0.037, respectively, which are in very good agreement with the experimentally determined values.

The Ochkur approximation is then used to calculate the cross sections for the excitation of the 6 ¹P₁ and 6 ³P_0,1,2 states of mercury by electron impact. Finally these excitation cross sections are employed to evaluate the percentage polarizations of the 2537 Angstrom and 1850 Angstrom lines of mercury excited by incident electrons.

A recent formulation of the three-body collision problem in the form of coupled multi-channel two-body Lippmann-Schwinger equations is applied to the electron-hydrogen collision problem. The relation between these equations and the close-coupling equations is studied by casting the latter into integral form. A simple high-energy approximation, which amounts to a unitary version of the Born-Oppenheimer approximation, is derived, and used in its simplest form to calculate elastic scattering. The results indicate that exchange effects and unitarity corrections are significant at least up to 400 ev.

The collisional cross sections for the excitation of a hydrogen atom from the 2p and 2s states to the 3s, 3p and 3d states are calculated in the approximation proposed by Morrison and Rudge. A comparison is made with the close-coupling calculations of Burke, Ormonde and Whitaker and with the dipole approximation calculations of Saraph. It is found that the Morrison and Rudge approximation does not give reliable results for the 2l₀ -> 3l transitions.

Coupled-channel calculations are performed for proton-hydrogen scattering using an expansion in atomic orbitals in which the effective charge seen by each orbital is allowed to vary with time. It is shown that optimum charges are determined by an Euler-Lagrange equation. At very low energies the method closely resembles an expansion in molecular orbitals, and the Euler-Lagrange equation minimizes the molecular energies. By comparison with previous calculations which use molecular and atomic expansions it is shown how the method bridges the gap between them. Excellent agreement is obtained with the oscillating probability measurements of Lockwood and Everhart for charge exchange at 3°. Cross sections are calculated at 25 kev and compared with experiment and other theories.

A windowless vacuum ultra-violet monochromator was used for the study of the photoionization curves of cadmium and mercury. The energy range covered was from the onsets of ionization to 19 ev and 17.7 ev for cadmium and mercury, respectively. Several autoionization peaks were observed. These correspond to excitations of inner d electrons of the neutral atoms. Oscillator strengths are given for the autoionization peaks in cadmium.

The electrical conductivity of sodium vapour at pressures above 10 torr cannot be calculated satisfactorily on the assumption that the vapour is monatomic. A theoretical assessment shows that clusters of three and four sodium atoms, which have exceptionally low ionization potentials, may make contributions to the conductivity out of all proportion to their concentrations, to the extent that under nearsaturated conditions their influence could predominate by an order of magnitude. The conclusions of this paper apply to all alkali metal vapours, and possibly to other metallic vapours also.

The relationship between bond length L and force constantf

L⁶ = 1.793 × 10⁶m₁m₂/n²f

where n is the group number of the di-atom andm₁, m₂ are the masses of the atoms comprising the bond, of a di-atom in all types of species is proposed and examined, and found to be satisfactory.

Refractive index measurements have been carried out on xenon liquid and vapour in coexistence from -59.0°c to 16.5°c, and also on fluid xenon at temperatures above the critical point (16.59°c). The results of over 500 measurements indicate that the Lorentz-Lorenz function (n²-1)/(n²+2)ρ remains constant to within ±3% over the whole density range studied (0.001 to 0.02 mol cm^-3) and that at the critical point n_c = 1.3799±0.0008 and LL_c = 10.5±0.1 cm³ mol^-1 (λ = 5893 Angstrom).

Further experiments are reported in which resonance fluorescence of an atomic vapour is excited by modulated light. The system studied was the ³P₁ level of cadmium excited by the λ 3261 λ intercombination line modulated at 462 kHz. Resonant changes in the amplitude of modulation of the fluorescent light have been observed in both static and time-dependent magnetic fields whenever the modulation frequency matches a frequency separation between the states of the excited atoms. Quantitative investigations of the shape and position of the observed resonances show good agreement between theory and experiment. The application of the technique to the spectroscopy of excited atoms is considered.

Measurements of the relative intensities of C V 2 ¹S-2 ¹P (3541 Angstrom), C V 2 ³S-2 ³P₂ (2271 Angstrom) and C IV 4 ²D-5 ²F (2524.4 Angstrom) lines from relatively low-energy (similar, equals 12.5 kJ) theta-pinch discharges in methane (electron density similar, equals 4 × 10¹⁷ cm^-3, electron temperature kT_e similar, equals 40 eV) are reported. From these experimental data, the total triplet to singlet excitation rate coefficient amongst the n = 2 levels of the C V ion is estimated to be about 4 × 10^-9 cm³ s^-1 at kT_e = 37 eV with an overall uncertainty of about a factor of 2. This observed value is substantially in agreement with the predicted maximum theoretical value for s-wave electrons.

A 40 cm curved mica crystal spectrograph was employed to study the x-ray L emission of the rare earth holmium. The analysis of the spectrograms showed two new lines at λ 1323·96 X.U. and λ 1340·16 X.U., corresponding to the non-quadrupole transition L_IO_I and the quadrupole transition L_IN_IV.V, respectively. The transitions L_IIO_I(γ₈), L_IM_IV(β₁₀) and L_IO_IV.V reported earlier only by Sakellaridis have been confirmed. However, the transitions L_IIO_IV(γ₆) and L_IIIO_IV.V(β₅) reported also by Sakellaridis remained unconfirmed.

The spectrum of the BeBr molecule has been excited in emission in a high-frequency discharge for the first time when a stream of bromine and argon mixture is passed over heated beryllium metal. The spectrum, photographed on a Hilger E₁ Quartz Littrow spectrograph, revealed the existence of three marked sequences of bands degraded to longer wavelengths in the region λλ 3660-3920 Angstrom. The system consists of double-double-headed bands and appears to be the analogue of the A ²II-X ²Σ systems in BeF and BeCl, with a doublet separation of about 197 cm^-1. The following vibrational quantum formulae represent the Q₁, R₁ and R₂heads:

ν_Q1 = 26357·2+701·2(vprime+½)-4·5(vprime+½)²-713·8(v−or++½)+3·5(v−or++½)²ν_R1 = 26401·85+686·4(vprime+½)-2·25(vprime+½)²-703·5(v−or++½)+4·25(v−or++½)²-2·4(vprime+½)(v−or++½) ν_R2 = 26558·3+694·5(vprime+½)-4·0(vprime+½)²-715·2(v−or++½)+5·2(v−or++½)²-2·5(vprime+½)(v−or++½).

The vibration spectra of ethylene oxide and ethylene oxide d₄ have been analysed simultaneously, yielding twenty-six valence-type potential constants. The method of steepest descent was used to obtain a least-squares fit of the thirty observed frequencies to those calculated from the secular equations deduced by the Wilson FG matrix method. The estimated error in the potential constants is given. The value 1379 cm^-1, reported by Kohlrausch and Reitz, is assigned to v₇ for C₂H₄O in place of the estimated value 1345 cm^-1 of Lord and Nolin. The values obtained for the principal potential constants agree well with those obtained for molecules having similar structures.

The L emission spectrum of thulium 69 has been investigated in the gamma region using a 40 cm curved mica crystal spectrograph of the transmission type. Three new diagram lines at 1246.3, 1283.1 and 1232.4 X.U. have been reported for the first time. The first corresponds to the quadrupole transition L_IN_IV,_V(γ11). The other two have been assigned to the forbidden transitions L_IN_I and L_IO_I, respectively. The measurements on the previously known diagram lines in the region have been compared with those of the earlier workers.

Using a 40 cm curved mica crystal spectrograph of the transmission type, the beta-gamma region of the L emission spectrum of thulium has been investigated. Four new diagram lines at 1439.1, 1489.4, 1331.5 and 1341.6 X.U. have been reported for the first time. The first line corresponds to the dipole transition L_IIIO_I(β₇), the next two to the quadrupole transitions L_IIIN_III and L_IIN_III, respectively, while the last one has been assigned to the forbidden transition L_IIN_II. The measurements on the previously known diagram lines in the region under study have been compared with those of the earlier workers.

This paper is concerned with the possible electric-dipole moments of an atom in a magnetic field. In order that the moment be non-zero, both parity and time-reversal invariance must be violated. The usual proof for this is not strictly valid in the presence of a magnetic field, and an alternative proof is given which does not suffer this disadvantage. The various forms that a violation of parity and time-reversal invariance can take are identified, and an effective dipole operator is constructed to reproduce the resulting electric-dipole moments within a given hyperfine structure multiplet. With plausible assumptions it is shown that this effective operator depends on only a small number of parameters. In order to bring out the symmetry of the problem, these parameters are chosen to be the coefficients in a spherical tensor expansion of the effective dipole operator. This expansion is then used to derive expressions which give the dipole moment for any state in a given hyperfine structure multiplet of a J = ½ atom, at any magnetic field.

A quantitative calculation is made of the electric-dipole moment on a free one-electron atom which would result from the existence of a non-zero moment on the electron. It is shown that in the non-relativistic approximation the atomic moment is zero, but that relativistic effects allow a non-zero value. For the ground state of hydrogen the atomic moment is found to be -2Z²α²d_e, while for the 2s state it is of order d_e/α; d_e is the electron moment and α is the fine-structure constant. The enhancement in the 2s state is closely connected with the near degeneracy of the 2s and 2p states.

The first Born approximation is used to calculate the cross sections for electron excitation of the ground state of helium to the 2 ¹S and 3 ¹S states. Various ground- and excited-state wave functions are employed and the calculations are performed using both the length and velocity formulations of the Born approximation integrals. The best differential cross sections for 2 ¹S are in good agreement with the experimental data. Camparison is also made with available experimental total cross section data.

The rotational structure of the (0, 0) and (0, 1) bands of the 2650-2850 Angstrom system of the BiF molecule has been photographed in emission in the third order of a 35 ft concave grating spectrograph (dispersion, 0.22 Angstrom mm^-1) and their rotational analysis carried out. The nature of the upper and lower states of this system has been discussed.

For the process

He(1s) + e^-(k₀) -> He²⁺ + e^-(k₁) + e^-(k₂) + e^-(k₃)

relations between the direct and the exchange amplitudes, similar to the relation of Peterkop for single ionizations, are given. It is also found that each of the two exchange amplitudes contributes to the cross sections as much as the direct amplitude at any energy.

Generalized oscillator strengths for the 1 ¹S-2 ¹S and 1 ¹S-3 ¹S transitions in atomic helium were calculated using many-parameter correlated orthogonal wave functions. The scattering amplitude for elastic scattering was also evaluated. From these values, the Born cross sections for electron scattering were obtained. There is good agreement between these results and those found using Hartree-Fock wave functions.