Table of contents

Cross sections are calculated for

at impact energies E in the range 0.1 MeV ⩽ E ⩽ 100 MeV, using the prior (i) and post interactions with the wave version of the first Born approximation. Cross sections for (A) and

have also been calculated for 20 keV ⩽ E ⩽ 100 MeV, using the distorted-wave interaction with the Born approximation. The cross sections of (B) agree with the calculated values of McCarroll and of McElroy for capture from H(1s), and the distorted-wave cross sections of (A) are also in good accord with those of Bransden and Sin Fai Lam. Newly calculated OBK cross sections for all subshells of Ar and previously calculated OBK values for N and O are used to obtain estimates of the total cross sections for capture by protons in the range 20 keV ⩽ E ⩽ 100 MeV. These predictions are likewise in fair accord with the measured values per gas atom of N₂, O₂ and Ar by Schryber, Welsh et al. and Barnett and Reynolds. Certain features of these cross sections are similar to the classical ones calculated by Bates and Mapleton and by Mapleton. The approximate effective Born prior interaction at high energies is used to derive the approximate asymptotic ratio

for the capture of 1s-orbital electrons from a neutral target of atomic number Z. It is found that L(Z) increases monotonically for increasing Z, and this increase possibly indicates a defect in the Born prior and post formulations.

Cross sections have been measured for the reaction Mg⁺ + e -> Mg² + 2e for electron energies between threshold and 2000 eV; the errors are estimated to be less than ±10% for electron energies greater than 50 eV. The cross section σ attains a maximum value 4·85 × 10^-17 cm² (±11%) at 35 eV, and, when E is greater than 11, it obeys the law σE = 9·8 × 10^-16 lg (0·216 E) cm², where E is the incident electron energy in units of the ionization energy of Mg⁺ (15·03 eV). No irregularities in the ionization function were found which could be attributed to autoionization.

The cross sections for photoionization from the 1sσ, 2sσ and 3sσ states of H₂⁺ are calculated for energies of ejection of up to 16 ryd. Contrary to what has been suggested, the photoionization cross section curves do not show undulations. A simple model of a more complex diatomic molecule is investigated. In this case a shoulder, rather similar to those found by Samson and Cairns in 1965, appears in the photoionization cross section curve. It is associated with the passage through zero of the matrix element of one of the Δl = 1 transitions, l being the azimuthal quantum number in the united atom limit. The Δl = 3 and 5 transitions are far too weak to be invoked in explanation of the structure observed by Samson and Cairns.

The cross sections for the vibrational excitation of N₂ molecules bombarded by electrons show a strong peak between 2 and 3 eV, split up into a regular sequence of minor peaks reminiscent of distinct resonances. However, the minor peaks appear in the different final channels at different energies and with slightly different spacings, a behaviour which could be understood on the resonance picture only as the result of some interference effect. An explanation of the phenomenon is offered, based on the assumption (for which reasons are given) that the nuclear wave function in the intermediate N₂^- ion is a standing wave whose amplitude varies slowly, and whose nodes move slowly as the energy changes. As the nodes drift over the nodes of the final states of the residual molecule, the overlap integrals of the intermediate and final states oscillate, and hence the cross sections oscillate too. The spacing of the minor peaks in energy and their relative displacement for the different final states can be understood in terms of the drifting nodes in an energy representation, and in the corresponding time representation in terms of the motion of the nuclear wave packet.

The classical theory of Gryzinski is used to obtain cross sections for the electron ionization of the degenerate levels of atomic hydrogen. The results are compared with the Born approximation cross sections and it is found that the agreement is good. As the principal quantum number is increased the classical and quantal cross sections tend to one another at all values of the incident electron energy for all azimuthal quantum numbers.

Cross sections for the process

H⁺ +H(1s) -> H⁺ +H(2s)

have been calculated in the quantal impulse approximation for proton energies in the range 1-500 keV. It is shown that a peaking approximation previously used in the evaluation of impulse approximation matrix elements is invalid and greatly underestimates the true impulse approximation cross section for this process.

The close-coupling approximation is applied to the problem of scattering of electrons by Mg⁺ and Ca⁺ ions. Positions and widths of autoionizing states of the corresponding neutral atoms are calculated, and, in the case of Ca, compared with experiment.

The electron impact excitation cross sections for the 3s -> 3p and 3s -> 3d transitions in Mg⁺ and for the 4s -> 4p and 4s -> 3d transitions in Ca⁺ are calculated with and without exchange. Agreement with Coulomb-Born calculations is quite good.

General requirements of analyticity and unitarity are shown to give restrictions on the possible behaviour of the complex potential energy curves of H₂^-. It is argued that these restrictions may be of importance in processes such as dissociative attachment.

The upper bound on the total transition probability p(t) previously obtained by Aspinall and Percival in 1967 is generalized to systems with an infinite or arbitrary finite number of states and to arbitrary time-dependent trial states |ψ_tr(t) > . The bound for transitions from |ψ_tr(t) > is

where |ψ_tr(- ∞) > coincides with the initial state, l = H -iℏ d/dt and H is the time-dependent Hamiltonian. A bound on total inelastic cross sections is obtained for collisions between heavy systems with sufficiently short-range interaction potentials. The method is applied in its simplest form to H-H and p-H collisions, but gives results of little physical significance. A reason is given and possible remedies suggested. A variational method for time-dependent states is proposed.

A number of approximate procedures for the calculation of long-range two- and three-atom interaction constants are discussed. All the procedures, of which that proposed by Öpik in 1967 is one, result from the inclusion of a first-order static distortion function in a variational trial function of either one- or two-centre type. It is shown that their application requires a knowledge of a limited number of oscillator strength sums (four at the most), and their accuracy is assessed by comparison with previous calculations.

Calculations are presented of the energies involved in the Auger effect for sulphur, aluminium and silicon, and associated with an atomic transition (K-LL) in which one electron from the L shell falls into the K-shell vacancy and a second electron from the L shell is ejected, carrying away the surplus energy. Agreement with the meagre available experimental data is qualitatively good. The whole group of energies varies almost linearly with the oxidation number of the atom, a phenomenon which suggests a possible correlation with chemical bond effects.

A theoretical study has been made of the satellite x-ray lines in sulphur which lie on the high-energy side of the strong Kα_1,2 lines. It is shown that a satisfactory account of the Kα_3,4 group of these lines (αprime, α₃, α₃prime, α₄) can be given in terms of transitions K^-1L^-1 -> L^-2 involving double ionization of inner shells. Not only is the observed sequence of these lines correctly predicted, but it is also shown, in agreement with experiment, that the satellite lines should be much more sensitive to chemical bonding of the emitting atom than are the parent Kα_1,2 lines, and that they should move as a group, with mutual separations nearly independent of oxidation number in the emitter. High oxidation numbers will be associated with larger transition energies.

Measurements have been made of the recoilless fraction and broadening of Mössbauer γ rays Rayleigh scattered from glycerol and sec-butyl benzene in the supercooled liquid, glassy and polycrystalline states, and from polycrystalline benzene. It is concluded that the vibration amplitude (possibly rotational in origin) in the supercooled liquids can be considerably larger than in the corresponding polycrystals at the same temperature. Energy broadening due to molecular diffusion was observed in supercooled liquid glycerol, in approximate agreement with what would be expected from viscosity values and a naïve application of the Einstein formula. No such broadening was observed in the scattered radiation from sec-butyl benzene, contrary to that expected from viscosity data. With polycrystalline benzene no broadening from the rotational motion deduced from nuclear magnetic resonance experiments was seen, and this is interpreted as evidence that the molecules rotate in discrete jumps, such that the spatial positions of a molecule both before and after a jump are the same, rather than continuously or as a rotational Brownian motion.

The least-squares method for finding the eigenvalues of the Schrödinger equation has the conceptual and practical advantage that it does not require the evaluation of integrals such as (ψ, Hψ) as does the variational method. In this paper we consider the evaluation of the expected value <Q> = (ψ, Qψ)/(ψ, ψ) of an arbitrary Hermitian operator Q. We give a least-squares method for the evaluation of <Q> which also does not involve the evaluation of any integrals. The method is illustrated with calculations for the expectation values of a number of operators over the ground state of the helium atom, using a mesh containing only 126 points. The relative accuracy obtained varies between 10^-4 and 10^-6.

Measurements have been made at room temperature of the rates of decay of the atomic ion species in afterglow plasmas in pure neon and argon at various pressures within the range 0·01-2 torr. In both gases, the variation of the measured decay rates with pressure, observed over about two orders of magnitude in pressure, is consistent with the loss of the atomic inert gas ions by diffusion to the plasma boundary and by conversion to molecular inert gas ions in three-body reactions with the neutral gas. The present measurements constitute the first observations of the three-body conversion process in argon by a method providing mass identification of the participating ion species. The values obtained for the rates of the conversion reaction in neon and in argon and for the reduced mobilities of the atomic inert gas ions in their pure parent gases are

νNe⁺ = (99±5)po²s^-1, νAr⁺ = (313±12)po²s^-1μNe⁺ = 4.6±0.4 cm²V^-1s^-1, μAr⁺ = 1.75±0.15) cm² V^-1s^-1.

These results are compared with the values which have been obtained by other workers and comparisons are also made with the existing theoretical estimates of the measured parameters.

Mass spectrometric observations of helium afterglows by ion sampling from the walls of a large discharge vessel are described. It is shown that in very pure cataphoretically-cleaned helium in the pressure range 0·3 to 2 torr the only important processes occurring in the late afterglow are ambipolar diffusion of atomic and molecular ions and electrons, and conversion of atomic to molecular ions by three-body collisions with neutral helium atoms. The atomic and molecular ion mobilities corresponding to the observed diffusion rates are respectively 11·2 ± 0·4 cm² v^-1 s^-1 and 15·9 ± 0·4 cm² v^-1 s^-1, in acceptable agreement with several previous mobility measurements, and the value obtained for the three-body conversion coefficient, 85 ± 3 torr^-2 s^-1 (pressure reduced to 0 °C) is in good agreement with a recent similar measurement by other workers in a higher pressure range. The wall temperature of the discharge vessel during these measurements was 295 °K. Measurements carried out in helium samples which were not subjected to cataphoretic purification demonstrated the serious effect of small amounts of impurity on the decay rate of the molecular helium ion.

Measurements are described of slow electron density decay rates in pure helium afterglow plasmas, using a very small single Langmuir probe, a technique not hitherto applied to the study of ambipolar diffusion. Values are obtained for the rate of conversion of He⁺ ions to He₂⁺ ions and for the respective mobilities of these ions at a wall temperature of 295 °K, which are in reasonable agreement with values obtained by other workers using different techniques. This agreement is considered to indicate that depletion problems, which are expected to be most severe in slowly decaying plasmas, have been overcome by the utilization of very small probes. Evidence is also presented for the existence of elevated electron temperatures at times as late as 10 ms in the afterglow, and these results, together with those above, are critically discussed and compared in detail with the complementary mass spectrometric observations described in I.

Laser and microwave interferometers have been used to measure electron densities over the range 1·8 × 10¹⁵ to 8 × 10¹¹ cm^-3 in a decaying helium plasma without a confining magnetic field, at gas pressures ranging from 82 to 1200 mtorr. Collisional radiative recombination and ambipolar diffusion were identified as the electron-loss mechanisms, with the former dominating at the highest pressures and densities. Spectroscopic measurements of electron temperature were in good accord with the recombination coefficients α inferred from theory, but the actual trend of α with density suggested the existence of elevated atom and ion temperatures. The loss of recombination energy from the plasma was mainly due to radiation and atom thermal conduction, but the electron-atom energy coupling in helium was sufficient to permit the latter mechanism only at the highest electron densities. The assumption of elevated ion temperatures also led to good agreement between the theoretical and experimental diffusion coefficients.

The behaviour of electronic terms and wave functions of the molecular ion H₂⁺ for large internuclear separations is considered. Comparisons of asymptotic formulae with numerical calculations are presented.

It is shown that `negative' Faraday rotation can be induced in a gas laser as a consequence of optical gain and is of opposite sign to that resulting from an absorbing transition. The magnitude of this rotation in the vicinity of a Gaussian gain line is derived theoretically and compared with measurements on two He-Ne laser tubes at a wavelength of 3·39 μm. The results offer a means of measuring Doppler linewidths and give rise to values of 380 MHz and 470 MHz for tubes of length 33 cm and 14 cm, respectively. These figures correspond to temperatures of 760 °K and 1140 °K, which are considerably higher values than have been quoted for larger laser tubes.

A crossed-beam electron spectrometer using hemispherical electrostatic velocity analysers is described. Electron energy-loss spectra for K have been obtained at 41, 51, 68, 101 and 201 eV incident electron kinetic energies. The f-sum rule has been used to obtain generalized oscillator strengths and absolute differential cross sections for the transitions 4 ²S -> 4 ²P, 5 ²S, 3 ²D, 5 ²P, 4 ²F, 6 ²P. The reduced matrix element (4 ²Sparallelr²parallel5 ²S) was found to be 54 A.U., and the electric quadrupole transition probability for 3 ²D -> 4 ²S found to be 5 × 10² s^-1. A method is suggested for absolute calibration of atomic beams in crossed-beam experiments.

The problem of the vibrational relaxation of a system of anharmonic oscillator molecules has been analysed numerically. Exchange of vibrational energy between molecules plays an important part in the relaxation mechanism. Calculations have been carried out for nitrogen, using transition probabilities similar to those calculated by Schwartz et al. These calculations show that, during vibrational excitation, the relaxation rate is only slightly different from that predicted by Landau and Teller, for harmonic oscillator molecules. However, very rapid vibrational deexcitation is found to occur, under conditions far from equilibrium, as a result of an upper-level population reversal, fed by rapid vibration-vibration exchanges.

The theoretical expression for the probability of two-photon decay of helium in the 2 ³S₁ metastable level is derived. It is found that this expression is quite different from the corresponding expression for the 2 ¹S₀ -> 1 ¹S₀ transition. It is shown that the transition probability computed by Mathis in 1957 is overestimated by a very large amount and that A(2 ³S₁ -> ¹S₀) less, similar 10^-10 s^-1.

The linewidth in level-crossing experiments as normally carried out is the sum of the natural widths of the levels concerned. We have reduced the linewidth by taking the fluorescent light, not from all atoms in the assembly, but from a sample biased in favour of those which have survived as excited atoms for times longer than the average. This was achieved by pulse techniques. Improved resolution was obtained of the components on the wing of the zero-field level-crossing curve for the level 3 ²P_3/2 in ²³Na.

The values obtained for the hyperfine-coupling constants are a = 18·5 ± 0·40 MHz, b = 3·0 ± 0·6 MHz, in agreement with values found in double-resonance experiments. The present values do not represent the limit of the method, since the experiment was designed to investigate the technique, not to make precision measurements.

A theoretical analysis of the method reveals that level-crossing curves obtained by this technique may, in certain circumstances, have undesirable satellites. It is shown how the line profile may be controlled and improved without too great a sacrifice in statistical accuracy.

Hartree-Fock solutions for the configurations 4d⁹5s²5p and 4d⁹5s²6p of Cd I have been calculated and used to study the peculiar behaviour of observed intensities of dipole transitions from the ground state.

Profiles of calcium absorption cross sections (σ) for transitions between 4s²¹S₀ and 3dnp ^1.3P₁⁰ (at 1926·5 Å, 1886·5 Å, 1777·5 Å and 1765·1 Å) and between 4s²¹S₀ and 5s4p ^1.3P₁⁰ (at 1740·3 Å and 1718·0 Å), which exhibit autoionization broadening, are fitted to the parameterization of Shore

and results are given for the profile parameters.

The absorption spectra of the SrH and SrD radicals have been obtained in a King furnace. In all, six new bands of SrH at 3031 Angstrom, 2914 Angstrom, 2836 Angstrom, 2680 Angstrom, 2620 Angstrom and 2420 Angstrom and two new bands of SrD at 3023 Angstrom and 2917 Angstrom have been observed. Of these the SrH bands at 3031 Angstrom and 2914 Angstrom have been analysed as the (0, 1) and the (1, 1) bands of the F ²Σ -> X ²Σ system (at 2927 Angstrom) and the SrD bands at 3023 Angstrom and 2917 Angstrom have been shown to be the (1, 0) and the (1, 1) bands of the systems G ²Σ -> X ²Σ (at 3115 Angstrom) and F ²Σ -> X ²Σ (at 2928 Angstrom), respectively. The SrH band at 2420 Angstrom, ring has been established as a new transition which may be called H ²Σ -> X ²Σ. The SrH bands at 2836 Angstrom, 2680 Angstrom and 2620 Angstrom, however, could not be classified at present because of lack of sufficient data and will form the subject of another paper.

An upper bound on the loss in probability from an arbitrary group of states is obtained for systems described by a time-dependent Schrödinger equation. The inequality could be of use for problems in which sets of states are closely coupled.

An estimate of the position of an intensity maximum in an absorption band is shown to be valid in greater generality than the original derivation suggested.

The validity of semi-theoretical expressions for the electronic transition moment variation with reference to the AlO (A ²Σ-X ²Σ) band system has been examined from the basic assumptions on which the expressions are built and other studies, and it is shown that none of the expressions can be a unique function for the system.

No evidence has been found for the production of H₂^- ions when 40 keV H₂⁺ ions are passed through a hydrogen gas target.