Table of contents

A counter example is given to a recently proposed theorem which asserts that individual axes of quantitization of coupled spins in an external magnetic field precess according to classical equations of motion.

The application of the Glauber-type eikonal approximation to multi-centre atomic collisions, such as atom-atom and electron-molecule collisions, is considered. The eikonal phases for such systems can be evaluated in closed forms and are independent of the z-component of the internal coordinates.

It is shown that the formula for the power widths of misalignment resonances recently derived by Pegg (1973) is not quite correct, because an inappropriate reference frame was used. The use of appropriate frames produces corrections to the formula for two higher order resonances. A correspondence is established between the general reference-frame approach and Shirley's Floquet matrix approach (1965), from which it is possible to write down the general corrected expression.

The inclined beam technique previously described by the authors (see abstr. A63316 of 1973) has been used to measure dissociative recombination cross sections of D₂⁺ (deuterium) ions for interaction energies between 0.28 and 4.0 eV. The initial vibrational population of the ions was close to that observed by von Busch and Dunn (1972), whilst the absolute accuracy of the measurement was of order +or-10%. At 1 eV the cross section was 9.2*10^-16 cm², which is about 40% larger than that previously measured for H₂⁺ ions.

Charge-fractions have been measured for H⁺ and H₂⁺ ion beams transmitted through thin (5-15 mu gcm^-2) carbon foils. The results for H⁺ ions show complete equilibration and agree with existing published data. The H₂⁺ beams show almost total dissociation at all energies studied. The measured charge fractions differ significantly from those of H⁺ beams having the same velocity, and show a foil thickness dependence even after correcting for energy losses in the foils. This is interpreted as a spatial correlation effect, due to the close proximity of the break-up atoms from each H₂⁺ ion as they leave the foil.

Electron scattering spectra of nitrous oxide are reported in the 5-10 eV energy-loss range at scattering angles of 20, 30, 90, and 130 degrees at a residual energy of 7.0 eV; and at residual energies of 10.0. 2.0, 1.0, 0.6, and 0.2 eV at a scattering angle of 90 degrees . Several new distinct and overlapping continua are observed to lie in this energy-loss range. The experimental spectra are discussed in the light of semiempirical INDO calculations of Chutjian and Segal (1972) of the vertical transition energies of N₂O. An assignment of the symmetries of the observed excitations consistent with the experimental and theoretical data is suggested.

Ar LMM Auger electron lines produced by H⁺, He⁺, O⁴⁺, and O⁵⁺ bombardment are measured with high instrumental resolution (0.02% FWHM). Individual heavy ion induced Auger satellite lines are resolved. Two strong lines are observed at 221 and 223 eV in the oxygen induced spectra. The ratio of satellite to normal line production is given for each projectile.

The rotational analysis of the (0,0)_3/2 sub-band of the C-X and G-X systems of the SnF molecule has been carried out. The rotational constants determined for Sn¹²⁰F and Sn¹¹⁸F from the analysis are reported.

The authors reply to the work of Tweed (see abstr. A20044/5 of 1973) which has thrown doubt on the previous work of Byron and Joachain (see abstr. A28934 of 1967) and Van der Wiel and Wiebes (1971).

A reply is made to the comments of Byron et al (see ibid., vol.6, 375 (1973)).

Collisional detachment cross sections of Li-, Na^-, and K^- are calculated by the Bethe-Born approximation using accurate photodetachment cross sections and a Coulomb gaunt factor. The reliability of this method is illustrated by comparison with low energy experiments for H^-.

Calculations of the free-free absorption coefficients of Ne^- and Ar^- by the asymptotic method are reported.

Consideration is given to a binary system in which the constituents are bound together by some general interaction (dependent only on their separation). Expressions are derived for the classical statistical equilibrium constants and for the normalized spatial and momental distribution functions both for the case of a given value of the internal energy and for the case of given values of the internal energy and of the square of the orbital angular momentum.

The virial theorem is applied to the elastic scattering of s wave electrons by helium using a variational ground state helium wavefunction. It is found that when the scaling parameter alpha is introduced into the wavefunction of the bound state electrons in the target atom, as well as the free electron function, this additional scaling has very little effect on the values of the variational phase shift eta _v in the exchange approximation but a profound effect when exchange is neglected. In the latter case it is not possible to optimize with respect to alpha and so Delta = delta _v/ delta k-( delta eta / delta k)_virial never vanishes. However, if the criterion that mod Delta mod be a local minimum is adopted, it is found that the resulting values of the phase shift closely approximate those obtained in the exchange approximation. In the case of positron scattering by hydrogen and helium, where exchange is not possible, the additional scaling of the atomic wavefunction produces neither an optimum value of the phase shift nor a local minimum in mod Delta mod .

Non-relativistic variational energies for the 1s3d(^1,3D) states of the helium isoelectronic sequence are calculated with a 50-term correlated basis set for Z=2-10, where Z is the nuclear charge, and the corresponding Z-expansion coefficients found through sixth order by fitting the energies to a series in Z^-1. A variational-perturbation calculation of these coefficients through eleventh order (with the same basis set) is presented for comparison, and agreement is satisfactory. The 3d energies obtained by summing the Z-expansion perturbation series are found to yield excellent approximations to the variational values. The calculations are extended to the 1s4d(^1,3D) states to furnish variational energies for neutral helium and perturbation energies for the higher sequence members. All of these results are the most accurate yet reported.

The S-wave scattering of positrons by hydrogen atoms is studied using the coupled static approximation with 26 correlation functions for energies up to the excitation threshold of hydrogen. Up to a certain energy, the formulation satisfies a bound principle. Below the positronium formation threshold, the calculated phase shifts are very close to those of Bhatia et al (1971). Above this threshold, the R matrix elements and the cross sections are very different from those of other earlier calculations. No resonances were detected in a search with energy spacing of about 0.02 eV over the region just below the excitation threshold.

The T-matrix elements for electron impact ionization of light atoms are evaluated with fully antisymmetrized wavefunctions. Rather than use direct, exchange and capture amplitudes, as is usually done, the author partition the T-matrix only into capture and transmission amplitudes, which describe whether the impinging electron is captured or not. The transmission amplitude involves both the direct and exchange amplitudes. All scattering amplitudes are reduced to two-particle matrix elements. The structure of the transmission amplitude is easily interpreted in terms of the pure electron-electron interaction, interaction with the screened nuclear potential, and exchange interactions of free electrons with bound ones. The five-fold differential cross section is obtained in rather simple form in terms of the amplitudes.

The electron-hydrogen scattering problem is formulated using the Dirac equation. A set of coupled equations is obtained for the radial wavefunctions for the various states of the incident electron, analogous to the coupled equations in the non-relativistic theory. A set of scattering amplitudes is obtained from which excitation cross sections, elastic and inelastic differential cross sections, and data on final electron and target polarizations can be obtained for any initial electron beam or target polarizations. Explicit formulae for the differential cross section and final electron polarization are given for certain special cases. Inclusion of magnetic and retardation effects in the interaction between the two electrons is discussed.

A simple approximation whereby exchange cross sections in helium may be calculated is described and applied to the calculation of the 1¹S-2³S, 1¹S-2³P and 2¹S-2³S cross sections. It is shown that the approximation yields results which are considerably better than those obtained by means of some other methods in the energy region near to the maximum of the cross section.

The procedure of McCavert and Rudge (1970) is extended to the case of proton-helium collisions and applied to the problem of calculating excitation cross sections from the ground state to the 2¹P, 3¹P, 4¹P and 5¹P states. It is found that the method gives cross section results which are substantially in agreement with experimental data over a wide energy range. Polarization fractions are also calculated and, in common with other theoretical treatments, are found to disagree with experimental values.

For pt. I see abstr. A33056 of 1973. Using the theoretical results of pt. I experimental data of the scattering of ⁷Li⁺-ions at Ar are evaluated. From the diffraction effect detailed statements about the repulsive term of the interaction potential are given. The simple Yukawa type screened Coulomb potential is very well suited for describing the small angle scattering between ions and atoms. A modification of this potential can be clearly excepted. The evaluation method for determining the potential parameters is described in detail and gives for ⁷Li⁺-Ar the parameters R_c=0.289 AA and A_aeff=54. In the region of the first undulation maximum the influence of the attractive potential term is found experimentally. Certainly the experiments show with decreasing scattering angle a shape of approximately 1/ Theta ² which is caused by inelastic scattering.

It is shown that despite their dissimilar appearance there is a close relationship between the formula of Bates et al. (1969) for elastic electron loss in classical collisions and a formula derived from an intermediate state of a development due to Thomas (1927). The former represents an average over differential elastic scattering cross sections and the latter an average over the corresponding rate coefficients. Part-quantal treatments are introduced. As examples H-Ne and H-Ar collisions are investigated. The adoption of Born differential cross sections leads to elastic electron loss cross sections which are much too large. Their replacement by the exchange-polarization differential cross sections of Thompson (1966) does not cause sufficient reduction. Of the formulae considered the original classical one involves much the least computational effort and appears to give the best results.

Five-fold differential cross sections for the ionization of hydrogen and helium have been calculated and in the case of helium compared with the experiments of Ehrhardt and co-workers (1972). It is shown that exchange and capture processes are relevant only for primary energies below 250 eV and 80 eV respectively. The two outgoing electrons are described by a product of Coulomb waves in which the charges are treated as parameters in order to simulate the screening of the residual ion. The different sets of effective charges yield results which greatly differ in the angular position of the binary encounter maximum and the ratio of intensities in the binary encounter and the recoil peak. The results indicate that it is more important to know the full wavefunction in the region where all particles are close together rather than to require fulfilment of the proper asymptotic conditions.

The ratio of the cross sections for single-electron detachment leading to metastable and ground-state atoms for 50 keV He^- ions in H₂ has been measured. Up to 58% of the resulting neutral He atoms are shown to be in one of the two metastable excited states. It is argued that mainly the 2³S state is populated.

The results of the theory are compared with those of experiments for the transverse resonances, i.e. Haroche's resonances and the Hanle effect, in the presence of the strong RF field. It is shown theoretically and experimentally that Horoche's resonance are not only shifted but also broadened as the intensity of RF field is increased. The positions and the shapes of Haroche's resonances are related to the broadening of the Hanle curve due to the oscillating RF field. The positions of Haroche's resonance observed for large intensity of RF field agree well with those of the authors continued fraction solutions rather than those of the perturbation theory. The saturation effect of resonance intensity, which is due to large intensity RF field, is also verified theoretically and experimentally.

The process of muonium ( mu ⁺, e) formation of electron capture mechanism in collisions of positive mesons with atomic systems is considered at high energies. The continuum distorted wave (CDW) method is used for calculation of the cross sections for mu ⁺-H and mu ⁺-He electron capture reactions from 10 keV to 1 MeV. The calculated cross sections are compared with those for electron capture from the same atomic systems by protons.

A study of the energy differences between the ¹ Pi _u and ³ Pi _u states of H₂ has been undertaken, and differences in kinetic energies, electron-nuclear attraction energies, and interelectronic repulsion energies are also given for a range of internuclear separations 0.5 au<or=R<or=5.0 au. Wavefunctions for both states were calculated as part of the study, using a basis set of twenty Slater-type orbitals to do a self-consistent-field calculation followed by configuration interaction. Optimized exponents were used for the most important orbitals at each internuclear separation. It has been found that the interelectronic repulsion energy of the triplet is greater than that of the singlet, and that the triplet lies lower in energy because of its greater electron-nuclear attraction energy.

Collisional detachment in oxygen was studied for pressures of about 20-60 Torr and with mass analysis which also allowed conversion rates to be calculated. For O^-, delta ₁/N (detachment coefficient/gas density) was found to be about 5*10^-18 cm² at E/N (field strength/gas density) of about 50 Td where for O₂^-, delta ₂/N approximately 1*10^-18 cm². The need for an accurate measurement of the conversion rate for O^- to O₂^- is emphasized.

The collisional detachment of electrons from SF₆^- in gaseous F₆ was measured with a double-chamber current growth technique. Mass spectrometer sampling of the negative ions enabled the in-molecule reactions to be identified. Thus the conversions SF₆^- to SF₅-, SF₅^- to F^- and F^- to SF₆^- were found to be important. At E/N of about 400 Td, the detachment coefficient was determined as about 5*10^-17 cm².

A mass spectrometric technique which achieves a high and uniform collection efficiency for all the product ions has been applied to study the secondary ions formed during the passage of 5-45 keV Ne⁺, Ne and Na⁺ beams through thin targets of CO, N₂, O₂ and H₂. Cross sections for the formation of particular secondary ions have been determined, and interpreted using measurements of charge-changing and ionization cross sections. The fragmentation pattern is satisfactorily explained in terms of two step processes involving the creation of excited states of the molecule (which have been observed in other measurements) followed by predissociation, leading to the observed fragment ions.

The band spectrum of SrI is excited in a high frequency discharge through a mixture of heated strontium metal and iodine vapour, from a 1 kW oscillator working at a frequency of 10-16 MHz. The spectrum reveals a number of new bands in the region lambda 3400- lambda 3600 AA degraded to shorter wavelengths. These bands are analysed and attributed to the D² Sigma -x² Sigma transition, analogous to the D-X system of SrF, SrCl and SrBr molecules. The P heads of the bands could be fitted into the following vibrational quantum formula within an accuracy of 1.0 cm^-1 nu _{nu ' nu "}=28938.34+202.74( nu '+¹/₂)-0.84( nu '+¹/₂)²-174.4( nu "+¹/₂)+0.4( nu "+¹/₂)².

The Woods band at 3840AA and the SiN bands in the region 3900-4900AA (A² Sigma -X² Sigma transition) have been excited strongly under well controlled conditions in a high frequency discharge. From the results of the present studies it has been shown that the emitter of the Woods band at 3840 AA is SiO⁺ and not SiN. A critical review of the data, used by Nagaraj and Verma (1968) to attribute the Woods band to B² Sigma -A² Sigma transition of SiN, supports our assignment of the Woods band to SiO⁺. The intensity behaviour of the SiN bands (3900-4900 AA) excited in the high frequency discharge and in the afterglow of nitrogen has also been described.

The transition amplitude for double ionization of the helium atom involving absorption of many-photons of intense field in the ground state has been evaluated using the nonperturbative method of Reiss. Results show an important non-linear effect at high intensity. It is also found that at high intensity higher order processes are more probable than low order processes.

The collisional-radiative model for the distribution of population densities among the energy states of a hydrogen-like ion plasma has been extended to lower electron densities by including the additional atomic processes of two-photon decay of the 2S level and electron- and proton-induced transitions between the component angular momentum sublevels in principal levels 2 and 3. The intensity ratio of the Lyman alpha (1S-2P) to Lyman beta (1S-3P)lines in the hydrogen-like ions (Lyman ratio) is calculated for a wide range of electron temperature and density. New experimental measurements give Lyman ratios about 60-80% of theoretical predictions, compared with about 35% for previously reported measurements. It is believed that these discrepancies are due to self-absorption.

Using an improved T-tube to produce high density helium plasmas, a high density effect connected with the presence of perturbers in the vicinity of a radiating ion has been studied. This effect, the plasma polarization shift, involves the shift of a line under the influence of a perturbing electron. When this electron is considered as bound and forms with the radiating electron a doubly excited state of the ion, the effect corresponds to the emission of dielectronic satellites and is shown to be negligible. When the additional electron is treated as a free perturber the approach of Greig et al. predicts a blue shift as observed here. The red shifts measured for the optically thick lower series members are shown to originate in far wing asymmetries due to higher order effects usually neglected in hydrogenic Stark profiles.

The effect of traces of oxygen on the recombination of nitrogen atoms is examined, free from further excitation, in the afterglow observed to follow a discharge in nitrogen. Processes occurring in the volume of the gas and at the wall are discussed quantitatively, and their importance assessed.