Table of contents

A relationship between the work of Barron and Gray (see abstr. A10321 of 1973) on the multipole Hamiltonian and the usual theory based on a unitary transformation is demonstrated.

A general analytical result has been obtained for the calculation of higher-order corrections to the momentum translation approximation. From this analytical result the numerical result has been obtained for the sum of all corrections to the momentum translation approximation for the case of threshold ionization of hydrogen from its ground state by the Nd-Glass laser. The numerical result shows that the validity of the momentum translation approximation increases as the intensity of the laser beam increases.

A method has been developed for calculating systematically the low intensity and the high intensity limits of the momentum translation approximation. In the low intensity limit the 'perturbation' theory type result is obtained and in the high intensity limit the 'tunnelling' theory type result is obtained. It is shown that the momentum translation approximation is basically non-perturbative in origin in the sense that even in the low intensity limit the higher order corrections appear in a fundamental way.

Electron capture processes in He⁺-He collisions are studied, using a time of flight technique. In particular, differential cross sections for both resonant electron capture and capture into excited states are measured. Cross sections for electron capture in n=2p states show an oscillatory behaviour which is out of phase with cross sections corresponding to direct n=2p excitation. This observation brings a new strong support to the interpretation of He⁺-He excitation in the keV energy range, through rotational coupling.

A modulated crossed-beams apparatus has been used to measure total cross sections for chemiionization in thermal energy collisions of He(2³S) and He(2¹S) metastable atoms with hydrogen atoms and molecules. In addition, partial cross sections have been measured for reactions in which specified product ions are formed. Results for hydrogen atoms are in good agreement with recent calculations.

Cross sections for ionization of atomic hydrogen by singlet and triplet metastable helium atoms have been calculated. It is argued that the autoionization width corresponding to the singlet interaction, which has not been accurately calculated, is similar to the width for the triplet interaction. The results are in good agreement with recent experimental measurements.

CW laser oscillation has been observed on eight transitions of singly ionized arsenic in a He-As mixture using a 3 mm bore, multiple anode-hollow cathode laser tube of metal construction. The dependence of laser intensity on helium pressure, arsenic partial pressure and discharge current has been studied. It is proposed that excitation of the upper laser level occurs via charge transfer reactions between ground state helium ions and ground state arsenic atoms.

The N₂⁺(B² Sigma _u⁺) ions were produced through vacuum ultraviolet irradiation at lambda 462, 555, 630 and 637 AA and the intensities of the N₂⁺(B² Sigma _u⁺ to X² Sigma _g⁺) bands were measured. The electronic transition moment of the system was found to be reasonably constant.

X-ray measurements from highly ionized chlorine yield lines from the few electron atomic system with nuclear charge seventeen. The 1s-2p Lyman K alpha transition in hydrogenic chlorine is observed. Other transitions in chlorine XII through XVII are identified.

Many questions concerning the theoretical understanding of the table of the elements still remain open. In particular the existence of atomic magic numbers associated with noble gas behaviour has led to a search for approximate hidden symmetries. Such a symmetry is obtained here without any postulates. Instead, the authors follow Fock's analysis of the hydrogen atom who projected it on a 4-dimensional hypersphere. In this case the corresponding mapped system is the quantal top in 4-dimensions. The top's symmetry group G provides representations corresponding exactly to the periods of Mendeleev. The chain G contains/implies O(4) contains/implies SO(3) yields the quantum numbers n, l necessary for predicting the correct subshell ordering through a modified Aufbau scheme. Finally the non-invariance groups of G are obtained. Every step in this procedure is justified purely through group theoretical considerations.

Using several angular momentum terms and a parametric expansion for the radial function, wavefunctions are obtained for certain excited S, P, D and F states of helium, the virial theorem being satisfied exactly.

The distribution function f(r₁₂) of the interelectronic distance r₁₂ in the 2³S and 2¹S states of helium is calculated for several different wavefunctions. Mean values of positive and negative integral powers of r₁₂ are reported. The dependence of f(r₁₂) on the atomic number is shown to provide some additional physical insight into the excited states of helium. The Coulomb holes of the 2³S and 2¹S states are calculated and found to be more complex than the Coulomb hole of the ground state. The effect of the Fermi hole in the triplet state is discussed. A new distribution function g(r₁₂,r₁) is introduced and is used to discuss the Coulomb hole in terms of the chosen position of electron 1. It is observed that when one electron is far from the nucleus the Coulomb hole is essentially centred on the nucleus, whereas at small distances from the nucleus the Coulomb hole follows the electron.

In the impact parameter method the electron hamiltonian depends upon the time through the motion of the nuclei and the consequences of time-reversal invariance are less obvious than they are for time-independent hamiltonians. The authors make use of the hermiticity of the electron hamiltonian and its invariance under time-reversal to derive some useful relations occurring in the impact parameter method. A basis set of either atomic or molecular eigenfunctions which exploit the reflection symmetry in the scattering plane, is adopted, and a quantization axis is chosen which may be fixed or rotating. Systems of arbitrary spin are considered, and require only that nuclei move in a central (but unspecified) potential.

A nonperturbative theory, the momentum translation method, is applied to multiphoton ionization of hydrogen by an intense electromagnetic field. Using an approximation depending on a large number of photons absorbed, analytical results are presented for transitions from a 1S state to Coulomb states in the continuum. Results not only show the characteristic perturbation theory dependence of the intensity raised to the Nth power for an Nth order process, but give an explicit expression for the transition as a function of the number of photons absorbed, and the final electron angular momentum and energy. This type of functional dependence is very obscure in perturbation theory by its very nature. In particular, transitions to states with angular momenta 2, 4, and 6 dominate the l=0 transition in the absorption of 12 photons with energy of 1.17 eV, while l=3, 5, 7 transitions dominate the l=1 transition when 13 photons are absorbed. Also for particular values of the field intensity and final angular momentum the transition matrix is larger for a larger number of photons absorbed.

The transition amplitude corresponding to a transition from the ground state to a final continuum state in the presence of an intense field is evaluated. Results show that the transition probability increases, while the slope of the curve decreases, with the increase in intensity. It is shown that higher order processes are more probable for high intensities, whereas lower order processes dominate for low intensities. It is found that the contribution of the S wave is more than that of other partial waves. Another feature found is the decrease of transition probability with increasing photon energy or decreasing wavelength.

The classical binary encounter theory in its symmetrical form has been applied to the double ionization of He and Li⁺. Process of double ionization has been assumed to proceed via double encounter. In both encounters correct quantum mechanical velocity distributions for the bound electron have been used. The results are compared with experimental observations and earlier calculations by Gryzinski's method. It is concluded that the single encounter model suggested by Mittleman (1966) is not entirely correct and substantial contributions are made by double encounter process.

For pt. III see abstr. A64033 of 1971. It is shown that the Born approximation and the sudden-dipole approximation, when applied to the excitation of hydrogenic ions by charged particles, may be cast into the same mathematical form although their regions of validity are complementary. The resulting matrix elements are evaluated using Heisenberg's correspondence principle and the cross sections are obtained in analytic form for a wide range of incident energies. The results for the Born approximation, which are valid for all initial and final states, n and n' such that n>> mod n-n' mod , are compared with available quantal calculations for small n and n' with satisfactory agreement.

For pt. IV see abstr. A26590 of 1973. Cross sections are calculated for the excitation by protons of ground state helium to the 2¹S and 2¹P levels at incident energies in the interval 25 to 500 keV. Cross sections are also calculated for electron capture by protons from helium at energies above 100 keV, using a distorted wave approximation.

Certain statistical factors which govern the probability that an electron or vacancy is initially in one of the molecular states used in the Fano-Lichten model of heavy ion collisions are calculated. Expressions for the probabilities p_i that a molecular orbital contains i vacancies are given in terms of overlap integrals involving the asymptotic wavefunctions of the collision partners. The basis for the calculation and the relationship of these factors to measurable quantities is discussed.

The scattering of N₂⁺ ions by He atoms is studied excluding any electronic excitation. A two centre-screened Coulomb model is taken for the scattering potential. In a first step the classical deflection function is determined for a specific molecular orientation, in assuming that the vibrational and rotational motions are negligible during the collision time. Then the corresponding differential cross section is calculated for an isotropic distribution of the molecular orientations. In a second step the amount of translational energy transferred into the internal degrees of freedom is evaluated and the vibro-rotational dissociation is taken into account. The 'pseudo-elastic' differential cross section is obtained and it is compared to experiment.

The electron impact cross sections for vibrational excitation of the A ³ Sigma _u⁺ and B ³ Pi _g valence states of the N₂ molecule show similar broad overlapping resonant peaks for impact energies from about 8.2 to 11 eV for the A ³ Sigma _u⁺ state and from about 9 to 11.5 eV for the B ³ Pi _g state. In each case, a sequence of minor oscillations is superimposed on these peaks. In the cross section of the vibrational levels of the B ³ Pi _g state, the minor peaks appear at different energies and with slightly different spacings.

For pt. I see ibid., vol.6, 862 of 1973. The study of the excitation function of the E state vibrational levels shows a strong threshold excitation, several bumps and extra structure. An angular analysis of these phenomena leads to the determination of the configuration and symmetry of four transient N₂^- states.

For pt. I see abstr. A56148 of 1972. Using an orbital model, predictions are made of the relative energies of electronic states arising from configurations containing more than half- filled open shells. It is shown that such cases are not always analogous to the corresponding less than half-filled cases. The predictions, which are purely algebraic and involve no computation, can aid the interpretation of electronic spectra, and are supported by available evidence.

The diffusion coefficients of binary mixtures of nitrogen with methane, ethane, n-propane and n-butane have been determined at atmospheric pressure, in the temperature range 300-700 K. The chromatographic technique has been employed for the measurements. The data have been utilized to test the suitability of various empirical potential models for the interactions of these polyatomic molecules. The entire body of experimental data can only be represented with the aid of the spherical shell potential. It is concluded that this potential provides a physically realistic model of the molecular interactions involved.

The velocity dependence of integral total cross sections for CsF in collisions with Ar, Kr, Xe has been measured in three different experiments to investigate the power of the radial dependence of the attractive part of the potential V(R)=-C/R^s. These experiments provide the first direct experimental confirmation of the expected s=6 power law for scattering of alkali-halides on rare gases.

The mobility was measured for gas densities 2< rho <40*10²⁰ atoms cm^-3, and for gas temperatures 4<T<300K. Refinements of former treatments of electron localization via the bubble model are presented which demonstrate a strong correlation between the mobility 'edge' and a localization criterion. Detailed agreement between theory and experiment is not realized, but the general features of the density and temperature dependence of the mobility are reproduced in a consistent manner.

The motion of K⁺ ions in electrostatic fields in argon has been investigated experimentally, in the field-to-density range 10<E/N<1150 Td. An estimate of the K⁺-Ar interaction potential has been obtained by comparing the measured mobilities and diffusion coefficients with values obtained from Monte-Carlo simulations. The value of the potential at the potential minimum is found to be approximately -0.14 eV, with an equilibrium internuclear separation r_m equivalent to 2.86 AA.

The current through a high temperature, high density helium arc plasma was removed in approximately 1 mu s and the subsequent plasma decay observed. Various spectroscopic methods of measuring electron temperature were investigated. The results were then used to deduce Collisional-Radiative recombination coefficients of He and He⁺ as functions of electron temperature. Dissociative recombination coefficients for He₂⁺ were also obtained.