Table of contents

Plasma satellite emission lines separated by twice the plasma frequency 2 omega _p from allowed lines should often be stronger than the weaker (far) Baranger-Mozer omega _p satellite of forbidden lines. Confusion between these features probably explains those observations in which the near Baranger-Mozer line has appeared to be anomalously weak relative to the far omega _p satellite.

For Pt. IV see abstr. A41769 of 1969. The classical and quantal problem of a charged particle moving in an attractive Coulomb potential with total energy zero is considered. A complete correspondence identity is obtained by expressing the kernel of the quantum-mechanical spectral operator I_E= delta (E-H) exactly in terms of the classical action function in momentum representation. Use is made of the dynamical symmetry properties exhibited by both the classical and quantal problems, and a path-integral method of evaluating the spectral operator kernel is also presented.

A theory of electron scattering by complex atoms is developed in which the target atomic eigenstates and pseudostates are written as linear sums of configurations and the incident electron wave function is expanded in terms of orbitals which satisfy logarithmic boundary conditions on the surface of a sphere. The radius of the sphere is chosen so that exchange between the scattered and atomic electrons is only important within the sphere but full allowance must be made for the long range atomic potentials which exist outside of the sphere. Both the bound and the continuum calculations involve a diagonalization of the Hamiltonian in the appropriate basis and these calculations are arranged so that they use the same analytic procedures and computer codes. Finally, the construction of the S-matrix and the cross section matrix is discussed.

The first Born approximation is used to calculate cross sections for electron loss from fast metastable hydrogen atoms passing through atomic hydrogen and atomic helium. Full account is taken of double transitions and in the case of a helium target the calculations are performed using length and velocity formulation values of the Born matrix elements. The results are remarkable for their prediction of double maxima in the cross sections and for the excellent agreement in shape with experiment over the energy range (10-30keV) which lies between the maxima.

The theory of the Stark effect in Hund's case (a) for strong and intermediate field strengths is developed when the lambda-doubling is included. A simplification of the secular problem is worked through for the cases of constant lambda-doubling, and small lambda-doubling for moderately strong fields. The errors resulting from the use of a limited set of basis functions when calculating the energy changes due to the field, are discussed. For completeness a brief review of the Stark effect for Hund's case (a) in the weak field case is given. A general formula is derived for the weak field Stark energy of molecules in multiplet Sigma -states. In the strong and intermediate field cases for molecules in multiplet Sigma -states it is shown that it is convenient first to consider the effect of the electric field and thereafter take the spin interactions into account. Formulae expressing the Stark interaction between the lambda components are given for molecules which can be described by a coupling scheme intermediate between Hund's cases (a) and (b). The equations and formulae derived are for a rigid molecule. Hyperfine interactions are neglected in the treatment.

The convergence of the faddeev-watson multiple scattering expansion is investigated for three-body rearrangement collisions, 1+(2,3)=(1,2)+3, for systems with coulomb interactions and arbitrary masses. The matrix elements of the expansion are evaluated to the second order in the two-body t-matrix using the nutt procedures. The result suggests that the expansion for rearrangement transition amplitudes (psi₁⁽³⁾?t_r?psi₁⁽¹⁾) between ground two-body states converges in the high energy limit for a nonrelativistic three-body coulomb system with arbitrary masses. The effect of the constituent particle masses on the rate of approaching this high-energy behaviour is discussed. It is pointed out that the controversies regarding the role of proton-proton interaction in electron-transfer collisions for the (p⁺,h) system arise from the improper high-energy behaviour of the born series.

The differential cross sections for the elastic scattering of 100-500 eV electrons by helium atoms are calculated in the plane wave approximation. The interaction potential consists of the first order static potential and the second order adiabatic and non-adiabatic polarization potentials. An alternative derivation of the asymptotic value of the non-adiabatic potential is presented and the second order scattering amplitude is compared with the second Born amplitude. In the calculation of differential cross sections the effect of exchange is included by employing the Ochkur approximation and terms up to only third order in the interaction energy are retained. The cross sections are within 15% of the experimental values. Similar agreement is obtained with more sophisticated calculations.

For two atoms whose ionization potentials are considerably different, an exact asymptotic expression for the exchange interaction is derived. This interaction is connected with the energy level shift of an excited atom, colliding with a ground state atom. From the general expression for this quantity the results of Smirnov and Ovchinikova are obtained as special cases.

In the framework of the impact-parameter method a formula for the collisional detachment cross section is derived and expressed in terms of averaged level widths of the quasi-stationary molecular states and the stabilization distances for auto-ionization. Using this formula the cross sections for h-h^- and o-o^- electron detachment are calculated and a comparison is made with the experimental data and previous theoretical calculations.

A general method of deducing some hypervirial theorems which are especially relevant to electrostatic problems and polarization phenomena is proposed. This is based on the commutator of the hamiltonian operator with general coordinate tensors from which several hypervirial theorems may be obtained by contraction with unit tensors. It is found that diagonal hypervirial theorems can be produced which given alternative forms for the crystal field splitting energy and diamagnetic susceptibility operators while off-diagonal theorems give alternative means of calculating transition multipole moments. Both constitute a useful check on the validity of the approximate wave functions employed in a given problem.

The first order unrestricted hartree-fock equations for the ground states of atomic systems with 4,5,...,10 electrons are solved exactly. The solutions are used to evaluate the corresponding second order energies exactly and the third order energies very accurately. A method is described whereby each atom can be treated as a special case of a general scheme. The third order uhf energy of lithium has been recalculated with greater accuracy and comparison is made between the uhf energy values obtained for the ground states of all the second row atoms and those obtained by other methods. The zero-order and first-order terms in the expectation values of the operators l?² and s?² are calculated and tables are given leading to those of 1/r³, 1/r, r, r² and delta(r).

Coulomb matrix elements are obtained for configuration interaction processes in Pr²⁺ and Pr³⁺, using Hartree-Fock-Slater wave functions. Second order perturbation theory is used to calculate the six parameters which characterize the effective three-particle operator for Pr²⁺. The results are compared with parameters obtained in a recent analysis of experimental data. 4f to nh processes are shown to be negligible; the contributions due to 4f to nf processes are calculated to within 20% of their true values; higher order perturbation terms are shown to be necessary for an adequate determination of the contributions due to the 4f to or from np processes.

Theoretical and experimental results are presented which go some way to resolving the problem of halogen separation in tungsten-halogen lamps. The classic work of Jones, Furry and Onsager on isotope separation in the Clusius and Dickel column is applied directly to this area of research. Results indicate a clear qualitative agreement between theory and experiment, showing that a forbidden pressure range exists in which the lamps will be subject to separation of the halogen and inert gas filling.

A group of visible diffuse bands has been observed from low power potassium discharges. These bands exhibit several anomalous features and have not, apparently, been previously recorded. A tentative explanation is outlined.

Lifetimes of positrons annihilating in a number of organic compounds consisting of aromatic hydrocarbons, substituted benzenes, phenols, anilines and ketones have been measured. Experimentally measured values of tau ₂ and I₂ are examined to determine whether positron annihilation takes place at a particular site of the molecule or whether it depends on average properties of the molecules. The intensity I₂ seems to be related to the width of Ore gap in organic molecules; the tau ₂ values in molecular liquids, however, can be interpreted in terms of additive atomic contributions to pick-off quenching. In substituted benzenes the results show changes due to substituent effects and these changes could be correlated with Hammett's sigma -constant. Results indicate that positron annihilation in organic media is determined by microscopic properties of the molecules such as ionization potentials (or width of Ore gap) and electron densities at the annihilation sites.

The true potential energy curves for x² Pi _r, A² Sigma ⁺, B² Sigma ⁺, D² Sigma ^- states of AsO and x ¹ Sigma ⁺ and A ¹ Pi states of AsO⁺ have been constructed by a modified form of Rees method. The results are in excellent agreement with those calculated by the RKRV and Jarmain methods. This modified form of the Rees method which is found to give identical results in the case of several other molecules, involves relatively simple calculations and can be adopted in the absence of computational aids. The r-centroids have been evaluated for all these systems. The Franck Condon factors have been evaluated for the A-X, B-X systems of AsO and the A-X system of AsO⁺.