Shape restricted wavefunctions: Ellipsoidal limits for ground and excited σg states of H2

Ellipsoidal as well as spherical limits for the energies of the 1sσ_g, 2sσ_g and 3sσ_g states of H₂⁺ have been obtained at various internuclear distances. The improvement obtained for the ground-state energy in the ellipsoidal limit is about 40% of the difference between the spherical limit and the exact energy.     

A Hohenberg-Kohn theorem for non-local potentials

It is shown that within any class of commuting one-body potentials a Hohenberg-Kohn type theorem is satisfied with respect to an appropriately defined density. The Hohenberg-Kohn theorem for local potentials follows as a special case.     

The continuity dilemma and hartree-fock instabilities

The stability criteria of the Hartree-Fock wavefunctions are implemented in the context of the Roothaan-Hartree-Fock procedure. Use is made of modified SCF equations, in which the total energy, rather than orbital energies, appears. The procedure is applied to the 2³S state of helium.     

The Gaussian potential: Bound states in the continuum?

Simple variational solutions to the problem of a single particle in a Gaussian potential well inN dimensions,N being positive and real, are investigated. The system exhibits locally bound states in the continuum, which are demonstrated to be artifacts of the variational procedure. The relevance of the conclusions to recent studies of the possible existence of bound states in the continuum is discussed.     

An interpretation of Hund's rule

An interpretation of Hund's rule is presented. The Pauli principle, the variational principle and the virial theorem are shown to be essentially sufficient to account for the roles of the various energetic components in establishing the inter-multiplet separation.

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Zusammenfassung Es wird eine Interpretation der Hundschen Regel gegeben. Das Pauliprinzip, das Variationsprinzip und das Virialtheorem sind im wesentlichen ausreichend, um die Rollen der verschiedenen energetischen Komponenten beim Zustandekommen der Inter-Multiplett-Separation zu erklärenwie hier gezeigt wird.

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Based on a section of a thesis to be submitted to the senate of the Technion — Israel Institute of Technology, in partial fulfilment of the requirements for the D. Sc. degree.     

Long-time limit for a class of quadratic infinite-dimensional dynamical systems inspired by models of viscoelastic fluids

We study a class of quadratic, infinite-dimensional dynamical systems, inspired by models for viscoelastic fluids. We prove that these equations define a semi-flow on the cone of positive, essentially bounded functions. As time tends to infinity, the solutions tend to an equilibrium manifold in the L²-norm. Convergence to a particular function on the equilibrium manifold is only proved under additional assumptions. We discuss several possible generalizations.     

A simple treatment of two-electron one-photon transitions

Two electron radiative transition probabilities from the L and M shells into a doubly vacant K shell are computed non-relativistically, introducing angular correlation in the simplest conceivable way. The relative cross-sections for the different possible processes are in agreement with recently reported experimental values for Fe and Ni and predict interesting changes in the spectra of heavier systems.     

Coupling of radial and angular correlations in two-electron atoms

The nature of interelectronic correlation in the ground and low lying excited states of the helium sequence is investigated. It is demonstrated that as a consequence of the coupling between radial and angular correlation the electrons are actually pulled together rather than pushed apart, in the low nuclear charge end of the isoelectronic sequence. A uniform treatment of correlation effects in both the ground and the excited states is thus shown to be feasible.     

Products of class-sums of the symmetric group: Generalizing the recurrence relations

The formulation of a combinatorial theory of the structure of the class-algebra of the symmetric group is pursued. Recurrence relations for reduced class-coefficients involving imbedded cycles are presented. It is pointed out that for bridging cycles one can obtain elimination rules that involve symmetrization over sets of reduced class-coefficients with common cycle-structures but inequivalent index distributions. Consequently, some of these reduced class-coefficients remain individually inaccessible. © 1993 John Wiley & Sons, Inc.