Hanno Essén

The characterization of atomic interactions

The theory of molecular structure determined by the gradient vector field of the charge density ρ identifies the set of atomic interactions present in a molecule. The interactions so defined are characterized in terms of the properties of the Laplacian of the charge density ∇2ρ(r). A scalar field is concentrated in those regions of space where its Laplacian is negative and depleted in those where it is positive. An expression derived from the quantum mechanical stress tensor relates the sign of the Laplacian of ρ to the relative magnitudes of the local contributions of the potential and kinetic energy densities to their virial theorem averages. By obtaining a map of those regions where ∇2ρ(r)<0, the regions where electronic charge is concentrated, one obtains a map of the regions where the potential energy density makes its dominant contributions to the energy of a system. It is demonstrated that atomic interactions fall into two broad general classes, closed‐shell and shared interactions, each characteri...

An RKR‐like inversion procedure for bound–continuum transition intensities

A semiclassical RKR‐like inversion procedure for determining a repulsive diatomic molecule potential energy curve from structured bound–continuum transition intensity data is derived and tested. The method presumes a knowledge of the (attractive) initial state potential well and of the energy and vibrational assignment of the absorbing or emitting level. Its application to a structured emission continuum of NaK observed by Breford and Engelke [Chem. Phys. Lett. 53, 282 (1979)] yields a potential energy curve which is incompatible with other known properties of this system, a result which confirms the suggestion of Kato and Noda [J. Chem. Phys. 73, 4940 (1980)] that the original assignment of the initial state for this spectrum is in error.

Force on a spinning sphere moving in a rarefied gas

The force acting on a spinning sphere moving in a rarefied gas is calculated. It is found to have three contributions with different directions. The transversal contribution is of opposite directio ...

Comparison of quantum mechanical and quasi-classical calculations of collinear reaction rate constants for the H+Cl2 and D+Cl2 systems

Comparison between quantum and classical mechanical reaction probabilities and rate constants for the collinear H + Cl2 and D + Cl2 systems is made. Different quasi-classical methods are compared and the QCRF method which fulfils the principle of detailed balance is suggested. Finally the total reaction rate constants are compared with results obtained from a simple transition state model.

Quantization and independent coordinates

This paper reviews canonical and other quantization methods, gives a quantization rule that gives results that agree with those obtained by direct transformation of the Laplacian, and thus expresses the correct Hamiltonian operator in terms of proper conjugate momentum operators. It gives applications to a number of curvilinear coordinates, introduces the class of independent coordinates, presents generalized Jacobi coordinates, and discusses the molecular vibration‐rotation Hamiltonian.

MAGNETIC FIELD AND CURRENT ARE ZERO INSIDE IDEAL CONDUCTORS

We prove a theorem on the magnetic energy minimum in a system of perfect, or ideal, conductors. It is analogous to Thomsons theorem on the equilibrium electric fleld and charge distribution in a system of conductors. We flrst prove Thomsons theorem using a variational principle. Our new theorem is then derived by similar methods. We flnd that magnetic energy is minimized when the current distribution is a surface current density with zero interior magnetic fleld; perfect conductors are perfectly diamagnetic. The results agree with currents in superconductors being conflned near the surface. The theorem implies a generalized force that expels current and magnetic fleld from the interior of a conductor that loses its resistivity. Examples of solutions that obey the theorem are presented.

Meissner effect, diamagnetism, and classical physics—a review

We review the literature on what classical physics says about the Meissner effect and the London equations. We discuss the relevance of the Bohr-van Leeuwen theorem for the perfect diamagnetism of superconductors and conclude that the theorem is based on invalid assumptions. We also point out results in the literature that show how magnetic flux expulsion from a sample cooled to superconductivity can be understood as an approach to the magnetostatic energy minimum. These results have been published several times but many textbooks on magnetism still claim that there is no classical diamagnetism, and virtually all books on superconductivity repeat Meissner’s 1933 statement that flux expulsion has no classical explanation.

Magnetism of matter and phase-space energy of charged particle systems

The (Darwin) Lagrangian, and energy, valid for systems of charged particles when radiation is negligible, are derived in a new way that avoids the usual -expansion. This shows more clearly their range of validity. Expressing the energy in terms of canonical momenta gives the corresponding Hamiltonian. When there are many particles it is intractable, but useful approximations are given and general conclusions about magnetism of matter are drawn from these. Macroscopic energy extremizing self-consistent vortex solutions are presented which can be interpreted as corresponding to superconductivity and ferromagnetism. There is a discussion of the quantum mechanics of the Hamiltonian for conduction electrons in a metal and a phase transition is predicted at low temperature.

From Least Action in Electrodynamics to Magnetomechanical Energy--A Review.

The equations of motion for electromechanical systems are traced back to the fundamental Lagrangian of particles and electromagnetic fields, via the Darwin Lagrangian. When dissipative forces can be neglected the systems are conservative and one can study them in a Hamiltonian formalism. The central concepts of generalized capacitance and inductance coefficients are introduced and explained. The problem of gauge independence of self-inductance is considered. Our main interest is in magnetomechanics, i.e. the study of systems where there is exchange between mechanical and magnetic energy. This throws light on the concept of magnetic energy, which according to the literature has confusing and peculiar properties. We apply the theory to a few simple examples: the extension of a circular current loop, the force between parallel wires, interacting circular current loops and the rail gun. These show that the Hamiltonian, phase space, form of magnetic energy has the usual property that an equilibrium configuration corresponds to an energy minimum.

Average angular velocity

This paper addresses the problem of the separation of rotational and internal motion. It introduces the concept of average angular velocity as the moment of inertia weighted average of particle angular velocities. It extends and elucidates the concept of Jellinek and Li of separation of the energy of overall rotation in an arbitrary (non-linear) N-particle system.