Scaling relations and the general effective-medium equation for isolator-conductor mixtures

The behaviour of the 'general effective-medium equation' near the percolation threshold of isolator-conductor mixtures has been analysed. A simple modification is proposed which renders the equation more consistent with fundamental scaling laws

Multipole expansion of the retarded interatomic dispersion energy. III. The long and short range behaviour

The long-range asymptotic expression for the multipole expansion of the retarded interatomic dispersion energy is shown to consist of contributions from electric dipole-dipole, dipole-quadrupole and quadrupole-quadrupole interactions, all varying as the inverse seventh power of the interatomic separation. The general expressions for these interactions lead to short-range series expansions which extend results obtained earlier with the help of the Breit hamiltonian

Diagrammatic analysis of adiabatic and time-independent perturbation theory for degenerate energy levels

Time-ordered folded diagrams are used to represent the effective hamiltonian in the adiabatic formalism. Resummation of the diagrams is shown to give a term-by-term correspondence with time-independent perturbation theory

Multipole expansion of the retarded interatomic potential energy. VI. Dispersion and induction energy for relativistic hydrogen atoms

The inductive and dispersive retarded interaction energies of two ground-state hydrogen atoms described by Dirac theory are derived up to all multipole orders. The results are obtained by evaluation of Feynman diagrams and with the help of dispersion-relation methods. The non-relativistic and semi-relativistic approximations of the interaction energy are given in a form that shows explicitly the contributions of electron spin

Block diagrams and the cancellation of divergencies in energy-level perturbation theory

The effective Hamiltonian for the degenerate energy-eigenvalue problem in adiabatic perturbation theory is cast in a form that permits an expansion in Feynman diagrams. By means of a block representation a resummation of these diagrams is carried out such that in the adiabatic limit no divergencies are encountered. The resummed form of the effective Hamiltonian is used to established a connexion with the S matrix

Multipole expansion of the retarded interatomic dispersion energy. I. Derivation from quantum electrodynamics

The multipole expansion of the retarded dispersion energy of two atoms in non-degenerate ground states is derived. The result shows that multipoles of different order may give rise to dispersion energies varying in the same way for large interatomic separations

The critical points of cubic equations of state for pure fluids

The critical point of an equation of state for a pure fluid generally has to be calculated from three coupled relations between the critical constants Vc, pc and Tc. It will be shown that for any cubic equation of state these relations may be decoupled in such a way that only one relation for Tc has to be solved, whereupon Vc and pc follow by direct substitution. For cubic equations with a Van der Waals-type repulsive term a second form of the solution is given. As examples the equations of Redlich and Kwong, of Ishikawa, Chung and Lu, and of Kumar are considered