M.A.J. Michels

Multipole expansion of the retarded interatomic dispersion energy: derivation from quantum electrodynamics

Abstract 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.

Multipole expansion of the retarded interatomic dispersion energy: evaluation in the spherical-tensor formalism

The multipole expansion of the retarded interatomic dispersion energy is evaluated in the spherical-tensor formalism. The multipole expansion of the electrostatic dispersion energy follows as a special case.

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.

Retardation in the atomic pair polarizability

Abstract The atomic pair polarizability for hydrogen atoms is calculated within the framework of covariant quantum electrodynamics. Retardation effects are shown to change the dependence on the interatomic separation R from R −6 to R −7 for R large compared with a characteristic wavelength of the atomic spectrum. For harmonic oscillators the pair polarizability is proved to be independent of the interparticle interaction.

Multipole expansion of the retarded interatomic potential energy: induction energy for degenerate ground-state atoms

The inductive contribution to the retarded interatomic potential energy of two atoms in degenerate ground states is calculated up to all multipole orders on the basis of quantum electrodynamics. The result, which is found to have nonretarded character, is written in such a way as to show the induction effects brought about in each of the atoms by the electrostatic and magnetostatic fields of the other.

Multipole expansion of the retarded interatomic potential energy: dispersion and induction energy for relativistic hydrogen atoms

Abstract 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.

Multipole expansion of the retarded interatomic dispersion energy: the long and the 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.

On adiabatic perturbation theory for the energy eigenvalue problem

The adiabatic perturbation formalism is used to derive several alternative expressions for the effective Hamiltonian of a discrete energy level. It is shown how in the nondegenerate case these expressions may be cast in the form of linked-cluster expansions. The connection between the energy shifts and the scattering matrix is investigated.

Multipole expansion of the retarded interatomic potential energy: Derivation from relativistic electron theory

Abstract The inductive and dispersive retarded interaction energies of two ground state hydrogen atoms described by Dirac theory are obtained up to all multipole orders. The long range terms are given as symmetric expression in the electric and magnetic dipole moments.

Energy shifts and the S matrix in degenerate perturbation theory

Adiabatic perturbation theory is employed to establish a relationship between the S-matrix and the averaged energy shift of a degenerate level.