Theory of Atomic and Molecular Non-Stationary States Within the Coordinate Rotation Method

Abstract

The recently developed dilation (coordinate rotation) theory of the Coulomb Hamiltonian allows the calculation of energies and widths of nonstationary atomic and molecular states using square-integrable basis sets only. In the pioneering applications of this theory to two electron atomic autoionizing states, it was found necessary to employ large basis sets in brute force CI calculations, an expensive approach which has significant limitations when it comes to larger systems. In this paper we present a many-body theory of autoionizing and autodissociating states which implements the dilatation theory in an efficient and consistent way. In the case of autodissociating states it is not required to invoke the Born-Oppenheimer approximation. The present approach first isolates in the ϑ-plane (ϑ is the rotation angle) the “localized” correlation effects from the “asymptotic” ones by rotating the coordinates of the localized function, ψ0, which, in the time dependent theory, represents the initially localized state before it decays. The coordinate rotation leaves the real energy of ψ0 invariant and allows the inclusion of “asymptotic” correlation vectors, in terms of “Gamow orbitals”, which perturb ψ0 and E0 and yield the decay energy shift and width. Our theory is supported by numerical examples on H and He.