Atoms in circularly polarised fields: the dilation-analytic approach

The time-evolution operator associated with an atom in a circularly polarised radiation field can be factorised as U(t)=exp(-i omega J 3 t)exp(-iHt), where J 3 is the component of the total angular momentum orthogonal to the two field components and H can explicitly be given in terms of the atomic Hamiltonian. The author establishes for a one-electron model the self-adjointness of H and in addition he develops a complex dilation theory for this operator. The purpose of this approach is to obtain an analytic continuation theory for multiphoton processes so that the imaginary parts of the complex eigenvalues of the complex dilated Hamiltonian H( zeta ) can be related to the various rate constants that govern such processes.