Atomic and molecular states in weak and strong external static and ac electromagnetic fields
When the interaction of strong fields with atomic and molecular states can be cycle-averaged, which includes the case of static fields, it is possible to tackle theoretically and computationally related physical problems in terms of a complex eigenvalue, many-electron many-photon theory, in which the full Hamiltonian is diagonalized by a properly optimized, state-specific complex wavefunction consisting of real and of complex basis functions and having the form, e.g., [1,2],
where ñ is a complex coordinate.
The solutions provide quantitative answers for properties and phenomena such as multiphoton single and multiple ionization in polychromatic fields, above threshold ionization, high order harmonic generation, dynamic polarizabilities and hyperpolarizabilities etc.. For example, the figure below shows He multiphoton ionization rates (Ã in a.u.) in the laser frequency (ù in a.u.) region where at least 3 photons are necessary for ionization. The intensity varies from 3.5x1012 W/cm2 up to 1.7x1014 W/cm2. The peaks correspond to (2+1) resonant enhanced multiphoton ionization with the 1sns 1S, 1snd 1D (n=...,6) states.
In the case of polychromatic fields, the structure of the theory is such that it allows the quantitative study of control of the multiphoton ionization processes as a function of the phases of the fields, e.g. .
 'Atoms in Strong Fields' , eds. C. A. Nicolaides, C. W. Clark and M. H. Nayfeh, Plenum Press, New York, (1990)
 Th. Mercouris and C. A. Nicolaides, 'Solution of the many-electron, many-photon problem for strong fields: Application to in one-and two-color laser' Phys. Rev. A 67, 063403 ((2003).
 Th. Mercouris,C. Haritos and C. A. Nicolaides, 'Interference generalized cross-setion for the multiphoton detachment of in dichromatic fields', J. Phys. B 38 , 399 (2005)