Localization of multiphoton ionization/dissociation resonance wave functions in AC fields

Abstract

Although it has been proved before J. Chem. Phys. 101, 9716 1995 that the complex scaled photoionizingrphotodissociating resonances are associated with square integrable functions only when the time-dependent Hamiltonian is represented . in the velocity or acceleration gauges , it is proved here that in the length gauge a narrow . resonance wave function and not a broad one! may diverge exponentially at some period of time but yet decays exponentially in space at some other time. When the exterior scaling method is used and the coordinate is rotated into the complex plane by . an angle less than 1808 the resonance quasi-energy state in the length gauge decays to zero, like a bound state, at any given time. The localization of the resonance quasi-energy . Floquet states in the length gauge as the laser frequency vanishes i.e., when the field is . varied slowly and can be considered as dc field is proven and found to be consistent w . . x with Herbst and Simon's proof Commun. Math. Phys. 64, 279 1978 ; Ibid, 80, 181 1981 for atoms in dc Stark fields. Q 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 279)285, 1997