Molecular Rydberg states: Classical chaos and its correspondence in quantum mechanics

The Rydberg spectrum of Na2 has been shown previously to alternate when increasing energy between ‘‘stroboscopic fringes’’ which correspond to a well known separable Hund’s coupling case (a), and a complex, unidentifiable intermediate coupling. We use this system as a prototypic example to test some current ideas on the correspondence between classical chaos and properties of quantum spectra. We first determine the phase space structure and transition to chaos in classical mechanics. We then determine the change in line intensities and level spacing statistics in quantum mechanics. We show that this system has the expected behavior in the semiclassical limit in the presence of classical chaos, except for a peculiarity in level spacing statistics, but that this behavior is not a signature of chaos, since the same system shows similar behavior for some values of the parameters which correspond to a nonchaotic situation in classical mechanics. We discuss also some problems related to the nonvalidity of the semiclassical limit.