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

International audienceThe 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 correspondance 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 semi-classical 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 show similar behavior for some values of the parameters which correspond to a non chaotic situation in classical mechanics. We discuss also some problems related to the nonvalidity of the semiclassical limit