BIFURCATIONS IN QUANTUM ROTATIONAL SPECTRA

The nonlinear effects in rotational spectra of molecules and atomic nuclei caused by the centrifugal and Coriolis forces are investigated for high values of angular-momentum quantum number I. It is shown that qualitative changes of the rotational-motion regime may occur in a rotational spectrum for the critical value I(c) due to the appearance or disappearance of a degeneracy in a rotational band. This critical phenomenon corresponds to the bifurcation in classical mechanics and manifests itself both in the rearrangement of rotational multiplet levels and in the qualitative change of electromagnetic transitions in the band. The classification of bifurcations for a purely rotational motion is given. The classification is based on the concept of a local symmetry group. There exist five types of bifurcations in rotational spectra, the most interesting of which are those analogous to the second-order phase transitions (local bifurcation). The difference between the local bifurcations in a finite many-body system and second-order phase transitions in macroscopic ones is discussed. It was shown that a universal effective rotational Hamiltonian exists in the neighborhood of I(c), which makes it possible to develop a phenomenological theory of local bifurcations. The existence of bifurcations of various types in experimentally observed molecular and nuclear rotational spectra is established. The bifurcations in high-spin rotational states of odd-A nuclei, nonlinear symmetrical three-atomic molecules XY2, and tetrahedral molecules XY4 are investigated theoretically and compared with experimental data.