Critical phenomena in rotational spectra

Nonlinear centrifugal distortion effects in the rotational spectra of molecules and atomic nuclei are investigated in the limit of large values of the angular momentum quantum number J. The theoretical analysis is based on a new representation of the effective rotational Hamiltonian. It is shown that qualitative changes of the rotational dynamics may occur at a certain value Jc. These phenomena are called critical phenomena. The critical phenomena are classified on the basis of the notion of a local symmetry group g. Special attention is paid to the local critical phenomena which take place in a limited region of rotational motion phase space. It is shown that for local critical phenomena in the vicinity of Jc there exists a universal rotation Hamiltonian which, with an accuracy to the parameters entering the Hamiltonian, does not depend on the internal structure of the system. A phenomenological theory of local critical phenomena is developed. The relation between the critical phenomena and the second order phase transitions in macroscopic systems is discussed