Semiclassical theory of high-excited rotational states in vibration-rotation spectra of molecules

A new approach for studying high-excited rotational states of polyatomic molecules is considered. Using the Hubbard-Stratonovich functional identity for the Wilson-Howard-Watson vibration-rotation Hamiltonian the time evolution operator is constructed as a functional integral taken over all possible configurations of the auxiliary fields. These fields transfer interactions between rotation of the molecule and vibrations of its nuclei. A set of self-consistent equations has been obtained in the mean-field approximation. The set describes rotation and vibrations independently and yields some quantities like to the quasi energies used in the quantization rules. These rules are obtained by use of the generalised WKB method for the Fourier transform of the trace of the evolution operator. The notion of periodic orbits in the cylindrical phase space of the molecular angular momentum is defined. It is shown that different quantization conditions take place for two-fold degenerate energy levels of the various symmetries in dependence on topology of the phase space. Expressions for the doublet splitting of the degenerate levels due to both vibration-rotation interactions and tunnelling or over barrier reflection when moving on orbits are derived. (author)