Doublet splitting and natural width of semiclassical high-excited rotational states in vibration-rotation spectra of molecules

Abstract

In the series of articles15 we have developed a semiclassical self-consistent approach to calculation of the highly excited rotational states in vibration-rotation (VR) spectra of polyatomic molecules. The central idea of the semiclassical approach is based on the introduction of the auxiliary time-periodical fields which transfer interactions between rotational and vibrational molecular degrees of freedom. This procedure leads to separation of variables in the VR Hamiltonian and, as a result, to simplification of the initial problem interpretation, which is reduced now to an independent solution of two nonsteady Schrodinger equations. In the first of them the Hamiltonian describes a motion of the molecular angular momentum J in some time-periodical field and does not depend on the vibrational coordinates explicitly, in the second -the Hamiltonian is a sum of usual vibrational energy and some additives, which describe a motion of the vibrational collective variables in auxiliary fields and do not depend on the angular coordinate explicitly.Further, using the theoretical field generalization of the WKB method the quantization rules are obtained for the VR energy of a molecule. They correspond to the semiclassical approximation of the initial quantum mechanical problem. In adiabat ic approximat ion, i . e. when the variat ion of fields in time is small in comparison with values of fields, these rules may be written asJ {v} where a(C) is the Berry's phase for the rotational problem, ' (C) is the {v) Berry's phase for the vibrational problem, {v} is the set of the quantum numbers, describing a given vibrat ional state, I J + 0. 5 , J is the angular momentum quantum number, N(C) is the integers running a series of values over the range (0,1,. . . ,J-l,J), p(C) is the Maslov's index.The closed circuit C in the parameter space of field variables can not be selected arbitrary, because it satisfies the classical energy conservation law. As a result a parameter space or, that is almost the same, the phase one of a molecular angular momentum is divided into four invariant regions. In two of them the Maslov's index p(C 2 for the corresponding circuits, in other two -p(C ) In fact, the circuits in a parameter space are the trajectories (orbits), which are described by the angular momentum vector in its phase space.The Berry's phases (C) and ' (C) with the condition (1) and the mean- {v) field configurations of the auxiliary fields are linked by the self-consistent procedure.Owing to orbit periodicity, the quantization rules (1) coincide for the first two regions and have the form 168 / SPIE Vol. 1811 High-Resolution Molecular Spectroscopy (1991) 0-8194-101 1-X/92/$4.00 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 07/04/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx