Vibron Model For Diatomic Molecules

In the past few years, algebraic models have been proposed as a useful tool for the analysis and interpretation of experimental rovibrational spectra of small and medium sizemolecules. Algebraic models that describe molecular rotation-vibration spectra are called vibron models, which are based upon the idea of expanding the Hamiltonian and other physical operators in terms of bilinear products of a set of boson creation and annihilation operators according to the second quantization theory, since the collective excitations of the physical systems are regarded as interacting bosons. The elementary excitations for diatomic molecules are sp-bosons. The appropriate spectrum generating algebra is the unitary Lie algebra U(4). Dynamical symmetries often play an important role in algebraic models. In U(4) vibron model, two limiting cases, O(4) and U(3), are related to rigid and non-rigid spectral structures, respectively, which can be exactly diagonalized by using a standard group theoretical technique. While the transitional region between the two limits, U(3)-P(4), can only be treated numerically since the analytic diagonalization of the Hamiltonian for this region is not so easy as for that in either of the limits.In this thesis, a most simple case for the U(4) algebraic vibron model Hamiltonian with only one- and two-body interactions is considered. It is noted that the U(3) -O(4) transitional region of the model can also be solved exactly by means of an infinite dimensional algebraic technique. Exact eigen-energies and the corresponding wave-functions of the model in the whole parameter space are obtained by using the Bethe ansatz within an infinite-dimensional Lie algebra. As an extension, an sl-boson system in the corresponding region, U(2l + 1) O(2l+ 2), is also solved by the same method. A numerical algorithm for solving the Bethe ansatz equations is introduced, which can easily be realized with a MATHEMATICA package. Phase transition from U(3) to O(4) in the model is also analyzed in detail. Finally, the vibron model is used to describe diatomic molecules. Fitting to vibrational energy spectra is performed using both transitional theory and dynamicalsymmetry limit theory within the same framework. A straightforward comparison with these two theories shows that the transitional theory is more accurate than that of the O(4) limit in description of vibrational spectra of diatomic molecules.