U(7) Spectrum Generating Algebra for Rotations and Vibrations in Triatomic Molecules

Abstract

Algebraic methods have proved to be very useful in providing a unified description of rotational and vibrational spectra, both in collective nuclei [1, 2] and in molecules [3, 4]. The first version of the vibron model [3] was introduced for diatomic molecules. It describes the spectra in terms of the three components of a dipole (or p-) boson and a scalar (or s-) boson, under the restriction that the total number of bosons N = n s +n p is conserved by the hamiltonian. The three dipole degrees of freedom are associated with the three components of the radius vector connecting the two atoms. The vibron model thus provides a unified description of rotational and vibrational excitations of diatomic molecules in terms of the spectrum generating algebra (SGA) of U(4). An interesting aspect is that one of the dynamic symmetries corresponds in lowest approximation to the Morse oscillator which has been used widely in the study of diatomic molecules. Other examples are the U(6) Interacting Boson Model (IBM) [1] for the description of quadrupole rotations and vibrations in collective nuclei and the U(4) vibron model for the relative coordinate between the quark and anti-quark in mesons [5].