Energy spectra of vibron and cluster models in molecular and nuclear systems

Abstract

The relation of the algebraic cluster model, i.e., of the vibron model and its extension, to the collective structure, is discussed. In the first section of the paper, we study the energy spectra of vibron model, for diatomic molecule then we derive the rotation-vibration spectrum of \( 2\alpha\), \( 3\alpha\) and \(4\alpha\) configuration in the low-lying spectrum of 8Be, 12C and 16O nuclei. All vibrational and rotational states with ground and excited A, E and F states appear to have been observed, moreover the transitional descriptions of the vibron model and \( \alpha\)-cluster model were considered by using an infinite-dimensional algebraic method based on the affine \(\widehat{SU(1,1)}\) Lie algebra. The calculated energy spectra are compared with experimental data. Applications to the rotation-vibration spectrum for the diatomic molecule and many-body nuclear clusters indicate that there are solvable models and they can be approximated very well using the transitional theory.