A symmetry adapted approach to vibrational excitations in atomic clusters

An algebraic method especially suited to describe strongly anharmonic vibrational spectra in molecules may be an appropriate framework to study vibrational spectra of Na$^+_n$ clusters, where nearly flat potential energy surfaces and the appearance of close lying isomers have been reported. As an illustration we describe the model and apply it to the Be$_4$, H$_3^+$, Be$_3$ and Na$_3^+$ clusters.Comment: 8 pages with 2 tables, invited talk at `Atomic Nuclei & Metallic Clusters: Finite Many-Fermion Systems', Prague, Czech Republic, September 1-5, 199

Comment on ``Boson-realization model for the vibrational spectra of tetrahedral molecules''

An algebraic model in terms of a local harmonic boson realization was recently proposed to study molecular vibrational spectra [Zhong-Qi Ma et al., Phys. Rev. A 53, 2173 (1996)]. Because of the local nature of the bosons the model has to deal with spurious degrees of freedom. An approach to eliminate the latter from both the Hamiltonian and the basis was suggested. We show that this procedure does not remove all spurious components from the Hamiltonian and leads to a restricted set of interactions. We then propose a scheme in which the physical Hamiltonian can be systematically constructed up to any order without the need of imposing conditions on its matrix elements. In addition, we show that this scheme corresponds to the harmonic limit of a symmetry adapted algebraic approach based on U(2) algebras.Comment: 9 pages Revtex, submitted February 199

A general algebraic model for molecular vibrational spectroscopy

We introduce the Anharmonic Oscillator Symmetry Model to describe vibrational excitations in molecular systems exhibiting high degree of symmetry. A systematic procedure is proposed to establish the relation between the algebraic and configuration space formulations, leading to new interactions in the algebraic model. This approach incorporates the full power of group theoretical techniques and provides reliable spectroscopic predictions. We illustrate the method for the case of ${\cal D}_{3h}$-triatomic molecules.Comment: 35 pages TEX, submitted to Annals of Physics (N.Y.

A symmetry-adapted algebraic approach to molecular spectroscopy

We apply a symmetry-adapted algebraic model to the vibrational excitations in D_3h and T_d molecules. A systematic procedure is used to establish the relation between the algebraic and configuration space formulations. In this way we have identified interaction terms that were absent in previous formulations of the vibron model. The inclusion of these new interactions leads to reliable spectroscopic predictions. We illustrate the method for the D_3h triatomic molecules, H_3^+, Be_3 and Na_3, and the T_d molecules, Be_4 and CH_4.Comment: 16 pages with 4 tables, invited talk at `Symmetries in Science IX', August 6-10, 199

A Symmetry Adapted Approach to Molecular Spectroscopy: The Anharmonic Oscillator Symmetry Model

We apply the Anharmonic Oscillator Symmetry Model to the description of vibrational excitations in ${\cal D}_{3h}$ and ${\cal T}_d$ molecules. A systematic procedure can be used to establish the relation between the algebraic and configuration space formulations, by means of which new interactions are found in the algebraic model, leading to reliable spectroscopic predictions. We illustrate the method for the case of ${\cal D}_{3h}$-triatomic molecules and the ${\cal T}_d$ Be-cluster.Comment: 12 pages, invited talk at XIX Oaxtepec Symposium on Nuclear Physics, January 199

Algebraic description of atom-molecule interactions

We describe a new method based on algebraic techniques, which leads to a model of atom-diatom collisions