Constraining scalar field properties with boson stars as black hole mimickers

Constraints to the mass of a scalar field and the strength of its self-interacting coupling constant are obtained. This was done using observations of stellar dynamics at the center of our galaxy and by assuming that the dark compact object responsible of such dynamics is a boson star and not a supermassive black hole. We show that if such scalar field represents a spin-zero particle with cross section high enough to be considered collisional dark matter, there is a region of parameters compatible with both conditions: that the scalar field play the role of collisional dark matter and that it can form objects with the mass and compactness compatible with stellar kinematics.Comment: To appear in the Procceedings of the VIII Workshop of the Gravitation and Mathematical Physics Division of the Mexican Physical Societ

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