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

Influence of Lorentz- and CPT-violating terms on the Dirac equation

The influence of Lorentz- and CPT-violating terms (in "vector" and "axial vector" couplings) on the Dirac equation is explicitly analyzed: plane wave solutions, dispersion relations and eigenenergies are explicitly obtained. The non-relativistic limit is worked out and the Lorentz-violating Hamiltonian identified in both cases, in full agreement with the results already established in the literature. Finally, the physical implications of this Hamiltonian on the spectrum of hydrogen are evaluated both in the absence and presence of a magnetic external field. It is observed that the fixed background, when considered in a vector coupling, yields no qualitative modification in the hydrogen spectrum, whereas it does provide an effective Zeeman-like splitting of the spectral lines whenever coupled in the axial vector form. It is also argued that the presence of an external fixed field does not imply new modifications on the spectrum.Comment: 13 pages, no figures, revtex4 styl

Rapid Assessment of Insect Fragments in Flour Milled from Wheat Infested with Known Densities of Immature and Adult \u3ci\u3eSitophilus oryzae\u3c/i\u3e (Coleoptera: Curculionidae)

Milling wheat, Triticum aestivum L., infested with low densities of internal feeding insects can result in flour containing insect fragments. The Food and Drug Administration (FDA) enforces a standard or defect action level stating that a maximum of 75 insect fragments per 50 g of flour is allowed. However, the relationship between level of infestation and number of resulting fragments is not well documented, and a more rapid method for enumerating insect fragments is needed. We characterized the number of insect fragments produced from milling small lots of wheat spiked with known densities and life stages of Sitophilus oryzae (L.) (Coleoptera: Curculionidae). Insect fragments were enumerated with near-infrared spectroscopy (NIRS), a quick nondestructive procedure, and with the industry standard flotation method. Results showed that an individual small larva, large larva, pupa, or adult produced 0.4, 0.7, 1.5, and 27.0 fragments, respectively. NIRS-predicted counts of ≤51 (from small larvae), ≤53 (from large larvae), ≤43 (from pupae), or 0 (from adults) indicated that there weresample, because the upper bound of associated 95% inverse prediction confidence intervals was less than the standard; NIRS-predicted counts of ≥98, ≥117, ≥108, or ≥225 fragments (same life stages as above) signaled that these flour samples contained \u3e75 actual fragments. These data suggest that NIRS could be adopted for rapid assessment of insect fragments resulting from relatively low levels of infestation with immature life states, but that it was not accurate enough for enumerating insect fragments, relevant to FDA standards, resulting from adults