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

Efficiency, Yield, and Nutritive Value of Perennial Warm-season Grass Under Liquid Fertilizer Applications

The efficacy of liquid fertilizer formulation in forage production is unclear. This preliminary study compared the impact of liquid fertilizers sources compared to traditional granular fertilizers in forage bahiagrass (Paspalum notatum) production. The experimental design was a randomized complete block replicated three times. Ten N fertilizer treatments were applied to forage systems: a well-established ‘Tifton 9’ bahiagrass. The N fertilizer treatments included a control (C, no nitrogen), two granular fertilizers [urea (U, 46-0-0) and urea ammonium sulfate (UAS, 33-0-0)], and four liquid N fertilizers [ urea ammonium nitrate solution (UAN, 32%), Royal Grow (RG, 30-0-0), Pasture Booster Prime (PBP, 30-0-0), and Agritech Plus (AGP, 10-20-10)]. The fertilizers RG, PBP, and AGP were applied at the recommended rate of 1 gal ac-1 and adjusted to meet the recommendation of 50 lb N ac-1. The granular fertilizers U and UAS, and UAN were applied to the equivalent of 50 lb N ac-1. Liquid fertilizers were applied using a 6-ft boom with a CO2 backpack sprayer to supply a rate of 20-gal ac-1 at 60 psi after harvest. The biomass yield of liquid fertilizers applied to the recommended manufacturer’s recommendation did not improve production. Nutritive value was only affected by harvest date. Crude protein was affected by fertilizer application rate rather than the fertilizer source. Further research is necessary to understand the limitation of liquid fertilizers based on application rates and costs