Construction of SU(3) irreps in canonical SO(3)-coupled bases

Alternative canonical methods for defining canonical SO(3)-coupled bases for SU(3) irreps are considered and compared. It is shown that a basis that diagonalizes a particular linear combination of SO(3) invariants in the SU(3) universal enveloping algebra gives basis states that have good $K$ quantum numbers in the asymptotic rotor-model limit.Comment: no figure

Coherent state triplets and their inner products

It is shown that if H is a Hilbert space for a representation of a group G, then there are triplets of spaces F_H, H, F^H, in which F^H is a space of coherent state or vector coherent state wave functions and F_H is its dual relative to a conveniently defined measure. It is shown also that there is a sequence of maps F_H -> H -> F^H which facilitates the construction of the corresponding inner products. After completion if necessary, the F_H, H, and F^H, become isomorphic Hilbert spaces. It is shown that the inner product for H is often easier to evaluate in F_H than F^H. Thus, we obtain integral expressions for the inner products of coherent state and vector coherent state representations. These expressions are equivalent to the algebraic expressions of K-matrix theory, but they are frequently more efficient to apply. The construction is illustrated by many examples.Comment: 33 pages, RevTex (Latex2.09) This paper is withdrawn because it contained errors that are being correcte

The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing

A connection is made between the exact eigen states of the BCS Hamiltonian and the predictions made by the Tamm-Dancoff Approximation. This connection is made by means of a parametrised algebra, which gives the exact quasi-spin algebra in one limit of the parameter and the Heisenberg-Weyl algebra in the other. Using this algebra to construct the Bethe Ansatz solution of the BCS Hamiltonian, we obtain parametrised Richardson-Gaudin equations, leading to the secular equation of the Tamm-Dancoff Approximation in the bosonic limit. An example is discussed in depth.Comment: Submitted to the proceedings of the Group28 conference (Newcastle-upon-Tyne, UK). Journal of Physics: Conference Serie

Sedimentation rates in the slope water of the northwest Atlantic Ocean measured directly with sediment traps

Four sedi ment trap arrays we re deployed in the Slope Water off the northeast United States for periods of 5.8 to 15.8 days from May to August 1976. Three traps, each a PVC cylinder 25 cm in diameter and 76 cm tall, were attached a t va rious distances above the bottom along bottom-anchored moorings. Closure of the individu al traps and release of each array from its expend able anchor was co ntrolled by a Williams Timed Release or an AMF acoustic release. DSRV ALVIN, making observations of one array, closed those traps and released that array from the bottom...

Representation of the five‐dimensional harmonic oscillator with scalar‐valued U(5) ⊇ SO(5) ⊇ SO(3)–coupled VCS wave functions

Vector coherent state methods, which reduce the U(5) ⊇ SO(5) ⊇ SO(3) subgroup chain, are used to construct basis states for the five‐dimensional harmonic oscillator. Algorithms are given to calculate matrix elements in this basis. The essential step is the construction of SO(5) ⊇ SO(3) irreps of type [v,0]. The methodology is similar to that used in two recent papers except that one‐dimensional, as opposed to multidimensional, vector‐valued wave functions are used to give conceptually simpler results. Another significant advance is a canonical resolution of the SO(5) ⊇ SO(3) multiplicity problem. © 1995 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70418/2/JMAPAQ-36-9-4711-1.pd

Mitigating effect of organic matter on the in vivo toxicity of metal oxide nanoparticles in the marine environment

This is the final version of the article. Available from the Royal Society of Chemistry via the DOI in this recordMajor constituents of seawater, i.e. ions and natural organic matter (NOM), can influence the environmental and toxicological behaviour of nanoparticles (NPs) in aquatic systems. By adsorbing-ligating-reacting to NP surface reactive sites, they can modify the NP surface structure and overall physico-chemical proprieties. This study explored the fate and in vivo toxicity of ZnO and MnO2NPs under artificial seawater conditions. These two nanomaterials are representative of metal oxide NPs inducing harm via dissolution and bandgap mechanisms, respectively. To gain a comprehensive understanding of the overall toxicological outcome, we traced the behaviour of NPs in the test systems (i.e. aggregation, sedimentation, dissolution, sorption), their fate in the model organism (i.e. ingestion and cellular internalization by oyster larvae), and the induction of a toxicological pathway (i.e. oxidative stress) up to pathogenesis. We found that ZnO NPs induced harm to oyster larvae under seawater conditions, but NOM mitigated its intensity. In contrast, MnO2NPs were not toxic at the tested concentrations (up to 200 μM), and their toxicological stasis was not modified by the presence of organic matter. We propose that strong ion sorption on the MnO2NP surface blocked redox-active sites thus preventing their bandgap mode of action.his project was funded by the European Union Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant agreement No 655134 (SOS-Nano project, Structure – Oxidative Stress relationships of metal oxide nanoparticles in the aquatic environment) and NERC FENAC access grant No PR120021. TG was further supported through NERC NE/N006178

Weak Gravitational Flexion

Flexion is the significant third-order weak gravitational lensing effect responsible for the weakly skewed and arc-like appearance of lensed galaxies. Here we demonstrate how flexion measurements can be used to measure galaxy halo density profiles and large-scale structure on non-linear scales, via galaxy-galaxy lensing, dark matter mapping and cosmic flexion correlation functions. We describe the origin of gravitational flexion, and discuss its four components, two of which are first described here. We also introduce an efficient complex formalism for all orders of lensing distortion. We proceed to examine the flexion predictions for galaxy-galaxy lensing, examining isothermal sphere and Navarro, Frenk & White (NFW) profiles and both circularly symmetric and elliptical cases. We show that in combination with shear we can precisely measure galaxy masses and NFW halo concentrations. We also show how flexion measurements can be used to reconstruct mass maps in 2-D projection on the sky, and in 3-D in combination with redshift data. Finally, we examine the predictions for cosmic flexion, including convergence-flexion cross-correlations, and find that the signal is an effective probe of structure on non-linear scales.Comment: 17 pages, including 12 figures, submitted to MNRA