Recurrence Formulas for Fully Exponentially Correlated Four-Body Wavefunctions

Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (>= -1) of all the interparticle distances r_ij, multiplied by an exponential containing an arbitrary linear combination of all the r_ij. These integrals are generalizations of those encountered using Hylleraas basis functions, and include all that are needed to make energy computations on the Li atom and other four-body systems with a fully exponentially correlated Slater-type basis of arbitrary quantum numbers. The only quantities needed to start the recursion are the basic four-body integral first evaluated by Fromm and Hill, plus some easily evaluated three-body "boundary" integrals. The computational labor in constructing integral sets for practical computations is less than when the integrals are generated using explicit formulas obtained by differentiating the basic integral with respect to its parameters. Computations are facilitated by using a symbolic algebra program (MAPLE) to compute array index pointers and present syntactically correct FORTRAN source code as output; in this way it is possible to obtain error-free high-speed evaluations with minimal effort. The work can be checked by verifying sum rules the integrals must satisfy.Comment: 10 pages, no figures, accepted by Phys. Rev. A (January 2009

Acousto-optic filter for electronic laser tuning

Electronically tunable lithium niobate filter utilizes acoustic-optic diffraction for tuning laser to desired frequencies. Filter placed inside laser cavity diffracts incident optical signal of one polarization into orthogonal polarization by collinearly propagating acoustic beam to desired wavelength

Can Multiband Observations Constrain Explanations for Knotty Jets?

One can imagine a number of mechanisms that could be the cause of brighter/fainter segments of jets. In a sense, jets might be easier to understand if they were featureless. However we observe a wide variety of structures which we call "knots". By considering the ramifications of the various scenarios for the creation of knots, we determine which ones or which classes are favored by the currently available multiwavelength data.Comment: 8 pages, to appear in the proceedings of "High Energy Phenomena In Relativistic Outflows II" (Buenos Aires, Argentina, October 26-30, 2009) International Journal of Modern Physics D. The editors of the special journal issue will be G.E. Romero, F.A. Aharonian and J.M. Parede

Proposed acousto-optic filter

Narrow band optical filter is electronically tunable over a large wavelength region. The filter utilizes collinear acousto-optic diffraction in an optically anisotropic media

On the adjoint representation of sln\mathfrak{sl}_n and the Fibonacci numbers

We decompose the adjoint representation of $\mathfrak{sl}_{r+1}=\mathfrak {sl}_{r+1}(\mathbb C)$ by a purely combinatorial approach based on the introduction of a certain subset of the Weyl group called the \emph{Weyl alternation set} associated to a pair of dominant integral weights. The cardinality of the Weyl alternation set associated to the highest root and zero weight of $\mathfrak {sl}_{r+1}$ is given by the $r^{th}$ Fibonacci number. We then obtain the exponents of $\mathfrak {sl}_{r+1}$ from this point of view.Comment: 9 page