Detection of positron-atom bound states through resonant annihilation

A method is proposed for detecting positron-atom bound states by observing enhanced positron annihilation due to electronic Feshbach resonances at electron-volt energies. The method is applicable to a range of open-shell transition metal atoms which are likely to bind the positron: Fe, Co, Ni, Tc, Ru, Rh, Sn, Sb, Ta, W, Os, Ir, and Pt. Estimates of their binding energies are provided.Comment: 5 pages, 1 figure; estimates of binding energies have been adde

Quantitative High Dynamic Range Beam Proling for Fluorescence Microscopy

Modern developmental biology relies on optically-sectioning uorescence microscope techniques to produce non-destructive in-vivo images of developing specimens at high resolution in three dimensions. As optimal performance of these techniques is reliant on the three-dimensional (3-D) intensity prole of the illumination employed, the ability to directly record and analyze these proles is of great use to the uorescence microscopist or instrument builder. Though excitation beam proles can be measured indirectly using a sample of uorescent beads and recording the emission along the microscope detection path, we demonstrate an alternative approach where a miniature camera sensor is used directly within the illumination beam. Measurements taken using our approach are solely concerned with the illumination optics as the detection optics are not involved. We present a miniature beam proling device and high dynamic range ux reconstruction algorithm that together are capable of accurately reproducing quantitative 3-D ux maps over a large focal volume. Performance of this beam proling system is veried within an optical test bench and demonstrated for uorescence microscopy by proling the low NA illumination beam of a single plane illumination microscope. The generality and success of this approach showcases a widely- exible beam amplitude diagnostic tool for use within the life sciences

Solving the radial Dirac equations: a numerical odyssey

We discuss, in a pedagogical way, how to solve for relativistic wave functions from the radial Dirac equations. After an brief introduction, in Section II we solve the equations for a linear Lorentz scalar potential, V_s(r), that provides for confinement of a quark. The case of massless u and d quarks is treated first, as these are necessarily quite relativistic. We use an iterative procedure to find the eigenenergies and the upper and lower component wave functions for the ground state and then, later, some excited states. Solutions for the massive quarks (s, c, and b) are also presented. In Section III we solve for the case of a Coulomb potential, which is a time-like component of a Lorentz vector potential, V_v(r). We re-derive, numerically, the (analytically well-known) relativistic hydrogen atom eigenenergies and wave functions, and later extend that to the cases of heavier one-electron atoms and muonic atoms. Finally, Section IV finds solutions for a combination of the V_s and V_v potentials. We treat two cases. The first is one in which V_s is the linear potential used in Sec. II and V_v is Coulombic, as in Sec. III. The other is when both V_s and V_v are linearly confining, and we establish when these potentials give a vanishing spin-orbit interaction (as has been shown to be the case in quark models of the hadronic spectrum).Comment: 39 pages (total), 23 figures, 2 table

A unified approach for the solution of the Fokker-Planck equation

This paper explores the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the Fokker-Planck equation. The unified features of the discrete singular convolution algorithm are discussed. It is demonstrated that different implementations of the present algorithm, such as global, local, Galerkin, collocation, and finite difference, can be deduced from a single starting point. Three benchmark stochastic systems, the repulsive Wong process, the Black-Scholes equation and a genuine nonlinear model, are employed to illustrate the robustness and to test accuracy of the present approach for the solution of the Fokker-Planck equation via a time-dependent method. An additional example, the incompressible Euler equation, is used to further validate the present approach for more difficult problems. Numerical results indicate that the present unified approach is robust and accurate for solving the Fokker-Planck equation.Comment: 19 page

Social preferences, accountability, and wage bargaining

We assess the extent of preferences for employment in a collective wage bargaining situation with heterogeneous workers. We vary the size of the union and introduce a treatment mechanism transforming the voting game into an individual allocation task. Our results show that highly productive workers do not take employment of low productive workers into account when making wage proposals, regardless of whether insiders determine the wage or all workers. The level of pro-social preferences is small in the voting game, while it increases as the game is transformed into an individual allocation task. We interpret this as an accountability effect

Solving the inhomogeneous Bethe-Salpeter equation

We develop an advanced method of solving homogeneous and inhomogeneous Bethe-Salpeter equations by using the expansion over the complete set of 4-dimensional spherical harmonics. We solve Bethe-Salpeter equations for bound and scattering states of scalar and spinor particles for the case of one meson exchange kernels. Phase shifts calculated for the scalar model are in agreement with the previously published results. We discuss possible manifestations of separability for one meson exchange interaction kernels.Comment: 9 pages, 11 eps-figures. Talk presented by S. S. Semikh at XVII International Baldin Seminar on High Energy Physics Problems "Relativistic Nuclear Physics and Quantum Chromodynamics", September 27 - October 2, 2004, Dubna, Russia; to appear in the proceedings of this conferenc

Dark-in-Bright Solitons in Bose-Einstein Condensates with Attractive Interactions

We demonstrate a possibility to generate localized states in effectively one-dimensional Bose-Einstein condensates with a negative scattering length in the form of a dark soliton in the presence of an optical lattice (OL) and/or a parabolic magnetic trap. We connect such structures with twisted localized modes (TLMs) that were previously found in the discrete nonlinear Schr{\"o}dinger equation. Families of these structures are found as functions of the OL strength, tightness of the magnetic trap, and chemical potential, and their stability regions are identified. Stable bound states of two TLMs are also found. In the case when the TLMs are unstable, their evolution is investigated by means of direct simulations, demonstrating that they transform into large-amplitude fundamental solitons. An analytical approach is also developed, showing that two or several fundamental solitons, with the phase shift $\pi$ between adjacent ones, may form stable bound states, with parameters quite close to those of the TLMs revealed by simulations. TLM structures are found numerically and explained analytically also in the case when the OL is absent, the condensate being confined only by the magnetic trap.Comment: 13 pages, 7 figures, New Journal of Physics (in press