Momentum Space Integral Equations for Three Charged Particles: Diagonal Kernels

It has been a long-standing question whether momentum space integral equations of the Faddeev type are applicable to reactions of three charged particles, in particular above the three-body threshold. For, the presence of long-range Coulomb forces has been thought to give rise to such severe singularities in their kernels that the latter may lack the compactness property known to exist in the case of purely short-range interactions. Employing the rigorously equivalent formulation in terms of an effective-two-body theory we have proved in a preceding paper [Phys. Rev. C {\bf 61}, 064006 (2000)] that, for all energies, the nondiagonal kernels occurring in the integral equations which determine the transition amplitudes for all binary collision processes, possess on and off the energy shell only integrable singularities, provided all three particles have charges of the same sign, i.e., all Coulomb interactions are repulsive. In the present paper we prove that, for particles with charges of equal sign, the diagonal kernels, in contrast, possess one, but only one, nonintegrable singularity. The latter can, however, be isolated explicitly and dealt with in a well-defined manner. Taken together these results imply that modified integral equations can be formulated, with kernels that become compact after a few iterations. This concludes the proof that standard solution methods can be used for the calculation of all binary (i.e., (in-)elastic and rearrangement) amplitudes by means of momentum space integral equations of the effective-two-body type.Comment: 36 pages, 2 figures, accepted for publication in Phys. Rev.

Proton-Deuteron Elastic Scattering from 2.5 to 22.5 MeV

We present the results of a calculation of differential cross sections and polarization observables for proton-deuteron elastic scattering, for proton laboratory energies from 2.5 to 22.5 MeV. The Paris potential parametrisation of the nuclear force is used. As solution method for the charged-composite particle equations the 'screening and renormalisation approach' is adopted which allows to correctly take into account the Coulomb repulsion between the two protons. Comparison is made with the precise experimental data of Sagara et al. [Phys. Rev. C 50, 576 (1994)] and of Sperison et al. [Nucl. Phys. A422, 81 (1984)].Comment: 24 pages, 8 eps figures, uses REVTe

Nuclear modification at sqrt{s_{NN}}=17.3 GeV, measured at NA49

Transverse momentum spectra up to 4.5 GeV/c were measured around midrapidity in Pb+Pb reactions at sqrt{s_{NN}}=17.3 GeV, for pi^{+/-}, p, pbar and K^{+/-}, by the NA49 experiment. The nuclear modification factors R_{AA}, R_{AA/pA} and R_{CP} were extracted and are compared to RHIC results at sqrt{s_{NN}}=200 GeV. The modification factor R_{AA} shows a rapid increase with transverse momentum in the covered region. The modification factor R_{CP} shows saturation well below unity in the pi^{+/-} channel. The extracted R_{CP} values follow the 200 GeV RHIC results closely in the available transverse momentum range for all particle species. For pi^{+/-} above 2.5 GeV/c transverse momentum, the measured suppression is smaller than that observed at RHIC. The nuclear modification factor R_{AA/pA} for pi^{+/-} stays well below unity.Comment: Proceedings of Quark Matter 2008 conferenc

Precision preparation of strings of trapped neutral atoms

We have recently demonstrated the creation of regular strings of neutral caesium atoms in a standing wave optical dipole trap using optical tweezers [Y. Miroshnychenko et al., Nature, in press (2006)]. The rearrangement is realized atom-by-atom, extracting an atom and re-inserting it at the desired position with sub-micrometer resolution. We describe our experimental setup and present detailed measurements as well as simple analytical models for the resolution of the extraction process, for the precision of the insertion, and for heating processes. We compare two different methods of insertion, one of which permits the placement of two atoms into one optical micropotential. The theoretical models largely explain our experimental results and allow us to identify the main limiting factors for the precision and efficiency of the manipulations. Strategies for future improvements are discussed.Comment: 25 pages, 18 figure

Long-range behavior of the optical potential for the elastic scattering of charged composite particles

The asymptotic behavior of the optical potential, describing elastic scattering of a charged particle $\alpha$ off a bound state of two charged, or one charged and one neutral, particles at small momentum transfer $\Delta_{\alpha}$ or equivalently at large intercluster distance $\rho_{\alpha}$, is investigated within the framework of the exact three-body theory. For the three-charged-particle Green function that occurs in the exact expression for the optical potential, a recently derived expression, which is appropriate for the asymptotic region under consideration, is used. We find that for arbitrary values of the energy parameter the non-static part of the optical potential behaves for $\Delta_{\alpha} \rightarrow 0$ as $C_{1}\Delta_{\alpha} + o\,(\Delta_{\alpha})$. From this we derive for the Fourier transform of its on-shell restriction for $\rho_{\alpha} \rightarrow \infty$ the behavior $-a/2\rho_{\alpha}^4 + o\,(1/\rho_{\alpha}^4)$, i.e., dipole or quadrupole terms do not occur in the coordinate-space asymptotics. This result corroborates the standard one, which is obtained by perturbative methods. The general, energy-dependent expression for the dynamic polarisability $C_{1}$ is derived; on the energy shell it reduces to the conventional polarisability $a$ which is independent of the energy. We emphasize that the present derivation is {\em non-perturbative}, i.e., it does not make use of adiabatic or similar approximations, and is valid for energies {\em below as well as above the three-body dissociation threshold}.Comment: 35 pages, no figures, revte

Implementation of a 6 Week Persuasive Reading and Writing Curriculum for Middle School Students

In this research project, the author presents a 6 week curricular unit that will be implemented at Soroco Middle School as a component of the Grade 7 language arts curriculum. This unit is designed to provide educators with: (a) a clear, concise method to prepare a wide variety of students for high stakes testing; (b) a deliberate approach to teach diverse students how to think critically and argue constructively; and (c) a concrete, effective method to teach a wide range of students how to use multiple writing strategies to construct persuasive paragraphs

A neutral atom quantum register

We demonstrate the realization of a quantum register using a string of single neutral atoms which are trapped in an optical dipole trap. The atoms are selectively and coherently manipulated in a magnetic field gradient using microwave radiation. Our addressing scheme operates with a high spatial resolution and qubit rotations on individual atoms are performed with 99% contrast. In a final read-out operation we analyze each individual atomic state. Finally, we have measured the coherence time and identified the predominant dephasing mechanism for our register.Comment: 4 pages, 4 figure

Chemical equilibrium study at SPS 158A GeV

A detailed study of chemical freeze-out in nucleus-nucleus collisions at beam energy 158A GeV is presented. By analyzing hadronic multiplicities within the statistical hadronization approach, the chemical equilibration of p-p, C-C, Si-Si and Pb-Pb systems is studied as a function of the number of participating nucleons in the system. Additionally, Two Component statistical hadronization model is applied to the data and is found to be able to explain the observed strangeness hadronic phase space under-saturation.Comment: 4 pages, 3 figures to appear in the proceedings of the ''Strangeness in Quark Matter 2004'' conferenc