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.

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

The Local Semicircle Law for Random Matrices with a Fourfold Symmetry

We consider real symmetric and complex Hermitian random matrices with the additional symmetry $h_{xy}=h_{N-x,N-y}$. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble naturally arises as the Fourier transform of a Gaussian orthogonal ensemble (GOE). It also occurs as the flip matrix model - an approximation of the two-dimensional Anderson model at small disorder. We show that the density of states converges to the Wigner semicircle law despite the new symmetry type. We also prove the local version of the semicircle law on the optimal scale.Comment: 20 pages, to appear in J. Math. Phy

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

Obesity and spatial context in Appalachia

The prevalence of obesity has increased substantially over the past 30 years. Obesity is a multi-factorial disorder, which is often associated with many other significant diseases such as diabetes, hypertension and other cardiovascular diseases, osteoarthritis and certain cancers. For these reasons, it is a complex health issue to address. The objective of this study is to identify the factors which are responsible for the spatial variation of adult obesity throughout the Appalachian region. In addition, preliminary examinations are made to identify potential associations between geographic variability in the prevalence of obesity and the characteristics of individuals and places with variable prevalence rates. Obese prevalence estimates were generated for all counties in Appalachia for adult males and females using data from the Behavioral Risk Factor Surveillance System (BRFSS). These data were used to create maps of obesity prevalence in Appalachia. Certain counties consistently experience higher prevalence of obesity for both genders. In areas with persistently high obesity prevalence rates, the burden is often highly localized among specific counties. A regression model was implemented to analyze the effect of a number of factors on obesity. Two significant contextual factors, employment change and labor force participation, were identified, even though they have not been addressed in the literature. The regression model results demonstrate poverty having a significant impact on female obesity, but no significant impact on male obesity. The regression model also found that urban-rural location is significant, but gender specific only for males in non-metro areas and small metro areas

Photoproduction of the doubly-strange Xi Hyperons

We report on the first measurement of exclusive Xi- and Xi0 photoproduction. The Xi- states are produced in the reaction gamma p --> K+ K+ Xi-, and the Xi0 states in gamma p --> K+ K+ pi- Xi0. Identification is made by the unique mass measured as the missing mass of the K+ K+ (or K+ K+ pi-) system using the CLAS detector at the Thomas Jefferson National Accelerator Facility. A systematic study of the excited Xi spectrum improves our understanding of the N* and Delta* states, since the Xi* states are related to them by SU(3) flavor symmetry. At the highest energies available at Jefferson Lab, we begin to find evidence for known excited Xi- states in the photoproduction process, and possibly new states at 1770 and 1860 MeV, although we do not have enough statistics to draw a strong conclusion. A search for the Xi5--(1862) pentaquark state seen by NA49 is made using the process gamma p -> K+ K+ pi+ X, but the result is inconclusive for lack of statistics.Comment: 7 pages, 9 figures; invited talk given at the 8th International Conference on Hypernuclear and Strange Particle Physics, Jefferson Lab, Newport News, VA, 14-18 October 200