450 research outputs found
Tests of Two-Body Dirac Equation Wave Functions in the Decays of Quarkonium and Positronium into Two Photons
Two-Body Dirac equations of constraint dynamics provide a covariant framework
to investigate the problem of highly relativistic quarks in meson bound states.
This formalism eliminates automatically the problems of relative time and
energy, leading to a covariant three dimensional formalism with the same number
of degrees of freedom as appears in the corresponding nonrelativistic problem.
It provides bound state wave equations with the simplicity of the
nonrelativistic Schroedinger equation. Here we begin important tests of the
relativistic sixteen component wave function solutions obtained in a recent
work on meson spectroscopy, extending a method developed previously for
positronium decay into two photons. Preliminary to this we examine the
positronium decay in the 3P_{0,2} states as well as the 1S_0. The two-gamma
quarkonium decays that we investigate are for the \eta_{c}, \eta_{c}^{\prime},
\chi_{c0}, \chi_{c2}, \pi^{0}, \pi_{2}, a_{2}, and f_{2}^{\prime} mesons. Our
results for the four charmonium states compare well with those from other quark
models and show the particular importance of including all components of the
wave function as well as strong and CM energy dependent potential effects on
the norm and amplitude. The results for the \pi^{0}, although off the
experimental rate by 15%, is much closer than the usual expectations from a
potential model. We conclude that the Two-Body Dirac equations lead to wave
functions which provide good descriptions of the two-gamma decay amplitude and
can be used with some confidence for other purposes.Comment: 79 pages, included new sections on covariant scalar product and added
pages on positronium decay for 3P0 and 3P_2 state
Singularity Structures in Coulomb-Type Potentials in Two Body Dirac Equations of Constraint Dynamics
Two Body Dirac Equations (TBDE) of Dirac's relativistic constraint dynamics
have been successfully applied to obtain a covariant nonperturbative
description of QED and QCD bound states. Coulomb-type potentials in these
applications lead naively in other approaches to singular relativistic
corrections at short distances that require the introduction of either
perturbative treatments or smoothing parameters. We examine the corresponding
singular structures in the effective potentials of the relativistic
Schroedinger equation obtained from the Pauli reduction of the TBDE. We find
that the relativistic Schroedinger equation lead in fact to well-behaved wave
function solutions when the full potential and couplings of the system are
taken into account. The most unusual case is the coupled triplet system with
S=1 and L={(J-1),(J+1)}. Without the inclusion of the tensor coupling, the
effective S-state potential would become attractively singular. We show how
including the tensor coupling is essential in order that the wave functions be
well-behaved at short distances. For example, the S-state wave function becomes
simply proportional to the D-state wave function and dips sharply to zero at
the origin, unlike the usual S-state wave functions. Furthermore, this behavior
is similar in both QED and QCD, independent of the asymptotic freedom behavior
of the assumed QCD vector potential. Light- and heavy-quark meson states can be
described well by using a simplified linear-plus-Coulomb-type QCD potential
apportioned appropriately between world scalar and vector potentials. We use
this potential to exhibit explicitly the origin of the large pi-rho splitting
and effective chiral symmetry breaking. The TBDE formalism developed here may
be used to study quarkonia in quark-gluon plasma environments.Comment: 23 pages, 4 figure
Tracking the evolution of a single composite particle during redox cycling for application in H-2 production
Composite materials consisting of metal and metal oxide phases are being researched intensively for various energy conversion applications where they are often expected to operate under redox conditions at elevated temperature. Understanding of the dynamics of composite evolution during redox cycling is still very limited, yet critical to maximising performance and increasing durability. Here we track the microstructural evolution of a single composite particle over 200 redox cycles for hydrogen production by chemical looping, using multi-length scale X-ray computed tomography. We show that redox cycling triggers a centrifugal redispersion of the metal phase and a centripetal clustering of porosity, both seemingly driven by the asymmetric nature of oxygen exchange in composites. Initially, the particle develops a large amount of internal porosity which boosts activity, but on the long term this facilitates structural and compositional reorganisation and eventually degradation. These results provide valuable insight into redox-driven microstructural changes and also for the design of new composite materials with enhanced durability
Explicit Solution of the Time Evolution of the Wigner Function
Previously, an explicit solution for the time evolution of the Wigner
function was presented in terms of auxiliary phase space coordinates which obey
simple equations that are analogous with, but not identical to, the classical
equations of motion. They can be solved easily and their solutions can be
utilized to construct the time evolution of the Wigner function. In this paper,
the usefulness of this explicit solution is demonstrated by solving a numerical
example in which the Wigner function has strong spatial and temporal variations
as well as regions with negative values. It is found that the explicit solution
gives a correct description of the time evolution of the Wigner function. We
examine next the pseudoparticle approximation which uses classical trajectories
to evolve the Wigner function. We find that the pseudoparticle approximation
reproduces the general features of the time evolution, but there are
deviations. We show how these deviations can be systematically reduced by
including higher-order correction terms in powers of .Comment: 16 pages, in LaTex, invited talk presented at the Wigner Centennial
Conference, Pecs, Hungary, July 8-12, 2002, to be published in the Journal of
Optics B: Quantum and Classical Optics, June 200
Heavy Quarkonia in Quark-Gluon Plasma
Using the color-singlet free energy F_1 and total internal energy U_1
obtained by Kaczmarek et al. for a static quark Q and an antiquark Qbar in
quenched QCD, we study the binding energies and wave functions of heavy
quarkonia in a quark-gluon plasma. By minimizing the grand potential in a
simplified schematic model, we find that the proper color-singlet Q-Qbar
potential can be obtained from the total internal energy U_1 by subtracting the
gluon internal energy contributions. We carry out this subtraction in the local
energy-density approximation in which the gluon energy density can be related
to the local gluon pressure by the quark-gluon plasma equation of state. We
find in this approximation that the proper color-singlet Q-Qbar potential is
approximately F_1 for T ~ T_c and it changes to (3/4)F_1+(1/4)U_1 at high
temperatures. In this potential model, the J/psi is weakly bound above the
phase transition temperature T_c, and it dissociates spontaneously above 1.62
T_c, while chi_c and psi' are unbound in the quark-gluon plasma. The bottomium
states Upsilon, chi_b and Upsilon' are bound in the quark-gluon plasma and they
dissociate at 4.10 T_c, 1.18 T_c, and 1.38 T_c respectively. For comparison, we
evaluate the heavy quarkonium binding energies also in other models using the
free energy F_1 or the total internal energy U_1 as the Q-Qbar potential. The
comparison shows that the model with the new Q-Qbar potential proposed in this
manuscript gives dissociation temperatures that agree best with those from
spectral function analyses. We evaluate the cross section for
sigma(g+J/psi->c+cbar) and its inverse process, in order to determine the J/psi
dissociation width and the rate of J/psi production by recombining c and cbar
in the quark gluon plasma.Comment: 30 pages, in Late
Laser Cooling of Optically Trapped Molecules
Calcium monofluoride (CaF) molecules are loaded into an optical dipole trap
(ODT) and subsequently laser cooled within the trap. Starting with
magneto-optical trapping, we sub-Doppler cool CaF and then load CaF
molecules into an ODT. Enhanced loading by a factor of five is obtained when
sub-Doppler cooling light and trapping light are on simultaneously. For trapped
molecules, we directly observe efficient sub-Doppler cooling to a temperature
of . The trapped molecular density of
cm is an order of magnitude greater than in the initial sub-Doppler
cooled sample. The trap lifetime of 750(40) ms is dominated by background gas
collisions.Comment: 5 pages, 5 figure
Relativistic Modification of the Gamow Factor
In processes involving Coulomb-type initial- and final-state interactions,
the Gamow factor has been traditionally used to take into account these
additional interactions. The Gamow factor needs to be modified when the
magnitude of the effective coupling constant increases or when the velocity
increases. For the production of a pair of particles under their mutual
Coulomb-type interaction, we obtain the modification of the Gamow factor in
terms of the overlap of the Feynman amplitude with the relativistic wave
function of the two particles. As a first example, we study the modification of
the Gamow factor for the production of two bosons. The modification is
substantial when the coupling constant is large.Comment: 13 pages, in LaTe
Correction Factors for Reactions involving Quark-Antiquark Annihilation or Production
In reactions with production or annihilation, initial-
and final-state interactions give rise to large corrections to the lowest-order
cross sections. We evaluate the correction factor first for low relative
kinetic energies by studying the distortion of the relative wave function. We
then follow the procedure of Schwinger to interpolate this result with the
well-known perturbative QCD vertex correction factors at high energies, to
obtain an explicit semi-empirical correction factor applicable to the whole
range of energies. The correction factor predicts an enhancement for
in color-singlet states and a suppression for color-octet states, the effect
increasing as the relative velocity decreases. Consequences on dilepton
production in the quark-gluon plasma, the Drell-Yan process, and heavy quark
production processes are discussed.Comment: 25 pages (REVTeX), includes 2 uuencoded compressed postscript figure
Mapping the Two-Component Atomic Fermi Gas to the Nuclear Shell-Model
The physics of a two-component cold fermi gas is now frequently addressed in
laboratories. Usually this is done for large samples of tens to hundreds of
thousands of particles. However, it is now possible to produce few-body systems
(1-100 particles) in very tight traps where the shell structure of the external
potential becomes important. A system of two-species fermionic cold atoms with
an attractive zero-range interaction is analogous to a simple model of nucleus
in which neutrons and protons interact only through a residual pairing
interaction. In this article, we discuss how the problem of a two-component
atomic fermi gas in a tight external trap can be mapped to the nuclear shell
model so that readily available many-body techniques in nuclear physics, such
as the Shell Model Monte Carlo (SMMC) method, can be directly applied to the
study of these systems. We demonstrate an application of the SMMC method by
estimating the pairing correlations in a small two-component Fermi system with
moderate-to-strong short-range two-body interactions in a three-dimensional
harmonic external trapping potential.Comment: 13 pages, 3 figures. Final versio
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