237 research outputs found
Particle Ratios as a Probe of the QCD Critical Temperature
We show how the measured particle ratios can be used to provide non-trivial
information about the critical temperature of the QCD phase transition. This is
obtained by including the effects of highly massive Hagedorn resonances on
statistical models, which are used to describe hadronic yields. The inclusion
of Hagedorn states creates a dependence of the thermal fits on the Hagedorn
temperature, , which is assumed to be equal to , and leads to an
overall improvement of thermal fits. We find that for Au+Au collisions at RHIC
at GeV the best square fit measure, , occurs at
MeV and produces a chemical freeze-out temperature of 172.6 MeV
and a baryon chemical potential of 39.7 MeV.Comment: 6 pages, 4 figure
Relativistic Coulomb Green's function in -dimensions
Using the operator method, the Green's functions of the Dirac and
Klein-Gordon equations in the Coulomb potential are derived for
the arbitrary space dimensionality . Nonrelativistic and quasiclassical
asymptotics of these Green's functions are considered in detail.Comment: 9 page
Closed form representation for a projection onto infinitely dimensional subspace spanned by Coulomb bound states
The closed form integral representation for the projection onto the subspace
spanned by bound states of the two-body Coulomb Hamiltonian is obtained. The
projection operator onto the dimensional subspace corresponding to the
-th eigenvalue in the Coulomb discrete spectrum is also represented as the
combination of Laguerre polynomials of -th and -th order. The latter
allows us to derive an analog of the Christoffel-Darboux summation formula for
the Laguerre polynomials. The representations obtained are believed to be
helpful in solving the breakup problem in a system of three charged particles
where the correct treatment of infinitely many bound states in two body
subsystems is one of the most difficult technical problems.Comment: 7 page
Renormalization of the QED of self-interacting second order spin 1/2 fermions
We study the one-loop level renormalization of the electrodynamics of spin
1/2 fermions in the Poincar\'e projector formalism, in arbitrary covariant
gauge and including fermion self-interactions, which are dimension four
operators in this framework. We show that the model is renormalizable for
arbitrary values of the tree level gyromagnetic factor g within the validity
region of the perturbative expansion, \alpha g^2 << 1. In the absence of tree
level fermion self-interactions, we recover the pure QED of second order
fermions, which is renormalizable only for |g|=2. Turning off the
electromagnetic interaction we obtain a renormalizable Nambu-Jona-Lasinio-like
model with second order fermions in four space-time dimensions.Comment: 32 pages, 9 figures. Published versio
On the limiting radial distribution function for hydrogenic orbitals
An exact reduced limiting expression for the generalized radial distribution function D n (r) is derived and compared with quantum distributions for various degrees of excitation. It represents the quantum result at large quantum numbers significantly better than a prior empirical representation of the universal reduced distribution and gives a somewhat larger electronic partition function for the hydrogen atom than that based on the previous distribution.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43065/1/10910_2005_Article_BF01166729.pd
Local correlations of different eigenfunctions in a disordered wire
We calculate the correlator of the local density of states
in quasi-one-dimensional disordered wires
in a magnetic field, assuming that |r_1-r_2| is much smaller than the
localization length. This amounts to finding the zero mode of the
transfer-matrix Hamiltonian for the supersymmetric sigma-model, which is done
exactly by the mapping to the three-dimensional Coulomb problem. Both the
regimes of level repulsion and level attraction are obtained, depending on
|r_1-r_2|. We demonstrate that the correlations of different eigenfunctions in
the quasi-one-dimensional and strictly one-dimensional cases are dissimilar.Comment: 5 pages, 2 figures. v2: an error in treating the spatial dependence
of correlations is correcte
Resonances and fluctuations in the statistical model
We describe how the study of resonances and fluctuations can help constrain
the thermal and chemical freezeout properties of the fireball created in heavy
ion collisions. This review is based on [1-5].Comment: Proceedings,"Hadronic resonance production in heavy ion and
elementary collisions" UT Austin, March 5-7 201
Ballistic matter waves with angular momentum: Exact solutions and applications
An alternative description of quantum scattering processes rests on
inhomogeneous terms amended to the Schroedinger equation. We detail the
structure of sources that give rise to multipole scattering waves of definite
angular momentum, and introduce pointlike multipole sources as their limiting
case. Partial wave theory is recovered for freely propagating particles. We
obtain novel results for ballistic scattering in an external uniform force
field, where we provide analytical solutions for both the scattering waves and
the integrated particle flux. Our theory directly applies to p-wave
photodetachment in an electric field. Furthermore, illustrating the effects of
extended sources, we predict some properties of vortex-bearing atom laser beams
outcoupled from a rotating Bose-Einstein condensate under the influence of
gravity.Comment: 42 pages, 8 figures, extended version including photodetachment and
semiclassical theor
Analytic Treatment of Positronium Spin Splittings in Light-Front QED
We study the QED bound-state problem in a light-front hamiltonian approach.
Starting with a bare cutoff QED Hamiltonian, , with matrix elements
between free states of drastically different energies removed, we perform a
similarity transformation that removes the matrix elements between free states
with energy differences between the bare cutoff, , and effective
cutoff, \lam (\lam < \Lam). This generates effective interactions in the
renormalized Hamiltonian, . These effective interactions are derived
to order in this work, with . is renormalized
by requiring it to satisfy coupling coherence. A nonrelativistic limit of the
theory is taken, and the resulting Hamiltonian is studied using bound-state
perturbation theory (BSPT). The effective cutoff, \lam^2, is fixed, and the
limit, 0 \longleftarrow m^2 \alpha^2\ll \lam^2 \ll m^2 \alpha \longrightarrow
\infty, is taken. This upper bound on \lam^2 places the effects of
low-energy (energy transfer below \lam) emission in the effective
interactions in the sector. This lower bound on \lam^2
insures that the nonperturbative scale of interest is not removed by the
similarity transformation. As an explicit example of the general formalism
introduced, we show that the Hamiltonian renormalized to reproduces
the exact spectrum of spin splittings, with degeneracies dictated by rotational
symmetry, for the ground state through . The entire calculation is
performed analytically, and gives the well known singlet-triplet ground state
spin splitting of positronium, . We discuss remaining
corrections other than the spin splittings and how they can be treated in
calculating the spectrum with higher precision.Comment: 46 pages, latex, 3 Postscript figures included, section on remaining
corrections added, title changed, error in older version corrected, cutoff
placed in a windo
An exactly solvable model for the Fermi contact interaction
A model for the Fermi contact interaction is proposed in which the nuclear moment is represented as a magnetized spherical shell of radius r 0 . For a hydrogen-like system thus perturbed, the Schrödinger equation is solvable without perturbation theory by use of the Coulomb Green's function. Approximation formulas are derived in terms of a quantum defect in the Coulombic energy formula. It is shown that the usual Fermi potential cannot be applied beyond first-order perturbation theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46454/1/214_2004_Article_BF00548828.pd
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