6,057 research outputs found
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.
Computing the Similarity Between Moving Curves
In this paper we study similarity measures for moving curves which can, for
example, model changing coastlines or retreating glacier termini. Points on a
moving curve have two parameters, namely the position along the curve as well
as time. We therefore focus on similarity measures for surfaces, specifically
the Fr\'echet distance between surfaces. While the Fr\'echet distance between
surfaces is not even known to be computable, we show for variants arising in
the context of moving curves that they are polynomial-time solvable or
NP-complete depending on the restrictions imposed on how the moving curves are
matched. We achieve the polynomial-time solutions by a novel approach for
computing a surface in the so-called free-space diagram based on max-flow
min-cut duality
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
Comments: What\u27s Yours Is Ours? Gamete Donation in the Marital Context: Why Courts and Legislatures Should Not Interfere with an Individual\u27s Fundamental Right to Privacy
Comments: What\u27s Yours Is Ours? Gamete Donation in the Marital Context: Why Courts and Legislatures Should Not Interfere with an Individual\u27s Fundamental Right to Privacy
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 off a bound state of two charged, or
one charged and one neutral, particles at small momentum transfer
or equivalently at large intercluster distance
, 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 as
. From this we derive for the
Fourier transform of its on-shell restriction for the behavior , 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 is derived; on the energy shell it reduces to the
conventional polarisability 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
Three- and Four-Body Scattering Calculations including the Coulomb Force
The method of screening and renormalization for including the Coulomb
interaction in the framework of momentum-space integral equations is applied to
the three- and four-body nuclear reactions. The Coulomb effect on the
observables and the ability of the present nuclear potential models to describe
the experimental data is discussed.Comment: Proceedings of the Critical Stability workshop, Erice, Sicily,
October 2008, to be published in Few-Body System
New results from fluctuation analysis in NA49 at the CERN SPS
The exploration of the phase diagram of strongly interacting matter,
particularly the study of the phase transition from hadronic to partonic matter
and the search for a hypothetical critical endpoint of the first order
transition line, is one of the most challenging tasks in present heavy ion
physics.
In this talk new results on chemical (particle ratio), transverse momentum,
multiplicity and azimuthal angle fluctuations will be presented. We also
discuss their connection to the onset of deconfinement and to the critical
endpoint.Comment: The Proceedings of the International Conference "Critical Point and
Onset of Deconfinement - CPOD 2011", Wuhan, November 7-11, 201
Three charged particles in the continuum. Astrophysical examples
We suggest a new adiabatic approach for description of three charged
particles in the continuum. This approach is based on the Coulomb-Fourier
transformation (CFT) of three body Hamiltonian, which allows to develop a
scheme, alternative to Born-Oppenheimer one.
The approach appears as an expansion of the kernels of corresponding integral
transformations in terms of small mass-ratio parameter. To be specific, the
results are presented for the system in the continuum. The wave function
of a such system is compared with that one which is used for estimation of the
rate for triple reaction which take place as a step of
-cycle in the center of the Sun. The problem of microscopic screening for
this particular reaction is discussed
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