5,474 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.
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 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
Cold Atom Physics Using Ultra-Thin Optical Fibers: Light-Induced Dipole Forces and Surface Interactions
The strong evanescent field around ultra-thin unclad optical fibers bears a
high potential for detecting, trapping, and manipulating cold atoms.
Introducing such a fiber into a cold atom cloud, we investigate the interaction
of a small number of cold Caesium atoms with the guided fiber mode and with the
fiber surface. Using high resolution spectroscopy, we observe and analyze
light-induced dipole forces, van der Waals interaction, and a significant
enhancement of the spontaneous emission rate of the atoms. The latter can be
assigned to the modification of the vacuum modes by the fiber.Comment: 4 pages, 4 figure
Triangle Diagram with Off-Shell Coulomb T-Matrix for (In-)Elastic Atomic and Nuclear Three-Body Processes
The driving terms in three-body theories of elastic and inelastic scattering
of a charged particle off a bound state of two other charged particles contain
the fully off-shell two-body Coulomb T-matrix describing the intermediate-state
Coulomb scattering of the projectile with each of the charged target particles.
Up to now the latter is usually replaced by the Coulomb potential, either when
using the multiple-scattering approach or when solving three-body integral
equations. General properties of the exact and the approximate on-shell driving
terms are discussed, and the accuracy of this approximation is investigated
numerically, both for atomic and nuclear processes including bound-state
excitation, for energies below and above the corresponding three-body
dissociation threshold, over the whole range of scattering angles.Comment: 22 pages, 11 figures, figures can be obtained upon request from the
Authors, revte
proton-deuteron elastic scattering above the deuteron breakup
The complex Kohn variational principle and the (correlated) hyperspherical
harmonics method are applied to study the proton-deuteron elastic scattering at
energies above the deuteron breakup threshold. Results for the elastic cross
section and various elastic polarization observables have been obtained by
fully taking into account the long-range effect of the Coulomb interaction and
using a realistic nucleon-nucleon interaction model. Detailed comparison
between the theoretical predictions and the accurate and abundant
proton-deuteron experimental data can now be performed.Comment: 6 pages, 2 figure
N-d scattering above the deuteron breakup threshold
The complex Kohn variational principle and the (correlated) Hyperspherical
Harmonics technique are applied to study the N--d scattering above the deuteron
breakup threshold. The configuration with three outgoing nucleons is explicitly
taken into account by solving a set of differential equations with outgoing
boundary conditions. A convenient procedure is used to obtain the correct
boundary conditions at values of the hyperradius fm. The
inclusion of the Coulomb potential is straightforward and does not give
additional difficulties. Numerical results have been obtained for a simple
s-wave central potential. They are in nice agreement with the benchmarks
produced by different groups using the Faddeev technique. Comparisons are also
done with experimental elastic N--d cross section at several energies.Comment: LaTeX, 13 pages, 3 figure
Analyzing symmetry breaking within a chaotic quantum system via Bayesian inference
Bayesian inference is applied to the level fluctuations of two coupled
microwave billiards in order to extract the coupling strength. The coupled
resonators provide a model of a chaotic quantum system containing two coupled
symmetry classes of levels. The number variance is used to quantify the level
fluctuations as a function of the coupling and to construct the conditional
probability distribution of the data. The prior distribution of the coupling
parameter is obtained from an invariance argument on the entropy of the
posterior distribution.Comment: Example from chaotic dynamics. 8 pages, 7 figures. Submitted to PR
- âŠ