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

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 $ppe$ 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 $p+p+e\to d+\nu,$ which take place as a step of $pp$-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 $\approx 100$ 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