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.

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

General Scheme of Risk – Oriented Audit Stages

The article examines the problem of applying risk-oriented approach in audit. A risk-oriented approach on the one hand allows to increase efficiency of auditors’ activity, the level of compliance with mandatory requirements, and on the other hand, to avoid the excessive inspections’ procedures in the formation of a scientifically grounded framework of reasonable sufficiency inherent to each specific audit. At the same time, risk-oriented approach needs to create its own methodological base, develop methodologies and relevant accompanying documents, and, most importantly, train personnel capable of implementing this innovative methodology. For this reason, topic of this paper is extremely relevant.     Keywords: audit, risk-oriented approach, planning, accounting (financial) statement

Scattering theory for arbitrary potentials

The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. New definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a Coulomb tail are presented. It is shown that for the Coulomb potential the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure.Comment: To be published in Phys Rev

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

Generalized Faddeev equations in the AGS form for deuteron stripping with explicit inclusion of target excitations and Coulomb interaction

Theoretical description of reactions in general, and the theory for $(d,p)$ reactions, in particular, needs to advance into the new century. Here deuteron stripping processes off a target nucleus consisting of ${A}$ nucleons are treated within the framework of the few-body integral equations theory. The generalized Faddeev equations in the AGS form, which take into account the target excitations, with realistic optical potentials provide the most advanced and complete description of the deuteron stripping. The main problem in practical application of such equations is the screening of the Coulomb potential, which works only for light nuclei. In this paper we present a new formulation of the Faddeev equations in the AGS form taking into account the target excitations with explicit inclusion of the Coulomb interaction. By projecting the $(A+2)$-body operators onto target states, matrix three-body integral equations are derived which allow for the incorporation of the excited states of the target nucleons. Using the explicit equations for the partial Coulomb scattering wave functions in the momentum space we present the AGS equations in the Coulomb distorted wave representation without screening procedure. We also use the explicit expression for the off-shell two-body Coulomb scattering $T$-matrix which is needed to calculate the effective potentials in the AGS equations. The integrals containing the off-shell Coulomb T-matrix are regularized to make the obtained equations suitable for calculations. For $NN$ and nucleon-target nuclear interactions we assume the separable potentials what significantly simplifies solution of the AGS equations.Comment: 34 pages, 13 figure

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

The thermal expansion and thermophysical properties of an aluminum and Al/B 4 C composite

The paper presents results of experimental studies of the thermal expansion and thermophysical properties of an Al/B 4 C composite with a boron carbide content of 20 wt% and technically pure aluminum in the temperature range from 100 to 600°C to evaluate the possible use of this composite as a neutron-protective material in the nuclear industry. © 2017 Author(s).We would like to appreciate the assistance of S. M. Zadvorkin, S. V. Lepikhin and L. S. Goruleva in conducting the investigations. Investigation was supported by Act 211 of the Government of the Russian Federation (agreement No. 02.A03.21.0006)