44 research outputs found
Many-Body Contributions to Green's Functions and Casimir Energies
The multiple scattering formalism is used to extract irreducible N-body parts
of Green's functions and Casimir energies describing the interaction of N
objects that are not necessarily mutually disjoint. The irreducible N-body
scattering matrix is expressed in terms of single-body transition matrices. The
irreducible N-body Casimir energy is the trace of the corresponding irreducible
N-body part of the Green's function. This formalism requires the solution of a
set of linear integral equations. The irreducible three-body Green's function
and the corresponding Casimir energy of a massless scalar field interacting
with potentials are obtained and evaluated for three parallel semitransparent
plates. When Dirichlet boundary conditions are imposed on a plate the Green's
function and Casimir energy decouple into contributions from two disjoint
regions. We also consider weakly interacting triangular--and parabolic-wedges
placed atop a Dirichlet plate. The irreducible three-body Casimir energy of a
triangular--and parabolic-wedge is minimal when the shorter side of the wedge
is perpendicular to the Dirichlet plate. The irreducible three-body
contribution to the vacuum energy is finite and positive in all the cases
studied.Comment: 22 pages, 8 figure
Application of the -matrix Method to Faddeev-Merkuriev equation: beyond pseudostates
A version of the -matrix method for solving numerically the three-body
Faddeev-Merkuriev differential equations is proposed. This version allows to
take into account the full spectrum of the two-body Coulomb subsystem. As a
result, a discrete analog of the Lippmann-Schwinger equation is obtained which
allows to interpret correctly the three-body wave function in two-body domains.
The scheme is applied to calculations of the fully resolved absolute
differential cross sections for the HeHe and HeHe
reactions at small energy and momentum transfers. The results are in good
agreement with the experiment both in shape and in absolute value.Comment: 22 pages, 7 figure
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
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
Three-body treatment of the penetration through the Coulomb field of a two-fragment nucleus
On the basis of the Faddeev integral equations method and the Watson-
Feshbach concept of the effective (optical) interaction potential, the first
fully consistent three-body approach to the description of the penetration of a
charged particle through the Coulomb field of a two-particle bound complex
(composed of one charged and one neutral particles) has been developed. A
general formalism has been elaborated and on its basis, to a first
approximation in the Sommerfeld parameter, the influence of the nuclear
structure on the probability of the penetration of a charged particle (the
muon, the pion, the kaon and the proton) through the Gamow barrier of a
two-fragment nucleus (the deuteron and the two lightest lambda hypernuclei,
lambda hypertriton and lambda hyperhelium-5, has been calculated and studied.Comment: LaTeX, 30 pages, 4 eps figure
Method of determining the optimal settings of automatic excitation regulators of synchronous machines in EPS
The stability of the electric power system can be improved by forming of the correct settings of automatic exciting regulators. Currently, there is no unified methodology of automatic exciting regulators, so analysis of their impact is still an urgent task. The article describes the approach to solving above-mentioned problem, which combines several methods. Research based on Hybrid Real Time Simulator of EPS developed in Tomsk Polytechnic University
Polarization observables in p-d scattering below 30 MeV
Differential and total breakup cross sections as well as vector and tensor
analyzing powers for p-d scattering are studied for energies above the deuteron
breakup threshold up to E(lab)=28 MeV. The p-d scattering wave function is
expanded in terms of the correlated hyperspherical harmonic basis and the
elastic S-matrix is obtained using the Kohn variational principle in its
complex form. The effects of the Coulomb interaction, which are expected to be
important in this energy range, have been rigorously taken into account. The
Argonne AV18 interaction and the Urbana URIX three-nucleon potential have been
used to perform a comparison to the available experimental data.Comment: 31 pages, 8 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
Four-Body Bound State Calculations in Three-Dimensional Approach
The four-body bound state with two-body interactions is formulated in
Three-Dimensional approach, a recently developed momentum space representation
which greatly simplifies the numerical calculations of few-body systems without
performing the partial wave decomposition. The obtained three-dimensional
Faddeev-Yakubovsky integral equations are solved with two-body potentials.
Results for four-body binding energies are in good agreement with achievements
of the other methods.Comment: 29 pages, 2 eps figures, 8 tables, REVTeX
Solutions of the Faddeev-Yakubovsky equations for the four nucleons scattering states
The Faddeev-Yakubowsky equations in configuration space have been solved for
the four nucleon system. The results with an S-wave interaction model in the
isospin approximation are presented. They concern the bound and scattering
states below the first three-body threshold. The elastic phase-shifts for the
N+NNN reaction in different () channels are given and the corresponding
low energy expansions are discussed. Particular attention is payed to the n+t
elastic cross section. Its resonant structure is well described in terms of a
simple NN interaction. First results concerning the S-matrix for the coupled
N+NNN-NN+NN channels and the strong deuteron-deuteron scattering length are
obtained.Comment: latex.tar.gz, 36 pages, 10 figures, 11 tables. To be published in
Physical Review