1,882 research outputs found
The structure of the atomic helium trimers: Halos and Efimov states
The Faddeev equations for the atomic helium-trimer systems are solved
numerically with high accuracy both for the most sophisticated realistic
potentials available and for simple phenomenological potentials. An efficient
numerical procedure is described. The large-distance asymptotic behavior,
crucial for weakly bound three-body systems, is described almost analytically
for arbitrary potentials. The Efimov effect is especially considered. The
geometric structures of the bound states are quantitatively investigated. The
accuracy of the schematic models and previous computations is comparable, i.e.
within 20% for the spatially extended states and within 40% for the smaller
^4He-trimer ground state.Comment: 32 pages containing 7 figures and 6 table
Non-commutative low dimension spaces and superspaces associated with contracted quantum groups and supergroups
Quantum planes which correspond to all one parameter solutions of QYBE for
the two-dimensional case of GL-groups are summarized and their geometrical
interpretations are given. It is shown that the quantum dual plane is
associated with an exotic solution of QYBE and the well-known quantum -plane
may be regarded as the quantum analog of the flag (or fiber) plane.
Contractions of the quantum supergroup and corresponding quantum
superspace are considered in Cartesian basis. The contracted
quantum superspace is interpreted as the non-commutative
analog of the superspace with the fiber odd part.Comment: Talk given at the XIII Int. Coll. on Integrable Systems and Quantum
Groups, June 17-19, 2004, Prague, Czech Republic. Submitted in Czech. J. of
Physic
Integrable magnetic geodesic flows on Lie groups
Right-invariant geodesic flows on manifolds of Lie groups associated with
2-cocycles of corresponding Lie algebras are discussed. Algebra of integrals of
motion for magnetic geodesic flows is considered and necessary and sufficient
condition of integrability in quadratures is formulated. Canonic forms for
2-cocycles of all 4-dimensional Lie algebras are given and integrable cases
among them are separated.Comment: 16 page
Higgsless Electroweak Model and Contraction of Gauge Group
A modified formulation of the Electroweak Model with 3-dimensional spherical
geometry in the target space is suggested. The {\it free} Lagrangian in the
spherical field space along with the standard gauge field Lagrangian form the
full Higgsless Lagrangian of the model, whose second order terms reproduce the
same experimentally verified fields with the same masses as the Standard
Electroweak Model. The vector bosons masses are automatically generated, so
there is no need in special mechanism of spontaneous symmetry breaking.
The limiting case of the modified Higgsless Electroweak Model, which
corresponds to the contracted gauge group is discussed.
Within framework of the limit model Z-boson, electromagnetic and electron
fields are interpreted as an external ones with respect to W-bosons and
neutrino fields. The W-bosons and neutrino fields do not effect on these
external fields. The masses of all particles remain the same, but the field
interactions in contracted model are more simple as compared with the standard
Electroweak Model due to nullification of some terms.Comment: Talk at the International Workshop "`Supersymmetries and Quantum
Symmetries"' (SQS-09), Dubna, Russia, July 29 -- August 3, 2009, 11
Efimov states and their Fano resonances in a neutron-rich nucleus
Asymmetric resonances in elastic n+C scattering are attributed to
Efimov states of such neutron-rich nuclei, that is, three-body bound states of
the n+n+C system when none of the pairs is bound or some of them only
weakly bound. By fitting to the general resonance shape described by Fano, we
extract resonance position, width, and the "Fano profile index". While Efimov
states have been discussed extensively in many areas of physics, there is only
one very recent experimental observation in trimers of cesium atoms. The
conjunction that we present of the Efimov and Fano phenomena may lead to
experimental realization in nuclei.Comment: 4 double-column pages, 3 figure
Bogolyubov-Hartree-Fock approach to studying the QCD ground state
The quark's behaviour while influenced by a strong stochastic gluon field is
analyzed. An approximate procedure for calculating the effective Hamiltonian is
developed and the corresponding ground state within the Hartree-Fock-Bogolyubov
approach is found. The comparative analysis of various Hamiltonian models is
given and transition to the chiral limit in the Keldysh model is discussed in
detail.Comment: 18 pages, 4 figures, new version of the manuscrip
Operator method in solving non-linear equations of the Hartree-Fock type
The operator method is used to construct the solutions of the problem of the
polaron in the strong coupling limit and of the helium atom on the basis of the
Hartree-Fock equation. is obtained for the polaron
ground-state energy. Energies for 2s- and 3s-states are also calculated. The
other excited states are briefly discussed.Comment: 7 page
Correlation diagrams in collisions of three identical particles
We discuss collision of three identical particles and derive scattering
selection rules from initial to final states of the particles. We use either
laboratory-frame, hyperspherical, or Jacobian coordinates depending on which
one is best suited to describe three different configurations of the particles:
(1) three free particles, (2) a quasi-bound trimer, or (3) a dimer and a free
particle. We summarize quantum numbers conserved during the collision as well
as quantum numbers that are appropriate for a given configuration but may
change during the scattering process. The total symmetry of the system depends
on these quantum numbers. Based on the selection rules, we construct
correlation diagrams between different configurations before and after a
collision. In particular, we describe a possible recombination of the system
into one free particle and a dimer, which can be used, for example, to identify
possible decay products of quasi-stationary three-body statesComment: 14 pages,4 figure
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