147 research outputs found
Explicit Representations for the T-Matrix on Unphysical Energy Sheets and Resonances in Two- and Three-Body Systems
We discuss the structure of the two- and three-body T-matrices, scattering
matrices, and resolvents continued to the unphysical energy sheets. Our
conclusions arise due to the representations that have been found for
analytically continued momentum-space kernels of the T-operators. These
representations are explicitly written only in terms of the physical-sheet
kernels of the T-matrix itself. One of advantages of the representations in the
three-body case is that they show which portions of the physical-sheet
three-body scattering matrix are ``responsible'' for the resonances associated
with a particular unphysical sheet. A resonance appears to be the energy where
the correspondingly truncated scattering matrix (taken on the physical sheet)
has eigenvalue zero. We also mention applications of this approach to some
specific three-body systems, based on the Faddeev differential equations.Comment: Based on a lecture given at the International Workshop ``Critical
Stability of Few-Body Quantum Systems'' (Dresden, October 17--22, 2005
Scattering and resonances in the ^4He three-atomic system
A mechanism of disappearance and formation of the Efimov levels of the helium
^4He_3 trimer is studied when the force of interatomic interaction is changed.
The resonances including virtual levels are calculated by the method based on
the solving the boundary value problem, at complex energies, for the Faddeev
differential equations describing the (2+1 --> 2+1; 1+1+1) scattering
processes.Comment: RevTeX, 5 pages; Contribution to Proceedings of the First
International Conference on Modern Trends in Computational Physics, June
15-20, 1998, Dubna (Russia
Kinetic energy in the collective quadrupole Hamiltonian from the experimental data
Dependence of the kinetic energy term of the collective nuclear Hamiltonian
on collective momentum is considered. It is shown that the fourth order in
collective momentum term of the collective quadrupole Hamiltonian generates a
sizable effect on the excitation energies and the matrix elements of the
quadrupole moment operator. It is demonstrated that the results of calculation
are sensitive to the values of some matrix elements of the quadrupole moment.
It stresses the importance for a concrete nucleus to have the experimental data
for the reduced matrix elements of the quadrupole moment operator taken between
all low lying states with the angular momenta not exceeding 4
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