15,661 research outputs found
Coupled-channel continuum eigenchannel basis
The goal of this paper is to calculate bound, resonant and scattering states
in the coupled-channel formalism without relying on the boundary conditions at
large distances. The coupled-channel solution is expanded in eigenchannel bases
i.e. in eigenfunctions of diagonal Hamiltonians. Each eigenchannel basis may
include discrete and discretized continuum (real or complex energy) single
particle states. The coupled-channel solutions are computed through
diagonalization in these bases. The method is applied to a few two-channels
problems. The exact bound spectrum of the Poeschl-Teller potential is well
described by using a basis of real energy continuum states. For deuteron
described by Reid potential, the experimental energy and the S and D contents
of the wave function are reproduced in the asymptotic limit of the cutoff
energy. For the Noro-Taylor potential resonant state energy is well reproduced
by using the complex energy Berggren basis. It is found that the expansion of
the coupled-channel wave function in these eigenchannel bases require less
computational efforts than the use of any other basis. The solutions are stable
and converge as the cutoff energy increases.Comment: Accepted to be published in Physics Letters
Two-Particle Resonant States in a Many-Body Mean Field
A formalism to evaluate the resonant states produced by two particles moving
outside a closed shell core is presented. The two particle states are
calculated by using a single particle representation consisting of bound
states, Gamow resonances and scattering states in the complex energy plane
(Berggren representation). Two representative cases are analysed corresponding
to whether the Fermi level is below or above the continuum threshold. It is
found that long lived two-body states (including bound states) are mostly
determined by either bound single-particle states or by narrow Gamow
resonances. However, they can be significantly affected by the continuum part
of the spectrum.Comment: 11 pages, 4 figure
On the p-Laplace operator on Riemannian manifolds
This thesis covers different aspects of the p-Laplace operators on Riemannian
manifolds. Chapter 2. Potential theoretic aspects: the Khasmkinskii condition.
Chapter 3: sharp eigenvalue estimates with Ricci curvature lower bounds.
Chapter 4: Critical sets of (2-)harmonic functions.Comment: PhD Thesis: Contains results obtained in collaboration with other
mathematicians, see section 1.4 for details. ADDED IN THIS VERSION:
correction of few typos, and added a reference brought to our attention by an
anonymous referee. Details in the introduction, end of section 1.
Shadow poles in a coupled-channel problem calculated with Berggren basis
In coupled-channel models the poles of the scattering S-matrix are located on
different Riemann sheets. Physical observables are affected mainly by poles
closest to the physical region but sometimes shadow poles have considerable
effect, too. The purpose of this paper is to show that in coupled-channel
problem all poles of the S-matrix can be calculated with properly constructed
complex-energy basis. The Berggren basis is used for expanding the
coupled-channel solutions. The location of the poles of the S-matrix were
calculated and compared with an exactly solvable coupled-channel problem: the
one with the Cox potential. We show that with appropriately chosen Berggren
basis poles of the S-matrix including the shadow ones can be determined.Comment: 11 pages, 4 figures, 59 reference
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