145 research outputs found
Three-body resonances Lambda-n-n and Lambda-Lambda-n
Possible bound and resonant states of the hypernuclear systems
and are sought as zeros of the corresponding three-body Jost
functions calculated within the framework of the hyperspherical approach with
local two-body S-wave potentials describing the , , and
interactions. Very wide near-threshold resonances are found
for both three-body systems. The positions of these resonances turned out to be
sensitive to the choice of the -potential. Bound and
states only appear if the two-body potentials are multiplied
by a factor of .Comment: 12 pages, 5 figures. Acknowledgments are added in the new versio
Analytic structure and power-series expansion of the Jost function for the two-dimensional problem
For a two-dimensional quantum mechanical problem, we obtain a generalized
power-series expansion of the S-matrix that can be done near an arbitrary point
on the Riemann surface of the energy, similarly to the standard effective range
expansion. In order to do this, we consider the Jost-function and analytically
factorize its momentum dependence that causes the Jost function to be a
multi-valued function. The remaining single-valued function of the energy is
then expanded in the power-series near an arbitrary point in the complex energy
plane. A systematic and accurate procedure has been developed for calculating
the expansion coefficients. This makes it possible to obtain a semi-analytic
expression for the Jost-function (and therefore for the S-matrix) near an
arbitrary point on the Riemann surface and use it, for example, to locate the
spectral points (bound and resonant states) as the S-matrix poles. The method
is applied to a model simlar to those used in the theory of quantum dots.Comment: 42 pages, 9 figures, submitted to J.Phys.
Extracting the resonance parameters from experimental data on scattering of charged particles
A new parametrization of the multi-channel S-matrix is used to fit scattering
data and then to locate the resonances as its poles. The S-matrix is written in
terms of the corresponding "in" and "out" Jost matrices which are expanded in
the Taylor series of the collision energy E around an appropriately chosen
energy E0. In order to do this, the Jost matrices are written in a
semi-analytic form where all the factors (involving the channel momenta and
Sommerfeld parameters) responsible for their "bad behaviour" (i.e. responsible
for the multi-valuedness of the Jost matrices and for branching of the Riemann
surface of the energy) are given explicitly. The remaining unknown factors in
the Jost matrices are analytic and single-valued functions of the variable E
and are defined on a simple energy plane. The expansion is done for these
analytic functions and the expansion coefficients are used as the fitting
parameters. The method is tested on a two-channel model, using a set of
artificially generated data points with typical error bars and a typical random
noise in the positions of the points.Comment: 15 pages, 7 figures, 2 table
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