79 research outputs found
Distributions of the -matrix poles in Woods-Saxon and cut-off Woods-Saxon potentials
The positions of the -matrix poles are calculated in generalized
Woods-Saxon (GWS) potential and in cut-off generalized Woods-Saxon (CGWS)
potential. The solutions of the radial equations are calculated numerically for
the CGWS potential and analytically for GWS using the formalism of Gy. Bencze
\cite{[Be66]}. We calculate CGWS and GWS cases at small non-zero values of the
diffuseness in order to approach the square well potential and to be able to
separate effects of the radius parameter and the cut-off radius parameter. In
the case of the GWS potential the wave functions are reflected at the nuclear
radius therefore the distances of the resonant poles depend on the radius
parameter of the potential. In CGWS potential the wave function can be
reflected at larger distance where the potential is cut to zero and the
derivative of the potential does not exist. The positions of most of the
resonant poles do depend strongly on the cut-off radius of the potential, which
is an unphysical parameter. Only the positions of the few narrow resonances in
potentials with barrier are not sensitive to the cut-off distance. For the
broad resonances the effect of the cut-off can not be corrected by using a
suggested analytical form of the first order perturbation correction.Comment: Accepted by Nucl. Phys.
Trajectories of the S-matrix poles in Salamon-Vertse potential
The trajectories of S-matrix poles are calculated in the finite-range
phenomenological potential introduced recently by P. Salamon and T. Vertse
(SV). The trajectories of the resonance poles in this SV potential are compared
to the corresponding trajectories in a cut-off Woods-Saxon (WS) potential for
l>0. The dependence on the cut-off radius is demonstrated. The starting points
of the trajectories turn out to be related to the average ranges of the two
terms in the SV potential
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
Calculating broad neutron resonances in a cut-off Woods-Saxon potential
In a cut-off Woods-Saxon (CWS) potential with realistic depth -matrix
poles being far from the imaginary wave number axis form a sequence where the
distances of the consecutive resonances are inversely proportional with the
cut-off radius value, which is an unphysical parameter. Other poles lying
closer to the imaginary wave number axis might have trajectories with irregular
shapes as the depth of the potential increases. Poles being close repel each
other, and their repulsion is responsible for the changes of the directions of
the corresponding trajectories. The repulsion might cause that certain
resonances become antibound and later resonances again when they collide on the
imaginary axis. The interaction is extremely sensitive to the cut-off radius
value, which is an apparent handicap of the CWS potential.Comment: 5 pages, 3 figure
Antibound poles in cutoff Woods-Saxon and in Salamon-Vertse potentials
The motion of l=0 antibound poles of the S-matrix with varying potential
strength is calculated in a cutoff Woods-Saxon (WS) potential and in the
Salamon-Vertse (SV) potential, which goes to zero smoothly at a finite
distance. The pole position of the antibound states as well as of the
resonances depend on the cutoff radius, especially for higher node numbers. The
starting points (at potential zero) of the pole trajectories correlate well
with the range of the potential. The normalized antibound radial wave functions
on the imaginary k-axis below and above the coalescence point have been found
to be real and imaginary, respectively
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
Modified two-potential approach to tunneling problems
One-body quantum tunneling to continuum is treated via the two-potential
approach, dividing the tunneling potential into external and internal parts. We
show that corrections to this approach can be minimized by taking the
separation radius inside the interval determined by simple expressions. The
resulting two-potential approach reproduces the resonance energy and its width,
both for narrow and wide resonances. We also demonstrate that, without losing
its accuracy, the two-potential approach can be modified to a form resembling
the R-matrix theory, yet without any uncertainties of the latter related to the
choice of the matching radius.Comment: 7 two-column pages, 3 figures, extra-explanation added, Phys. Rev. A,
in pres
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