Distributions of the SS-matrix poles in Woods-Saxon and cut-off Woods-Saxon potentials

The positions of the $l=0$ $S$-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 $S$-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