Calculating broad neutron resonances in a cut-off Woods-Saxon potential

Abstract

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.

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

“…The distributions of the complex poles can be visualized if we plot the landscape of the function −F (k) defined in Ref. [15] on the same domain of the complex k-plane as we considered in Fig. 1.…”

“…It was observed in Ref. [15] that close lying resonances interact with each other, therefore we analyze the first mountain only when the other one is far enough not to interact with the resonances of the first mountain.…”

“…Refs. [13], [14], [15], let us sketch briefly how the pole solutions of the radial equation are calculated numerically. We introduce left and right solutions of the radial equation in Eq.…”

Matching polynomial tails to the cut-off Woods–Saxon potential

“…Naturally, the accuracy of the estimated distance might be influenced by the nonlinearity of the polynomial in (14). Nonlinearities can be caused by the interaction of the close lying poles 8 and by the accuracy of the calculated k m values.…”

“…Gamow shell model (GSM) 1 became a useful tool in analyzing drip line nuclei produced in laboratories with radioactive beam facilities. A most recent analysis of this type is that of the 7 Be(p,γ) 8 B and the 7 Li(n,γ) 8 Li reactions in Ref. 2 The key elements of GSM are the Berggren-ensembles of single particle states.…”