Global method for all S-matrix poles identification new classes of poles and resonant states
A global method to identify all the S-matrix poles k = k l ( g) in the k-plane for a central potential gV( r) ( g ϵ C ) is presented. The method involves construction of the Riemann surface R g ( l) over the g-plane, on which the function k = k l ( g) is single valued and analytic. It implies the di...
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Published in | Annals of physics Vol. 218; no. 2; pp. 346 - 383 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Amsterdam
Elsevier Inc
01.09.1992
Elsevier |
Subjects | |
Online Access | Get full text |
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Summary: | A global method to identify all the
S-matrix poles
k =
k
l
(
g) in the
k-plane for a central potential
gV(
r) (
g ϵ
C
) is presented. The method involves construction of the Riemann surface
R
g
(
l)
over the
g-plane, on which the function
k =
k
l
(
g) is single valued and analytic. It implies the division of the Riemann surface
R
g
(
l)
into
Σ
n
(
l)
sheets and the construction of the sheet images
Σ′
n
(
l)
in the
k-plane. The method is first applied to potentials having Jost entire functions in both variables
g and
k. In this case the general properties of the function
k =
k
l
(
g) and of its Riemann surface
R
g
(
l)
are obtained. The method is then extended to other classes of potentials. The construction of the Riemann surface
R
g
(
l)
as well as the construction of the images of its sheets in the
k-plane for some particular potentials is given in detail. The method is allowed to identify new classes of resonant state poles. These poles remain in a neighborhood of some special points called “stable-points” as the strength of the potential increases to infinity; i.e., these resonant state poles do not become bound or virtual state poles. Moreover, the wave functions of the resonant states corresponding to the new-class poles situated in the neighborhood of the stable-points are almost completely localized outside the potential well. The method provides a quantum number
n, characterizing the bound and resonant state
S-matrix poles. This quantum number has a topological significance: it is the label of the sheets of the Riemann surface
R
g
(
l)
. The existence of new classes of resonant state poles seems to be a general property of the potentials with barriers used in nuclear scattering theory. |
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ISSN: | 0003-4916 1096-035X |
DOI: | 10.1016/0003-4916(92)90091-Y |