[en] We propose a procedure based on phase equivalent chains of Darboux transformations to generate local potentials satisfying the radial Schrodinger equation and sharing the same scattering data. For potentials related by a chain of transformations, an analytic expression is derived for the Jost function. It is shown how the same system of S-matrix poles can be differently distributed between poles and zeros of a Jost function that corresponds to different potentials with equal phase shifts. The concept of shallow and deep phase equivalent potentials is analyzed in connection with distinct distributions of poles. It is shown that phase equivalent chains do not violate the Levinson theorem. The method is applied to derive a shallow and a family of deep phase equivalent potentials describing the S-1(0) partial wave of the nucleon-nucleon scattering.
Disciplines :
Physics
Author, co-author :
Samsonov, B. F.
Stancu, Floarea ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Département d'astrophys., géophysique et océanographie (AGO)
Language :
English
Title :
Phase equivalent chains of Darboux transformations in scattering theory
Publication date :
11 September 2002
Journal title :
Physical Review. C, Nuclear Physics
ISSN :
0556-2813
eISSN :
1089-490X
Publisher :
American Physical Soc, College Pk, United States - Maryland
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