The relation between resonances and K-matrix poles for the potential scattering problem is investigated. The analysis is carried out in two stages. We first discuss the analytic properties of a K-matrix related to a model phase-shift which embodies the relevant features of a potential scattering resonance; we then consider the specific case of a square-well potential. The result emerging from the analysis is that to each resonance two poles of the K-matrix are associated; they appear either as a real resonance-echo pair or as a complex conjugate doublet, according to the value of a suitable background parameter. The relevance of this result in connection with the Huby theory is briefly discussed. © 1974 Springer-Verlag.
On the relation between resonances and K-matrix poles
VITTURI, ANDREA;
1974
Abstract
The relation between resonances and K-matrix poles for the potential scattering problem is investigated. The analysis is carried out in two stages. We first discuss the analytic properties of a K-matrix related to a model phase-shift which embodies the relevant features of a potential scattering resonance; we then consider the specific case of a square-well potential. The result emerging from the analysis is that to each resonance two poles of the K-matrix are associated; they appear either as a real resonance-echo pair or as a complex conjugate doublet, according to the value of a suitable background parameter. The relevance of this result in connection with the Huby theory is briefly discussed. © 1974 Springer-Verlag.
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