Tools for Assigning Resonance Structures in Collisions of Few-Body Quantum Systems

Elander, Nils; Shilyaeva, Ksenia; Ostrovsky, V N; Yarevsky, E. A.; Rakityanski, Sergey

doi:10.1007/s00601-005-0144-9

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2006

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“…These two approaches as well as the Siegert pseudo‐state method 49–51 make it possible to express the local influence of a resonance on a cross section, through the S‐matrix as a S‐matrix residue [see Eqs. (10) and (17)].…”

Section: Resultsmentioning

confidence: 99%

Role of resonances in building cross sections: Comparison between the Mittag–Leffler and the T‐matrix Green function expansion approaches

Shilyaeva

Elander

Yarevsky

2006

Int J of Quantum Chemistry

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Peaks in collision cross sections are often interpreted as resonances.The complex dilation method, as well as other methods relying on analytic continuation of the scattering formalism, can be used to clarify whether these structures are true resonances in the sense that they are poles of the S-matrix and the associated Green function. The performance of the Mittag-Leffler expansion and T-matrix Green function expansion methods are formally and computationally compared. The two methods are applied to two model potentials. Eigenenergies, s-wave residues, and cross sections are computed with both methods. The resonance contributions to the cross sections are further analyzed by removing the residue contributions from the Mittag-Leffler and Green function expansion sums, respectively. It is suggested that the contribution of a resonance to a cross section should be defined through its S-matrix residue.

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Section: Resultsmentioning

confidence: 99%