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Role of resonances in building cross sections : Comparison between the Mittag-Leffler and the T-matrix green function expansion approaches. / Shilyaeva, Ksenia; Elander, Nils; Yarevsky, Evgeny.

In: International Journal of Quantum Chemistry, Vol. 107, No. 6, 01.05.2007, p. 1301-1315.

Research output: Contribution to journal › Article › peer-review

Harvard

Shilyaeva, K, Elander, N & Yarevsky, E 2007, 'Role of resonances in building cross sections: Comparison between the Mittag-Leffler and the T-matrix green function expansion approaches', International Journal of Quantum Chemistry, vol. 107, no. 6, pp. 1301-1315. https://doi.org/10.1002/qua.21257

APA

Shilyaeva, K., Elander, N., & Yarevsky, E. (2007). Role of resonances in building cross sections: Comparison between the Mittag-Leffler and the T-matrix green function expansion approaches. International Journal of Quantum Chemistry, 107(6), 1301-1315. https://doi.org/10.1002/qua.21257

Vancouver

Shilyaeva K, Elander N, Yarevsky E. Role of resonances in building cross sections: Comparison between the Mittag-Leffler and the T-matrix green function expansion approaches. International Journal of Quantum Chemistry. 2007 May 1;107(6):1301-1315. https://doi.org/10.1002/qua.21257

Author

Shilyaeva, Ksenia ; Elander, Nils ; Yarevsky, Evgeny. / Role of resonances in building cross sections : Comparison between the Mittag-Leffler and the T-matrix green function expansion approaches. In: International Journal of Quantum Chemistry. 2007 ; Vol. 107, No. 6. pp. 1301-1315.

BibTeX

@article{524bc050f1f544fb8f9b16a87f7bb127,
title = "Role of resonances in building cross sections: Comparison between the Mittag-Leffler and the T-matrix green function expansion approaches",
abstract = "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.",
keywords = "Complex dilation, Cross section, Green function, S-matrix expansion, Scattering theory",
author = "Ksenia Shilyaeva and Nils Elander and Evgeny Yarevsky",
year = "2007",
month = may,
day = "1",
doi = "10.1002/qua.21257",
language = "English",
volume = "107",
pages = "1301--1315",
journal = "International Journal of Quantum Chemistry",
issn = "0020-7608",
publisher = "Wiley-Blackwell",
number = "6",

}

RIS

TY - JOUR

T1 - Role of resonances in building cross sections

T2 - Comparison between the Mittag-Leffler and the T-matrix green function expansion approaches

AU - Shilyaeva, Ksenia

AU - Elander, Nils

AU - Yarevsky, Evgeny

PY - 2007/5/1

Y1 - 2007/5/1

N2 - 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.

AB - 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.

KW - Complex dilation

KW - Cross section

KW - Green function

KW - S-matrix expansion

KW - Scattering theory

UR - http://www.scopus.com/inward/record.url?scp=33947575147&partnerID=8YFLogxK

U2 - 10.1002/qua.21257

DO - 10.1002/qua.21257

M3 - Article

AN - SCOPUS:33947575147

VL - 107

SP - 1301

EP - 1315

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

IS - 6

ER -

ID: 36536670