Charge-overlap effect on the electronic transitions in moderate-energy collisions between closed-shell particles with rare-gas structure

Int J of Quantum Chemistry

Yarevsky

2006

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.

Section: Introductionmentioning

confidence: 99%

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

Shilyaeva

Int J of Quantum Chemistry

Yarevsky

2006

“…The group lead by Shimakura, studied several charge-transfer reactions with the initial channel N 5+ + H (see Refs. [22,23,24,25]) while Bacchys-Montabonel and Ceyzeriat [26] did calculations for the ion-atom collision Si 4+ + He. Both groups predicted resonances in these reactions.…”

Section: Introductionmentioning

confidence: 99%

Analyzing the contribution of individual resonance poles of the S‐matrix to two‐channel scattering

Rakityansky

Int J of Quantum Chemistry

2005

ABSTRACT:A two-channel problem is considered within a method based on firstorder differential equations that are equivalent to the corresponding Schrödinger equation but more convenient for dealing with resonant phenomena. Using these equations, it is possible to calculate directly the Jost matrix for practically any complex value of the energy. The spectral points (bound and resonant states) can therefore be located in a rigorous way, namely, as zeros of the Jost matrix determinant. When calculating the Jost matrix, the differential equations are solved and thus, at the same time, the wave function is obtained with the correct asymptotic behavior analytically embedded in the solution. The method offers a very accurate way of calculating not only total widths of resonances but their partial widths as well. For each pole of the S-matrix, its residue can be calculated rather accurately, which makes it possible to obtain the Mittag-Leffler-type expansion of the Smatrix as a sum of the singular terms (representing the resonances) and the background term (contour integral). As an example, the two-channel model by Noro and Taylor is considered. It is demonstrated how the contributions of individual resonance poles to the scattering cross section can be analyzed using the Mittag-Leffler expansion and the Argand plot technique. This example shows that even poles situated far away from the physical real axis may make significant contributions to the cross section.

“…Here W = {A, B} is the Wronskian of the matrices A and B while ϕ and f ± describe regular and Jost solution matrices respectively. They are based on (6) and arranged in the same way as Ψ in (9).…”

Section: Complex Scaling Emphasizing the Analytic Continuation Of The...mentioning

confidence: 99%

“…The group led by Shimakura studied several chargetransfer reactions with the initial channel N 5+ + H (see [5][6][7][8]) while Bacchys-Montabonel and Ceyzeriat [9] did calculations for the ion-atom collision Si 4+ + He. Both groups predicted resonances in these reactions.…”

Section: Introductionmentioning

confidence: 99%

Identifying resonance structures in a scattering cross section using the N³⁺+ H → NH³⁺→ N²⁺+ H⁺reaction as an example

Shilyaeva

Yarevsky

J. Phys. B: At. Mol. Opt. Phys.

2009

The many-channel partial wave S-matrix is shown to have a meromorphic continuation into the fourth quadrant of the complex momentum plane. This allows one to expand this S-matrix in terms of its poles, inside a contour, and an integral along this contour. The contribution of a resonance is defined in terms of the corresponding residue. A reduced partial wave S-matrix as well as a reduced partial wave cross section are defined and used to identify if a given structure in a cross section can be associated with an S-matrix pole. The theory presented contains both short-range and Coulomb interactions. The formalism is applied to a realistic two-channel model of a charge transfer process.