Complex angular momentum analysis of diffraction scattering in atomic collisions

Connor, J. N. L.; Farrelly, David; Mackay, D.C.

doi:10.1063/1.441533

Cited by 33 publications

(17 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…TheẪ ÂðJ Þ curve decreases almost linearly from 179:7 at J ¼ 0 (and 183:3 at ¼ 0, i.e., J ¼ À1=2) until it reaches a minimum of À24:0 at J r ¼ 25.2. SinceẪ Â 0 ðJ r Þ ¼ 0, this minimum corresponds to a rainbow; however the usual Airy characteristic shape for a rainbow is not present in figure 1 since the scattering is dominated by diffraction (a similar effect is well understood for elastic scattering [45]). .…”

Section: Quantum Deflection Functionmentioning

confidence: 88%

Theory of forward glory scattering for chemical reactions: accuracy of semiclassical approximations using aJ-shifted Eckart parameterization for the scattering matrix element

Xiahou

Connor

2006

Molecular Physics

Self Cite

View full text Add to dashboard Cite

The accuracy of the semiclassical theory of forward glory scattering for a state-to-state chemical reaction is investigated using a J-shifted Eckart parameterization for the scattering matrix element. The parameters are chosen initially to model the angular scattering of the H þ D 2 ! HD(v f ¼ 3) þ D reaction, following D. Sokolovski (Chem. Phys. Lett., 370, 805 (2003)). Then the parameters are systematically varied to generate different scattering patterns. The theory assumes that the scattering amplitude can be expanded in a Legendre partial wave series (PWS). The theoretical techniques applied to the PWS include: a nearsidefarside decomposition, and a local angular momentum (LAM) analysis; both techniques include resummations of the PWS. The semiclassical techniques used include: a uniform semiclassical approximation (USA), a primitive semiclassical approximation, a classical semiclassical approximation, an integral transitional approximation, a semiclassical transitional approximation and a semiclassical LAM. The LAM for the classical collision of two hard spheres is also employed. It is demonstrated that the USA can accurately describe glory oscillations for scattering angles on and near the forward direction (as defined by the axial caustic associated with the glory); in favourable cases the USA is accurate for sideward scattering angles and even for angles close to the backward direction.

show abstract

Section: Quantum Deflection Functionmentioning

confidence: 88%

Theory of forward glory scattering for chemical reactions: accuracy of semiclassical approximations using aJ-shifted Eckart parameterization for the scattering matrix element

Xiahou

Connor

2006

Molecular Physics

Self Cite

View full text Add to dashboard Cite

show abstract

“…If there is Airy-type rainbow in the DCS, then we also expect Re J 0 ≈ J r , where J r is the rainbow angular momentum variable, which separates the bright and dark sides of the rainbow. 5,22,23,27,55,56 The imaginary part of J 0 is related to the life-angle (written 0 θ R ) by 0 θ R = 1/ (2ImJ 0 ); it controls the decay of a surface (or creeping) wave which propagates around the interaction zone. Note that the life-angle can be very small (short-lived or direct scattering), or very large (for long-lived collisions), as well as taking any value in between.…”

Section: Important Properties Of Cam Scattering Theoriesmentioning

confidence: 99%

Resonance Regge poles and the state-to-state F + H2 reaction: QP decomposition, parametrized S matrix, and semiclassical complex angular momentum analysis of the angular scattering

Connor

2013

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

Three new contributions to the complex angular momentum (CAM) theory of differential cross sections (DCSs) for chemical reactions are reported. They exploit recent advances in the Padé reconstruction of a scattering (S) matrix in a region surrounding the ReJ axis, where J is the total angular momentum quantum variable, starting from the discrete values, J = 0, 1, 2, .... In particular, use is made of Padé continuations obtained by Sokolovski, Castillo, and Tully [Chem. Phys. Lett. 313, 225 (1999)] for the S matrix of the benchmark F + H2(v(i) = 0, j(i) = 0, m(i) = 0) → FH(v(f) = 3, j(f) = 3, m(f) = 0) + H reaction. Here v(i), j(i), m(i) and v(f), j(f), m(f) are the initial and final vibrational, rotational, and helicity quantum numbers, respectively. The three contributions are: (1) A new exact decomposition of the partial wave (PW) S matrix is introduced, which is called the QP decomposition. The P part contains information on the Regge poles. The Q part is then constructed exactly by subtracting a rapidly oscillating phase and the PW P matrix from the input PW S matrix. After a simple modification, it is found that the corresponding scattering subamplitudes provide insight into the angular-scattering dynamics using simple partial wave series (PWS) computations. It is shown that the leading n = 0 Regge pole contributes to the small-angle scattering in the centre-of-mass frame. (2) The Q matrix part of the QP decomposition has simpler properties than the input S matrix. This fact is exploited to deduce a parametrized (analytic) formula for the PW S matrix in which all terms have a direct physical interpretation. This is a long sort-after goal in reaction dynamics, and in particular for the state-to-state F + H2 reaction. (3) The first definitive test is reported for the accuracy of a uniform semiclassical (asymptotic) CAM theory for a DCS based on the Watson transformation. The parametrized S matrix obtained in contribution (2) is used in both the PW and semiclassical parts of the calculation. Powerful uniform asymptotic approximations are employed for the background integral; they allow for the proximity of a Regge pole and a saddle point. The CAM DCS agrees well with the PWS DCS, across the whole angular range, except close to the forward and backward directions, where, as expected, the CAM theory becomes non-uniform. At small angles, θ(R) ≲ 40°, the PWS DCS can be reproduced using a nearside semiclassical subamplitude, which allows for a pole being close to a saddle point, plus the farside surface wave of the n = 0 pole sub-subamplitude, with the oscillations in the DCS arising from nearside-farside interference. This proves that the n = 0 Regge resonance pole contributes to the small-angle scattering.

show abstract

“…9c the integral term in eqn (6) (shown by a dot-dashed line). The dot-dashed curve also contains the cusp, which must, therefore, be attributed to the background term s back in eqn (6). In ref.…”

Section: The Near-threshold Range: Resonances B C D and Ementioning

confidence: 99%

“…42 The approximant analytically continues the S matrix element into the complex J-plane, and correctly represents it in the vicinity of the integral J values used in its construction. For resonance poles sufficiently close to the real J-axis we can, therefore, evaluate all relevant quantities in eqn (3)- (6). The poles further away from the real axis may not be represented correctly.…”

Section: Regge Pole Decomposition Of An Integral Cross Sectionmentioning

confidence: 99%

Complex angular momentum theory of state-to-state integral cross sections: resonance effects in the F + HD → HF(v′ = 3) + D reaction

Sokolovski

Akhmatskaya

Echeverría‐Arrondo

et al. 2015

Phys. Chem. Chem. Phys.

View full text Add to dashboard Cite

State-to-state reactive integral cross sections (ICSs) are often affected by quantum mechanical resonances, especially near a reactive threshold. An ICS is usually obtained by summing partial waves at a given value of energy. For this reason, the knowledge of pole positions and residues in the complex energy plane is not sufficient for a quantitative description of the patterns produced by resonance. Such description is available in terms of the poles of an S-matrix element in the complex plane of the total angular momentum. The approach was recently implemented in a computer code ICS_Regge, available in the public domain [Comput. Phys. Commun., 2014, 185, 2127. In this paper, we employ the ICS_Regge package to analyse in detail, for the first time, the resonance patterns predicted for integral cross sections

show abstract

Complex angular momentum analysis of diffraction scattering in atomic collisions

Cited by 33 publications

References 39 publications

Theory of forward glory scattering for chemical reactions: accuracy of semiclassical approximations using aJ-shifted Eckart parameterization for the scattering matrix element

Theory of forward glory scattering for chemical reactions: accuracy of semiclassical approximations using aJ-shifted Eckart parameterization for the scattering matrix element

Resonance Regge poles and the state-to-state F + H2 reaction: QP decomposition, parametrized S matrix, and semiclassical complex angular momentum analysis of the angular scattering

Complex angular momentum theory of state-to-state integral cross sections: resonance effects in the F + HD → HF(v′ = 3) + D reaction

Contact Info

Product

Resources

About