Theory of forward glory scattering for chemical reactions: accuracy of semiclassical approximations using a<b><i>J</i></b>-shifted Eckart parameterization for the scattering matrix element

Xiahou, Chengkui; Connor, J. N. L.

doi:10.1080/00268970500314159

Cited by 30 publications

(85 citation statements)

References 42 publications

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“…Section III describes the theory of the QP decomposition for the S matrix and the scattering amplitude, and makes an application to the F + H 2 reaction using quantum numerical S matrix elements. 6 The techniques of nearside-farside (NF) decomposition 8,18,19,22,23, and Local Angular Momentum (LAM) analysis 22,23,31,34,[36][37][38][39][40][41][42][43][45][46][47][48] for resummed Legendre PWS 22,23,30,31,36,38,[42][43][44][45][46][47] are also employed in Sec. III.…”

Section: Uniform Semiclassical Cam Theory Of Angular Scatteringmentioning

confidence: 99%

“…(31)- (34), the args are, in general, not principal values in order that the derivatives be well defined. The Qmod and Pmod PWS subamplitudes (19) and (20) can also be resummed if desired 22,23,30,31,36,38,[42][43][44][45][46][47] before making the NF decompositions, since it is known this helps "clean" the N and F un-resummed DCSs and LAMs of unphysical structure. The resummation equations have been described in detail by Totenhofer et al; 42 they are easily adapted to Eqs.…”

Section: Qp Decomposition Of the Scattering Amplitude And Its Modimentioning

confidence: 99%

“…(36) and (37), we obtain the result (39) where the N,F sub-subamplitudes are given by Eq. (26) and (28).…”

Section: E Nearside-farside Decomposition Of the Full Scattering Ampmentioning

confidence: 99%

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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

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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.

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Section: Uniform Semiclassical Cam Theory Of Angular Scatteringmentioning

confidence: 99%

Section: Qp Decomposition Of the Scattering Amplitude And Its Modimentioning

confidence: 99%

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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

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“…11, 12, 17-20, 22, 24 The purpose of this paper is to apply semiclassical (SC), i.e., asymptotic (¯→ 0), techniques to the T-domain scattering amplitude in order to provide physical insight into the forward scattering of the delayed mechanism. We prove that the forward scattering is an example of a glory; we do this by applying SC methods developed earlier for the E-domain, 7,[25][26][27][28][29][30] to the T-domain. Our work is the first application of (uniform) SC techniques to the PWP formalism and the first discovery of a glory in the T-domain.…”

Section: Introductionmentioning

confidence: 99%

“…In this section, we shall present an example for the H + D 2 reaction, where the direct E-domain SC glory theory 7,[25][26][27][28][29][30] fails at E = 1.82 eV, yet by following the solid blue path in Fig. 1 and carrying out a SC glory analysis in the T-domain, we can obtain an improved description of the glory scattering in the E-domain.…”

Section: A Introductionmentioning

confidence: 99%

Semiclassical glory analyses in the time domain for the H + D2(vi = 0, ji = 0) → HD(vf = 3, jf = 0) + D reaction

Xiao

Connor

2012

The Journal of Chemical Physics

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We make the first application of semiclassical (SC) techniques to the plane-wavepacket formulation of time-domain (T-domain) scattering. The angular scattering of the state-to-state reaction, H + D(2)(v(i) = 0, j(i) = 0) → HD(v(f) = 3, j(f) = 0) + D, is analysed, where v and j are vibrational and rotational quantum numbers, respectively. It is proved that the forward-angle scattering in the T-domain, which arises from a delayed mechanism, is an example of a glory. The SC techniques used in the T-domain are: An integral transitional approximation, a semiclassical transitional approximation, a uniform semiclassical approximation (USA), a primitive semiclassical approximation and a classical semiclassical approximation. Nearside-farside (NF) scattering theory is also employed, both partial wave and SC, since a NF analysis provides valuable insights into oscillatory structures present in the full scattering pattern. In addition, we incorporate techniques into the SC theory called "one linear fit" and "two linear fits", which allow the derivative of the quantum deflection function, Θ̃(')(J), to be estimated when Θ̃J exhibits undulations as a function of J, the total angular momentum variable. The input to our SC analyses is numerical scattering (S) matrix data, calculated from accurate quantum collisional calculations for the Boothroyd-Keogh-Martin-Peterson potential energy surface No. 2, in the energy domain (E-domain), from which accurate S matrix elements in the T-domain are generated. In the E-domain, we introduce a new technique, called "T-to-E domain SC analysis." It half-Fourier transforms the E-domain accurate quantum scattering amplitude to the T-domain, where we carry out a SC analysis; this is followed by an inverse half-Fourier transform of the T-domain SC scattering amplitude back to the E-domain. We demonstrate that T-to-E USA differential cross sections (DCSs) agree well with exact quantum DCSs at forward angles, for energies where a direct USA analysis in the E-domain fails.

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Time-dependent wave packet state-to-state quantum dynamics study of the abstraction reaction S(3P)+H2(v=0, j=0) on 13A″ electronic state

Liang

Zhang

2015

Chemical Physics

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

Cited by 30 publications

References 42 publications

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

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

Semiclassical glory analyses in the time domain for the H + D2(vi = 0, ji = 0) → HD(vf = 3, jf = 0) + D reaction

Time-dependent wave packet state-to-state quantum dynamics study of the abstraction reaction S(3P)+H2(v=0, j=0) on 13A″ electronic state

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