Local angular momentum–local impact parameter analysis: Derivation and properties of the fundamental identity, with applications to the F+H2, H+D2, and Cl+HCl chemical reactions

Abstract

The technique of local angular momentum-local impact parameter (LAM-LIP) analysis has recently been shown to provide valuable dynamical information on the angular scattering of chemical reactions under semiclassical conditions. The LAM-LIP technique exploits a nearside-farside (NF) decomposition of the scattering amplitude, which is assumed to be a Legendre partial wave series. In this paper, we derive the "fundamental NF LAM identity," which relates the full LAM to the NF LAMs (there is a similar identity for the LIP case). Two derivations are presented. The first uses complex variable techniques, while the second exploits an analogy between the motion of the scattering amplitude in the Argand plane with changing angle and the classical mechanical motion of a particle in a plane with changing time. Alternative forms of the fundamental LAM-LIP identity are described, one of which gives rise to a CLAM-CLIP plot, where CLAM denotes (Cross section) x LAM and CLIP denotes (Cross section) x LIP. Applications of the NF LAM theory, together with CLAM plots, are reported for state-to-state transitions of the benchmark reactions F+H2-->FH+H, H+D2-->HD+D, and Cl+HCl-->ClH+Cl, using as input both numerical and parametrized scattering matrix elements. We use the fundamental LAM identity to explain the important empirical observation that a NF cross section analysis and a NF LAM analysis provide consistent (and complementary) information on the dynamics of chemical reactions.

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

“…It is analogous to the fundamental identity 37 for NF DCSs. Thus if we plot σ (θ R ), σ (Q) (θ R ), and σ (P) (θ R ) versus θ R we can obtain information on the origin of interference effects in the full DCS.…”

“…(67) and (68) to test the physical effectiveness of the PWS NF decomposition as given by Eqs. (35)- (37) in Sec. III E. The DCSs for the subamplitudes and sub-subamplitudes introduced in this section are defined, as usual, as the modulus squared of the corresponding f • • (θ R ).…”

“…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.…”

“…8,37,41,42 r The parametrization (42) forQ param J can be generalized using polynomials of higher degree in the phase, the pre-exponential factor, or in the argument of the exponential function.…”

Nearside-Farside Analysis of the Angular Scattering for the State-to-State H + HD → H2 + D Reaction: Nonzero Helicities

“…The corresponding N and F DCSs are given by With the help of eqs 2 and ( 8 ), we obtain Equation 9 is the Fundamental Identity for Full and NF DCSs and is exact. 25 …”