Application of the Partial Wave QP Decomposition to the Angular Scattering of the State-to-State F + H₂ Reaction at E_trans = 0.04088 eV

Abstract

We analyze the physical content of structures present in the product differential cross sections (DCSs) of the benchmark F + H 2 (v i , j i , m i ) → FH(v f , j f , m f ) + H reaction, where v, j, and m are the vibrational, rotational, and helicity quantum numbers, respectively, for the initial and final states. We analyze three state-to-state transitions: 000 → 300, 000 → 310, and 000 → 320. Accurate quantum S matrix elements are employed at a translational energy of 0.04088 eV for the Fu−Xu−Zhang potential energy surface. Our analysis of the DCSs uses a new technique called the QP decomposition; it makes an exact decomposition of the scattering (S) matrix into a Q part and a P part. The P part consists of a partial wave (PW) sum of Regge poles (involving both positions and residues) together with a rapidly oscillating quadratic phase. The Q part of the decomposition is then constructed exactly by subtracting the rapidly oscillating phase and the PW Regge pole sum from the input PW S matrix. In practice, it is convenient to make a small modification, which we call the QmodPmod decomposition. All our calculations use only integer values of the total angular momentum quantum number, namely, J = 0, 1, 2,... We find that the QmodPmod decomposition is successful and physically meaningful, in that the properties of Qmod matrix are simpler than those of the input S matrix. We then carry out a QmodPmod analysis of the DCSs, which provides novel insights into interference structures present in the angular scattering. In particular, we find for all three reactions that Regge resonances contribute across the whole angular range of the DCSs, being particularly pronounced at small angles. The techniques of nearside−farside decomposition and local angular momentum analysis for resummed Legendre PW series are also employed to provide additional insights into the angular scattering.

A single resonance Regge pole dominates the forward-angle scattering of the state-to-state F + H2 → FH + H reaction at Etrans = 62.09 meV

“…It is known, from many TRI pole computations, 60,[67][68][69][70]83,84,91,92,[99][100][101][102] that an elliptical curve approximately separates the stable and unstable regions. The greendashed ellipses in Fig.…”

Numerical Regge pole analysis of resonance structures in state-to-state reactive differential cross sections

“…Some applications of the poles to the angular scattering and integral cross sections are discussed in Refs. [17]- [50]. For a description of the type-II Padé approximation, used by the software, the reader is referred to Refs.…”