Complex angular momentum analysis of resonance scattering in the Cl+HCl→ClH+Cl reaction

Abstract

Resonance effects in the differential cross sections of the Cl+HCl(v,j)→ClH(v′,j′)+Cl reaction are analyzed using Regge pole and complex angular momentum (CAM) techniques. This is the first detailed application of CAM theory to reactive molecular scattering. The rovibrational transitions studied are v=1, j=5→v′=0, j′=15, and v=1, j=5→v′=1, j′=5 at total energies E=0.66, 0.68, 0.70 eV. The CAM theory expresses the scattering amplitude as a background subamplitude plus a pole subamplitude. The uniform (and nonuniform) semiclassical evaluation of the background subamplitude is discussed. It is necessary to include explicitly the resonance Regge pole in the semiclassical theory because it has a small imaginary part. We derive a new generic semiclassical formula, involving the complementary error function for the resonance angular scattering. The position and residue of the resonance Regge pole at each E are extracted numerically from scattering matrix elements calculated by the centrifugal sudden hyperspherical (CSH) quantum scattering method. There is good agreement between the semiclassical CAM and CSH angular distributions. However, the latter involve summing a partial wave (PW) series with a large number of numerically significant terms—as a result the PW computations provide no physical insight. We also show that a simple semiclassical optical model becomes inaccurate when the rotational period of the ClHCl complex is comparable to the resonance lifetime. We derive a new ‘‘sticky’’ optical model which allows for rotation of the complex. All our calculations use the Bondi–Connor–Manz–Römelt semiempirical potential energy surface.

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

“…We then fit the pole position by a linear function of L = J( J + 1), thus obtaining the values for coefficients A 1,2 and B 1,2 in eqn (12). These values are inserted into eqn (13), and the approximate Regge trajectory for pole A is drawn. This trajectory is then compared with the exact Regge trajectory obtained independently by the Padé reconstruction of the S-matrix element in the energy range of interest.…”

Analysis of Regge poles for the Schrödinger equation

“…In recent times, there has been renewed interest in Regge theory, no doubt owing to the rise in the development of disciplines such as reactive molecular collisions (Connor et al 1981;Connor 1990;Sokolovski et al 1995) and particle physics, and in particular, the theory of resonance angular scattering (Sokolovski et al 2007). The theoretical aspects of low-energy electron elastic scattering are best studied using Regge poles, particularly in gaining an understanding of the formation of temporary anion states during electron attachment, which is fundamental to the physical mechanism by which the scattering process deposits *Author for correspondence (hiscoxaj@cf.ac.uk).…”

Nearside—farside theory of elastic angular scattering for strongly absorptive collisions

“…It is important to realize that both the N subamplitude (FyL-)(0) and the F subamplitude (F)f,,)(0) depend on m, although their sum, f ( O ) , does not. An examination of equations (6) and (8) reveals that the m dependence comes from the series 00 (1 -cos e)-" xa(")Ql(cos 0), m = 0,1,2,. . .…”

“…. , (8) and the superscript (F) indicates that the Fuller N F decomposition is being used. It is important to realize that both the N subamplitude (FyL-)(0) and the F subamplitude (F)f,,)(0) depend on m, although their sum, f ( O ) , does not.…”

“…If we carry out the (")NF/YRW(m) procedure using equations (5), (6) and (9), we obtain Comparing equations (7) and (8) with equations (10) and (1 1) shows that m = 0, 1 \ 2 , . .…”