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.