Integral cross section, reactive scattering theory

The last few years have seen dramatic advances in the rigorous theoretical description of elementary chemical reactions, i.e. in exact quantum mechanical reactive scattering calculations [1 6]. These theoretical developments are especially timely because of parallel advances in experimental studies of elementary reactions [7-12]. Several groups have reported new studies of the H+H2, D+H2, and H-1-D2 reactions, and this makes possible comparisons of unprecedented detail between theory and experiment. Most intriguing are the integral cross section results of Nieh and Valentini [10, 11] for the reaction... 

Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D+H2 — H2/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. 

In the next section (Sec. 2), we will develop the theory of the BCRLM. We discuss the solution of the coupled-channel equations in both natural collision coordinates " and hyperspherical coordinates. " Both coordinate systems are widely used to treat collinear reactive scattering processes. We will discuss the projection " of the hyperspherical equations on coordinate surfaces appropriate for applying scattering boundary conditions and review the definition of integral and differential scattering cross sections in this model. 

---