Abstract
Several aspects involved in the theoretical formulation and the practical calculation of reactive cross sections, for atom-diatom systems, are reviewed and discussed, focusing on the time-independent hyperspherical-propagative approach. The general trends of the formalism, that allows a complete scattering calculation for a reactive process, is presented first. Then, the discussion is divided into four additional parts. The first one briefly discusses the coordinate and reference frame problem, showing how the democratic version of the hyperspherical coordinates provides a solution for the cumbersome transition between rearrangement channels. The second part deals with the details of the systematic expansion of the nuclear wavefunction, on a conveniently chosen basis set for the internal (angular) coordinates, performed at fixed values of the remaining (scattering or hyperradial) coordinate. The third part deals with the approach to solving the resulting set of coupled second-order differential equations, the propagative method, which obtains (the logarithmic derivative transform of) the hyperradial solution for a number of increasing discrete values of the hyperradial independent variable. Finally, the fourth part discusses the extraction of the asymptotic information and the calculation for reaction probabilities and integral cross sections. Some examples illustrate each stage into which the calculation process is divided.
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Bolloni, A., Huarte-Larrañaga, F., Gimenez, X. (2000). The exact Computation of Reactive Cross Sections for Atom-Diatom Systems. The Hyperspherical Propagative Approach. In: Laganà, A., Riganelli, A. (eds) Reaction and Molecular Dynamics. Lecture Notes in Chemistry, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57051-3_16
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DOI: https://doi.org/10.1007/978-3-642-57051-3_16
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