Numerical Regge pole analysis of resonance structures in elastic, inelastic and reactive state-to-state integral cross sections

We present a detailed description of a FORTRAN code for evaluation of the resonance contribution a Regge trajectory makes to the integral state-to-state cross section (ICS) within a specified range of energies. The contribution is evaluated with the help of the Mulholland formula (Macek et al., 2004) and its variants (Sokolovski et al., 2007; Sokolovski and Akhmatskaya, 2011). Regge pole positions and residues are obtained by analytically continuing S-matrix element, evaluated numerically for the physical values of the total angular momentum, into the complex angular momentum plane using the PADE-II program (Sokolovski et al., 2011). The code decomposes an elastic, inelastic, or reactive ICS into a structured, resonance, and a smooth, 'direct', components, and attributes observed resonance structure to resonance Regge trajectories. The package has been successfully tested on various models, as well as the F+H 2‚ÜíHF+H benchmark reaction. Several detailed examples are given in the text

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

State-to-state reactive integral cross sections (ICSs) are often affected by quantum mechanical resonances, especially near a reactive threshold. An ICS is usually obtained by summing partial waves at a given value of energy. For this reason, the knowledge of pole positions and residues in the complex energy plane is not sufficient for a quantitative description of the patterns produced by resonance. Such description is available in terms of the poles of an S-matrix element in the complex plane of the total angular momentum. The approach was recently implemented in a computer code, available in the public domain [Comput. Phys. Commun., 2014, 185, 2127]. In this paper, we employ the package to analyse in detail, for the first time, the resonance patterns predicted for integral cross sections (ICSs) of the benchmark F + HD → HF(v′ = 3) + D reaction. The v = 0, j = 0, Ω = 0 → v′ = 3, j′ = 0, 1, 2, and Ω′ = 0, 1, 2 transitions are studied for collision energies from 58.54 to 197.54 meV. For these energies, we find several resonances, whose contributions to the ICS vary from symmetric and asymmetric Fano shapes to smooth sinusoidal Regge oscillations. Complex energies of metastable states and Regge pole positions and residues are found by Padé reconstruction of the scattering matrix elements. The accuracy of the code, relation between complex energies and Regge poles, various types of Regge trajectories, and the origin of the J-shifting approximation are also discussed

Computer software for understanding resonances and resonance-related phenomena in chemical reactions

In numerical modelling of chemical reactions one calculates the scattering matrix for the required values of energy and angular momentum. Having done so, one still faces the non-trivial task of extracting detailed information about the reaction mechanism. We discuss the methods and numerical tools for such an analysis in terms of resonance poles and semiclassical trajectories. Our approach avoids calculating the scattering matrix in semiclassical approximation, and employs its numerical values computed previously by an accurate scattering code

Laboratory directed research and development. FY 1995 progress report

This document presents an overview of Laboratory Directed Research and Development Programs at Los Alamos. The nine technical disciplines in which research is described include materials, engineering and base technologies, plasma, fluids, and particle beams, chemistry, mathematics and computational science, atmic and molecular physics, geoscience, space science, and astrophysics, nuclear and particle physics, and biosciences. Brief descriptions are provided in the above programs