R-matrix explained

The term R-matrix has several meanings, depending on the field of study.

C [S _{n]} of the symmetric group in the work of A. A. Jucys in 1966.^[3]

The classical R-matrix arises in the definition of the classical Yang - Baxter equation.^[4]

In quasitriangular Hopf algebra, the R-matrix is a solution of the Yang - Baxter equation.

The numerical modeling of diffraction gratings in optical science can be performed using the R-matrix propagation algorithm.^[5]

R-matrix method in quantum mechanics

There is a method in computational quantum mechanics for studying scattering known as the R-matrix. This method was originally formulated for studying resonances in nuclear scattering by Wigner and Eisenbud.^[6] Using that work as a basis, an R-matrix method was developed for electron, positron and photon scattering by atoms.^[7] This approach was later adapted for electron, positron and photon scattering by molecules.^{[8] [9] [10]}

R-matrix method is used in UKRmol^[11] and UKRmol+^[12] code suits. The user-friendly software Quantemol Electron Collisions (Quantemol-EC) and its predecessor Quantemol-N are based on UKRmol/UKRmol+ and employ MOLPRO package for electron configuration calculations.

See also

• UK Molecular R-matrix Codes

Notes and References

1. McGuire . J. B. . Study of Exactly Soluble One‐Dimensional N‐Body Problems . Journal of Mathematical Physics . The American Institute of Physics (AIP) . 5 . 5 . 1964-05-01 . 0022-2488 . 10.1063/1.1704156 . 622-636 . 1964JMP.....5..622M .
2. Yang . C. N. . Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction . Physical Review Letters . American Physical Society (APS) . 19 . 23 . 1967-12-04 . 0031-9007 . 10.1103/PhysRevLett.19.1312 . 1312-1315 . 1967PhRvL..19.1312Y .
3. Jucys . A. A. . On the Young operators of the symmetric group . Lietuvos Fizikos Rinkinys . Gos. Izd-vo Polit. i Nauch. literatury. . 11 . 23 . 1966 . 163-180 .
4. Kupershmidt . Boris A. . What a Classical r-Matrix Really Is . Journal of Nonlinear Mathematical Physics . Informa UK Limited . 6 . 4 . 1999 . 1402-9251 . 10.2991/jnmp.1999.6.4.5 . 448–488. 1999JNMP....6..448K . math/9910188 .
5. Li . Lifeng . Bremmer series, R-matrix propagation algorithm, and numerical modeling of diffraction gratings . Journal of the Optical Society of America A . The Optical Society . 11 . 11 . 1994-11-01 . 1084-7529 . 10.1364/josaa.11.002829 . 2829–2836. 1994JOSAA..11.2829L .
6. Wigner . E. P. . Eisenbud . L. . Higher Angular Momenta and Long Range Interaction in Resonance Reactions . Physical Review . American Physical Society (APS) . 72 . 1 . 1947-07-01 . 0031-899X . 10.1103/physrev.72.29 . 29–41. 1947PhRv...72...29W .
7. Burke . P G . Hibbert . A . Robb . W D . Electron scattering by complex atoms . Journal of Physics B: Atomic and Molecular Physics . IOP Publishing . 4 . 2 . 1971 . 0022-3700 . 10.1088/0022-3700/4/2/002 . 153–161. 1971JPhB....4..153B .
8. Schneider . Barry . R-matrix theory for electron-atom and electron-molecule collisions using analytic basis set expansions . Chemical Physics Letters . Elsevier BV . 31 . 2 . 1975 . 0009-2614 . 10.1016/0009-2614(75)85010-x . 237–241. 1975CPL....31..237S .
9. Schneider . Barry I. . R-matrix theory for electron-molecule collisions using analytic basis set expansions. II. Electron-H₂ scattering in the static-exchange model . Physical Review A . American Physical Society (APS) . 11 . 6 . 1975-06-01 . 0556-2791 . 10.1103/physreva.11.1957 . 1957–1962. 1975PhRvA..11.1957S .
10. C J Gillan, J Tennyson, and P G Burke, in Computational Methods for Electron-Molecule Collisions, eds. W M Huo and F A Gianturco, (Plenum, New York, 1995), p. 239
11. Carr . J.M. . Galiatsatos . P.G. . Gorfinkiel . J.D.. Harvey . A.G. . Lysaght . M.A. . Madden . D. . Mašín . Z. . Plummer . M.. Tennyson . J. . The UKRmol program suite. . Eur. Phys. J. D . 2012 . 66 . 58. 10.1140/epjd/e2011-20653-6 .
12. Computer Physics Communications . 249 . 107092 . Mašín . Zdeněk . Benda . Jakub . Gorfinkiel . Jimena D. . Harvey . Alex G.. Tennyson . Jonathan . UKRmol+: A suite for modelling electronic processes in molecules interacting with electrons, positrons and photons using the R-matrix method . 2019-12-07 . 10.1016/j.cpc.2019.107092. 1908.03018 .