R-matrix

From HandWiki

The term R-matrix has several meanings, depending on the field of study. The term R-matrix is used in connection with the Yang–Baxter equation. This is an equation which was first introduced in the field of statistical mechanics, taking its name from independent work of C. N. Yang and R. J. Baxter. The classical R-matrix arises in the definition of the classical Yang–Baxter equation.[1]

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.[2]

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.[3] Using that work as a basis, an R-matrix method was developed for electron, positron and photon scattering by atoms.[4] This approach was later adapted for electron, positron and photon scattering by molecules.[5][6][7]

R-matrix method is used in UKRmol[8] and UKRmol+[9] 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

References

  1. ↑ Kupershmidt, Boris A. (1999). "What a Classical r-Matrix Really Is". Journal of Nonlinear Mathematical Physics (Informa UK Limited) 6 (4): 448–488. doi:10.2991/jnmp.1999.6.4.5. ISSN 1402-9251. Bibcode: 1999JNMP....6..448K. 
  2. ↑ Li, Lifeng (1994-11-01). "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): 2829–2836. doi:10.1364/josaa.11.002829. ISSN 1084-7529. Bibcode: 1994JOSAA..11.2829L. 
  3. ↑ Wigner, E. P.; Eisenbud, L. (1947-07-01). "Higher Angular Momenta and Long Range Interaction in Resonance Reactions". Physical Review (American Physical Society (APS)) 72 (1): 29–41. doi:10.1103/physrev.72.29. ISSN 0031-899X. Bibcode: 1947PhRv...72...29W. 
  4. ↑ Burke, P G; Hibbert, A; Robb, W D (1971). "Electron scattering by complex atoms". Journal of Physics B: Atomic and Molecular Physics (IOP Publishing) 4 (2): 153–161. doi:10.1088/0022-3700/4/2/002. ISSN 0022-3700. Bibcode: 1971JPhB....4..153B. 
  5. ↑ Schneider, Barry (1975). "R-matrix theory for electron-atom and electron-molecule collisions using analytic basis set expansions". Chemical Physics Letters (Elsevier BV) 31 (2): 237–241. doi:10.1016/0009-2614(75)85010-x. ISSN 0009-2614. Bibcode: 1975CPL....31..237S. 
  6. ↑ Schneider, Barry I. (1975-06-01). "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): 1957–1962. doi:10.1103/physreva.11.1957. ISSN 0556-2791. Bibcode: 1975PhRvA..11.1957S. 
  7. ↑ 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
  8. ↑ Carr, J.M.; Galiatsatos, P.G.; Gorfinkiel, J.D.; Harvey, A.G.; Lysaght, M.A.; Madden, D.; Mašín, Z.; Plummer, M. et al. (2012). "The UKRmol program suite.". Eur. Phys. J. D (66): 58. doi:10.1140/epjd/e2011-20653-6. 
  9. ↑ Mašín, Zdeněk; Benda, Jakub; Gorfinkiel, Jimena D.; Harvey, Alex G.; Tennyson, Jonathan (2019-12-07). "UKRmol+: A suite for modelling electronic processes in molecules interacting with electrons, positrons and photons using the R-matrix method". Computer Physics Communications 249: 107092. doi:10.1016/j.cpc.2019.107092. 



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