R-matrix

<h2 id="other-meanings-and-uses">Other meanings and uses</h2>
The term R-matrix is used in connection with the <a href="/facts/Yang%25E2%2580%2593Baxter_equation/FEzKGDYh">Yang–Baxter equation</a>, first introduced in the field of <a href="/facts/Statistical_mechanics/6zMsNYYG">statistical mechanics</a> in the works of J. B. McGuire in 1964<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a> and <a href="/facts/C._N._Yang/VjoM4raz">C. N. Yang</a> in 1967<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a> and in the <a href="/facts/Group_ring/TJlkt5Te">group algebra</a> 
 
 
 
 
 C
 
 [
 
 S
 
 n
 
 
 ]
 
 
 {\displaystyle \mathbb {C} [S_{n}]}
 
 of the <a href="/facts/Symmetric_group/RUksK5l5">symmetric group</a> in the work of <a href="/facts/Algimantas_Adolfas_Jucys/t0PdMebW"> A. A. Jucys</a> in 1966.<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> The classical R-matrix arises in the definition of the classical Yang–Baxter equation.<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a>
In <a href="/facts/Quasitriangular_Hopf_algebra/Y6acUkBu">quasitriangular Hopf algebra</a>, the R-matrix is a solution of the <a href="/facts/Yang%25E2%2580%2593Baxter_equation/FEzKGDYh">Yang–Baxter equation</a>.
The numerical modeling of diffraction gratings in <a href="/facts/Optical_science/6HeJIr7P">optical science</a> can be performed using the R-matrix propagation algorithm.<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a>

<h2 id="r-matrix-method-in-quantum-mechanics">R-matrix method in quantum mechanics</h2>
There is a method in computational <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a> for studying scattering known as the R-matrix. Using the original R-matrix theory as a basis, a method was developed for <a href="/facts/Electron/L0KBo5cW">electron</a>, <a href="/facts/Positron/HgV4zBzA">positron</a> and <a href="/facts/Photon/mFNhAEzA">photon</a> scattering by <a href="/facts/Atom/FoQ4kGN5">atoms</a>.<a class="footnote-ref" id="fnref:12" href="#fn:12">12</a> This approach was later adapted for electron, positron and photon scattering by <a href="/facts/Molecule/N9ljSfFq">molecules</a>.<a class="footnote-ref" id="fnref:13" href="#fn:13">13</a><a class="footnote-ref" id="fnref:14" href="#fn:14">14</a><a class="footnote-ref" id="fnref:15" href="#fn:15">15</a>

<h2 id="other-applications">Other applications</h2>
R-matrix method is used in <a href="/facts/UK_Molecular_R-matrix_Codes/WuRMvHU7">UKRmol</a><a class="footnote-ref" id="fnref:16" href="#fn:16">16</a> and UKRmol+<a class="footnote-ref" id="fnref:17" href="#fn:17">17</a> code suits. The user-friendly software <a href="/facts/Quantemol/9YuUqJ20"> Quantemol Electron Collisions (Quantemol-EC)</a> and its predecessor <a href="/facts/Quantemol/9YuUqJ20">Quantemol-N</a> are based on UKRmol/UKRmol+ and employ <a href="/facts/MOLPRO/Xp3IeRhw">MOLPRO</a> package for electron configuration calculations.

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Nuclear_reaction/202yClUr">Compound nucleus</a></li>
<li><a href="/facts/Born_approximation/UoAaCasx">Distorted Waves Born Approximation</a></li>
<li><a href="/facts/Nuclear_force/A2MyJoWE">Optical model</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Lane, A. M.; Thomas, R. G. (1958-04-01). "R-Matrix Theory of Nuclear Reactions". Reviews of Modern Physics. 30 (2): 257–353. doi:10.1103/RevModPhys.30.257. ISSN 0034-6861. <a href="https://link.aps.org/doi/10.1103/RevModPhys.30.257" target="_blank">https://link.aps.org/doi/10.1103/RevModPhys.30.257</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Wigner, Eugene P. (1946-11-01). "Resonance Reactions". Physical Review. 70 (9–10): 606–618. doi:10.1103/PhysRev.70.606. <a href="https://journals.aps.org/pr/abstract/10.1103/PhysRev.70.606" target="_blank">https://journals.aps.org/pr/abstract/10.1103/PhysRev.70.606</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Wigner, Eugene P. (1946-07-01). "Resonance Reactions and Anomalous Scattering". Physical Review. 70 (1–2): 15–33. doi:10.1103/PhysRev.70.15. <a href="https://journals.aps.org/pr/abstract/10.1103/PhysRev.70.15" target="_blank">https://journals.aps.org/pr/abstract/10.1103/PhysRev.70.15</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Breit, G.; Wigner, E. (1936-04-01). "Capture of Slow Neutrons". Physical Review. 49 (7): 519–531. doi:10.1103/PhysRev.49.519. <a href="https://journals.aps.org/pr/abstract/10.1103/PhysRev.49.519" target="_blank">https://journals.aps.org/pr/abstract/10.1103/PhysRev.49.519</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Wigner, E. P.; Eisenbud, L. (1947-07-01). "Higher Angular Momenta and Long Range Interaction in Resonance Reactions". Physical Review. 72 (1). American Physical Society (APS): 29–41. Bibcode:1947PhRv...72...29W. doi:10.1103/physrev.72.29. ISSN 0031-899X. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Paetz gen. Schieck, Hans (2014). Nuclear Reactions: An Introduction. Lecture Notes in Physics. Vol. 882. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-642-53986-2. ISBN 978-3-642-53985-5. <a href="978-3-642-53985-5" target="_blank">978-3-642-53985-5</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">McGuire, J. B. (1964-05-01). "Study of Exactly Soluble One-Dimensional N-Body Problems". Journal of Mathematical Physics. 5 (5). The American Institute of Physics (AIP): 622–636. Bibcode:1964JMP.....5..622M. doi:10.1063/1.1704156. ISSN 0022-2488. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">Yang, C. N. (1967-12-04). "Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction". Physical Review Letters. 19 (23). American Physical Society (APS): 1312–1315. Bibcode:1967PhRvL..19.1312Y. doi:10.1103/PhysRevLett.19.1312. ISSN 0031-9007. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">Jucys, A. A. (1966). "On the Young operators of the symmetric group" (PDF). Lietuvos Fizikos Rinkinys. 11 (23). Gos. Izd-vo Polit. i Nauch. literatury.: 163–180. <a href="https://www.lietuvos-fizikai.lt/chessidr/straipsniai/LietFizRink/LFR-1971-v11-p5-AlgJucys-Factorization_of_Young_projection_operators_for_the_symmetric_group.pdf" target="_blank">https://www.lietuvos-fizikai.lt/chessidr/straipsniai/LietFizRink/LFR-1971-v11-p5-AlgJucys-Factorization_of_Young_projection_operators_for_the_symmetric_group.pdf</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">Kupershmidt, Boris A. (1999). "What a Classical r-Matrix Really Is". Journal of Nonlinear Mathematical Physics. 6 (4). Informa UK Limited: 448–488. arXiv:math/9910188. Bibcode:1999JNMP....6..448K. doi:10.2991/jnmp.1999.6.4.5. ISSN 1402-9251. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">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. 11 (11). The Optical Society: 2829–2836. Bibcode:1994JOSAA..11.2829L. doi:10.1364/josaa.11.002829. ISSN 1084-7529. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">Burke, P G; Hibbert, A; Robb, W D (1971). "Electron scattering by complex atoms". Journal of Physics B: Atomic and Molecular Physics. 4 (2). IOP Publishing: 153–161. Bibcode:1971JPhB....4..153B. doi:10.1088/0022-3700/4/2/002. ISSN 0022-3700. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">Schneider, Barry (1975). "R-matrix theory for electron-atom and electron-molecule collisions using analytic basis set expansions". Chemical Physics Letters. 31 (2). Elsevier BV: 237–241. Bibcode:1975CPL....31..237S. doi:10.1016/0009-2614(75)85010-x. ISSN 0009-2614. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">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. 11 (6). American Physical Society (APS): 1957–1962. Bibcode:1975PhRvA..11.1957S. doi:10.1103/physreva.11.1957. ISSN 0556-2791. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
<li id="fn:15">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 <a href="#fnref:15" class="footnote-back-ref">↩</a></li>
<li id="fn:16">Carr, J.M.; Galiatsatos, P.G.; Gorfinkiel, J.D.; Harvey, A.G.; Lysaght, M.A.; Madden, D.; Mašín, Z.; Plummer, M.; Tennyson, J. (2012). "The UKRmol program suite". Eur. Phys. J. D (66): 58. doi:10.1140/epjd/e2011-20653-6. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></li>
<li id="fn:17">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. arXiv:1908.03018. doi:10.1016/j.cpc.2019.107092. <a href="/wiki/ArXiv_(identifier)" target="_blank">/wiki/ArXiv_(identifier)</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></li>
</ol>

R-matrix open-in-new

R-matrix