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Wigner and Racah coefficients for SU3
dc.contributor.authorDraayer, J. P.en_US
dc.contributor.authorAkiyama, Yoshimien_US
dc.date.accessioned2010-05-06T21:42:44Z
dc.date.available2010-05-06T21:42:44Z
dc.date.issued1973-12en_US
dc.identifier.citationDraayer, J. P.; Akiyama, Yoshimi (1973). "Wigner and Racah coefficients for SU3." Journal of Mathematical Physics 14(12): 1904-1912. <http://hdl.handle.net/2027.42/70151>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/70151
dc.description.abstractA general yet simple and hence practical algorithm for calculating SU3⊃SU2×U1SU3⊃SU2×U1 Wigner coefficients is formulated. The resolution of the outer multiplicity follows the prescription given by Biedenharn and Louck. It is shown that SU3 Racah coefficients can be obtained as a solution to a set of simultaneous equations with unknown coefficients given as a by‐product of the initial steps in the SU3⊃SU2×U1SU3⊃SU2×U1 Wigner coefficient construction algorithm. A general expression for evaluating SU3⊃R3SU3⊃R3 Wigner coefficients as a sum over a simple subset of the corresponding SU3⊃SU2×U1SU3⊃SU2×U1 Wigner coefficients is also presented. State conjugation properties are discussed and symmetry relations for both the SU3⊃SU2×U1SU3⊃SU2×U1 and SU3⊃R3SU3⊃R3 Wigner coefficients are given. Machine codes based on the results are available.en_US
dc.format.extent3102 bytes
dc.format.extent793267 bytes
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dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleWigner and Racah coefficients for SU3en_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Physics, The University of Michigan, Ann Arbor, Michigan 48105en_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/70151/2/JMAPAQ-14-12-1904-1.pdf
dc.identifier.doi10.1063/1.1666267en_US
dc.identifier.sourceJournal of Mathematical Physicsen_US
dc.identifier.citedreferenceE. P. Wigner, Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra, translated from the German by J. J. Griffin (Academic, New York, 1959).en_US
dc.identifier.citedreferenceG. Racah, “Theory of Complex Spectra,” in Quantum Mechanics of Angular Momentum, edited by L. C. Biedenham and H. Van Dam (Academic, New York, 1965).en_US
dc.identifier.citedreferenceJ. P. Elliott, Proc. R. Soc. A 245, 128, 562 (1958).en_US
dc.identifier.citedreferenceY. Ne’eman, Nucl. Phys. 26, 222 (1961). M. Gell‐Mann, Phys. Rev. 125, 1067 (1962).en_US
dc.identifier.citedreferenceSee, for example, references cited by C. K. Chew and R. T. Sharp, Nucl. Phys. B 2, 697 (1967).en_US
dc.identifier.citedreferenceL. C. Biedenham and J. D. Louck, J. Math. Phys. 13, 1985 (1972).en_US
dc.identifier.citedreferenceL. C. Biedenhard, J. D. Louck, E. Chacón, and M. Ciftan, J. Math. Phys. 13, 1957 (1972).en_US
dc.identifier.citedreferenceE. Chacón, M. Ciftan, and L. C. Biedenham, J. Math. Phys. 13, 577 (1972).en_US
dc.identifier.citedreferenceJ. D. Louck and L. C. Biedenham, J. Math. Phys. 12, 173 (1971).en_US
dc.identifier.citedreferenceJ. D. Louck and L. C. Biedenham, J. Math. Phys. 11, 2368 (1970).en_US
dc.identifier.citedreferenceJ. A. Castilho Alcaŕs, L. C. Biedenham, K. T. Hecht, and G. Neeley, Ann. Phys. (N.Y.) 60, 85 (1970).en_US
dc.identifier.citedreferenceJ. D. Louck, Am. J. Phys. 38, 3 (1970) presents a bibliography and synthesis of published results on the theory of tensor operators in the unitary groups.en_US
dc.identifier.citedreferenceJ. P. Elliott and M. Harvey, Proc. R. Soc. A 272, 557 (1962).en_US
dc.identifier.citedreferenceR. E. Behrends, J. Dreitlin, C. Fronsdal, and B. W. Lee, Rev. Mod. Phys. 34, 1 (1962). J. J. deSwart, Rev. Mod. Phys. 35, 916 (1963).en_US
dc.identifier.citedreferenceI. M. Gel’fand and M. L. Zeitlin, Dokl. Akad. Nauk SSSR 71, 825 (1950).en_US
dc.identifier.citedreferenceG. Racah, “Group Theory and Spectroscopy” (Lecture Notes, Princeton, 1951). V. Bargmann and M. Moshinsky, Nucl. Phys. 18, 697 (1960); Nucl. Phys. 23, 177 (1961). R. T. Sharp and Hans C. Von Baeyer, Nucl. Phys. A. 127, 513 (1969).en_US
dc.identifier.citedreferenceM. Harvey, in Advances in Nuclear Physics, edited by M. Baranger and and E. Vogt (Plenum, New York, 1971), Vol. 1.en_US
dc.identifier.citedreferenceJ. D. Vergados, Nucl. Phys. A 111, 681 (1968).en_US
dc.identifier.citedreferenceK. T. Hecht, Nucl. Phys. 62, 1 (1965).en_US
dc.identifier.citedreferenceA. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U.P., Princeton, N.J., 1957).en_US
dc.identifier.citedreferenceIn addition to Refs. 14 and 19 see, for example, M. Moshinsky, Rev. Mod. Phys. 34, 813 (1962). A. R. Edmonds, Proc. R. Soc. A 268, 567 (1963).en_US
dc.identifier.citedreferenceA. deShalit and I. Talmi, Nuclear Shell Theory (Academic, New York, 1963).en_US
dc.identifier.citedreferenceJ. P. Draayer and S. A. Williams, Nucl. Phys. A 129, 647 (1969).en_US
dc.identifier.citedreferenceE. Chacón and M. Moshinsky, Phys. Lett. 23, 567 (1966); in Spectroscopic and Group Theoretical Concepts and Methods in Elementary Particle Physics, edited by F. Bloch, S. G. Cohen, A. deShalit, S. Sambursky, and I. Talmi (North‐Holland, Amsterdam, 1968).en_US
dc.identifier.citedreferenceA. Bohr and Ben R. Mottelson, Nuclear Structure (Benjamin, New York, 1969).en_US
dc.identifier.citedreferenceFor a coupled system (λ1μ1)×(λ2μ2)→(λ3μ3),(λ1μ1)×(λ2μ2)→(λ3μ3), Eq. (32) cannot simultaneously be applied to all three representations (λ1μ1),(λ2μ2),(λ1μ1),(λ2μ2), and (λ3μ3),(λ3μ3), in a consistent fashion. An additional dependence upon the multiplicity label is required. See, for example, J. J. deSwart, Rev. Mod. Phys. 35, 916 (1963), Sec. 14 and Sec. 4B of the current article.en_US
dc.identifier.citedreferenceJ. P. Draayer, Bull. Am. Phys. Soc. 18 (1), 137 (1973). R. D. Ratna Raju, J. P. Draayer, and K. T. Hecht, Nucl. Phys. A 202, 433 (1973).en_US
dc.identifier.citedreferenceJ. P. Draayer and Yoshimi Akiyama, Comput. Phys. Commun. 5, 405 (1973).en_US
dc.owningcollnamePhysics, Department of


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