Programs in Physics & Physical Chemistry
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|Manuscript Title: Construction of SO(5) ⊃ SO(3) spherical harmonics and Clebsch-Gordan coefficients|
|Authors: M.A. Caprio, D.J. Rowe, T.A. Welsh|
|Program title: GammaHarmonic|
|Catalogue identifier: AECY_v1_0|
Distribution format: tar.gz
|Journal reference: Comput. Phys. Commun. 180(2009)1150|
|Programming language: Mathematica 6.|
|Computer: Any which support Mathematica.|
|Operating system: Any which support Mathematica; tested under Microsoft Windows XP and Linux.|
|Keywords: SO(5), spherical harmonics, Clebsch-Gordan coefficients, coupling coefficients, isoscalar factors, Bohr Hamiltonian, SU(1, 1) × SO(5) algebraic collective model.|
|PACS: 02.20.Qs, 02.70.-c, 21.60.Ev, 21.60.Fw.|
Nature of problem:
Explicit construction of SO(5) ⊃ SO(3) spherical harmonics on S4. Evaluation of SO(3)-reduced matrix elements and SO(5) ⊃ SO(3) Clebsch-Gordan coefficients (isoscalar factors).
Construction of SO(5) ⊃ SO(3) spherical harmonics by orthonormalization, obtained from a generating set of functions, according to the method . Matrix elements and Clebsch-Gordan coefficients follow by construction and integration of SO(3) scalar products.
Depends strongly on the maximum SO(5) and SO(3) representation labels involved. A few minutes for the calculation in the Mathematica notebook.
|||D. J. Rowe, P. S. Turner, and J. Repka (J. Math. Phys. 45 (2004) 2761).|
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