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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_0Distribution 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. | ||

Classification: 4.2. | ||

Nature of problem:Explicit construction of SO(5) ⊃ SO(3) spherical harmonics on S_{4}. Evaluation of SO(3)-reduced matrix elements and SO(5) ⊃ SO(3) Clebsch-Gordan coefficients (isoscalar factors). | ||

Solution method:Construction of SO(5) ⊃ SO(3) spherical harmonics by orthonormalization, obtained from a generating set of functions, according to the method [1]. Matrix elements and Clebsch-Gordan coefficients follow by construction and integration of SO(3) scalar products. | ||

Running time:Depends strongly on the maximum SO(5) and SO(3) representation labels involved. A few minutes for the calculation in the Mathematica notebook. | ||

References: | ||

[1] | D. J. Rowe, P. S. Turner, and J. Repka (J. Math. Phys. 45 (2004) 2761). |

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