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Manuscript Title: Programs for generating Clebsch-Gordan coefficients of SU(3) in SU(2) and SO(3) bases..
Authors: C. Bahri, D.J. Rowe, J.P. Draayer
Program title: SU3CGVCS
Catalogue identifier: ADTN
Journal reference: Comput. Phys. Commun. 159(2004)121
Programming language: Fortran 77.
Computer: SGI Origin 2000, HP Apollo 9000, Sun, IBM SP, Pentium.
Operating system: IRIX 6.5, HP UX 10.01, SunOS, AIX, Linux.
Keywords: Clebsch-Gordan (CG) coefficients, Coupling coefficients, SU(3), SU(2), SO(3), Vector coherent state (VCS) theory, General purpose, Rotation groups, Algebras, Nuclear physics, Fractional parentage.
Classification: 4.1, 4.2, 17.18.

Nature of problem:
The group SU(3) and its Lie algebra su(3) have important applications, for example, in elementary particle physics , nuclear physics, and quantum optics. The code presented is particularly relevant for the last two fields. Clebsch-Gordan (CG) coefficients are required whenever the symmetries of many-body systems are used for the evaluation of matrix elements of tensor operators. Moreover, the construction of CG coefficients for SU(3) serves as a nontrivial prototype for larger compact semi-simple Lie algebras and even for non semi-simple Lie algebras. It is the simplest Lie algebra to have multiplicity in its outer products and a non-canonical subalgebra i.e., SO(3).

Solution method:
Vector coherent state theory is first used to construct bases for the products of two irreducible representations (irreps). The bases are SU(2)-coupled so that SU(2)-reduced CG (or isoscalar factors) can be constructed naturally. The CG coefficients in the SO(3) bases are constructed subsequently from the overlaps between the SU(2) and SO(3) bases.

The programs are limited by computer memory and the maximum size of the variable arrays. As dimension overflow conditions are possible, they are flagged and can be fixed by following the directions given as part of the error message.

Unusual features:
Intrinsic bit functions and, or, and shift called iand, ior and ishft, respectively in FORTRAN, are used for packing and unpacking the labels for the irreps. Intrinsic logical btest is used to test the bit for the phase factor.

Running time:
The calculation time for a single SU(3) CG coefficient is very different for SU(2) and SO(3) bases. It varies between 7.3 - 54.1 ns in SGI Origin 2000, 0.81-5.48 ms in HP Apollo 9000, or 0.055-0.373 ms in Intel Pentium 4 for SU(2) bases while it is between 0.027-0.255 s in Intel Pentium 4 for SO(3) bases.