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Manuscript Title: Program for generating tables of SU(3) supset SU(2) times U(1) coupling coefficients.
Authors: T.A. Kaeding, H.T. Williams
Program title: SU3
Catalogue identifier: ADDY_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 98(1996)398
Programming language: C.
Computer: DEC VAX 4000/90.
Operating system: VMS v6.2, MS-DOS 6.x, HP UNIX 9.0.
RAM: 998K words
Word size: 32
Peripherals: disc.
Keywords: General purpose, Algebras, Su(3), Clebsch-Gordan coefficient, Wigner coefficient, Vector coupling Coefficient, Isoscalar factors.
Classification: 4.2.

Nature of problem:
Calculations using models based on SU(3) symmetry often require the Clebsch-Gordan coefficients which give the amplitudes for the expansion of direct products of irreducible representations.

Solution method:
Recursion relations [1] are used to construct tables of the isoscalar factors for the product of two irreducible representations. The SU(2) Clebsch-Gordan coefficients [2] [3] are then used with the isoscalar factors to produce the SU(3) Clebsch-Gordan coefficients.

Restrictions:
The program is limited by computer memory and maximum size of the integer variables. On the DEC VAX with 32-bit integers, the largest product that has been successfully computed is 27 times 27.

Unusual features:
The program has these unique features: it determines the representations in the Clebsch-Gordan series; it uses recursion relations to efficiently compute the isoscalar factors; it presents exact results; it provides results as LaTeX [4] formatted tables.

Running time:
Running time varies according to the sizes of p1, q1, p2 and q2 in the product (p1,q1) times (p2,q2). On the VAX for 3 times 3 the CPU time is 1.2 sec for computig values and formatting tables. For 27 times 27 the CPU time is 13 min 11 sec. On the Alpha, the latter time is 1 min 13 sec, only about one-half second of which is for computation.

References:
[1] H.T. Williams, Symmetry Properties of SU3 Vector Coupling Coefficients, WLUPY-9-93.
[2] E.U. Condon and G.H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, London, 1957).
[3] E.P. Wigner, Group Theory and its Application to the Quantum Mechanics of Atomic Spectra, trans. by J.J. Griffin (Academic Press, New York, 1959).
[4] L. Lamport, LaTeX: A Document Preparation System (Addison-Wesley, Menlo Park CA, 1986).