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Manuscript Title: Arbitrary 3n-j symbols for SU(2).
Authors: J. Shapiro
Program title: 3N-J SYMBOLS FOR SU(2)
Catalogue identifier: AAYA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 1(1970)207
Programming language: Fortran.
Computer: CDC 6600.
Operating system: BKY 37.
RAM: 14K words
Word size: 60
Peripherals: disc.
Keywords: Nuclear physics, Atomic physics, General purpose, Nuclear spectra, Nuclear structure, Atomic spectra, Atomic structure, Angular momentum, Crossing matrices, Transformation matrices, Recoupling coefficient, Racah coefficient, Wigner coefficient, Fano coefficient, 3j-symbol, 9j-symbol, 12j-symbol, 15j-symbol, 18j-symbol, 21j-symbol, 3nj-symbol, Representtion of three Dimensional Rotation group.
Classification: 4.1.

Nature of problem:
An arbitrary 3n-j, or recoupling, coefficient can be represented by a diagram consisting of 2n vertices connected by 3n directed line segments, with three lines connected to each vertex. This Fortran program will write a Fortran function to evaluate a given arbitrary 3n- j coefficient.

Solution method:
Triangles within the diagram are eliminated by multiplying by a 6-j symbol. If no triangles exist, the polynomial with the smallest number of sides is reduced, one side at a time, by multiplying by a 6-j symbol and summing over one angular momentum. In the end, the symbol is reduced to a sum of products of 6-j symbols.

The current program will work for n<=20. Adjustments for larger n are discussed in the long write-up. The output function must be used together with a 6-j function. The present 6-j routine requires the sum of four of the angular momenta to be < 100.

Unusual features:
The compilation and execution of the program is in two sections. The first part of the deck is read in, compiled and executed, causing the generation of Fortran Function subprograms defining 3n-j symbols as specified by data cards. The rest of the subroutines are then read in and compiled together with the newly generated Functions. More data is then read and the values of the 3n-j symbols are calculated.