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Manuscript Title: Calculation of general recoupling coefficients using graphical methods.
Authors: V. Fack, S.N. Pitre, J. Van der Jeugt
Program title: NEWGRAPH
Catalogue identifier: ADFJ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 101(1997)155
Programming language: C.
Computer: 486-based PCs.
Operating system: MS-DOS, Linux, Unix.
Keywords: General purpose, Rotation group, Atomic structure, Nuclear structure, Scattering, General recoupling Coefficient, Angular momentum, Racah coefficient, Sn-j coefficient, Coupling tree, Binary trees, Yutsis graphs.
Classification: 4.1.

Subprograms used:
Cat Id Title Reference

Nature of problem:
A general recoupling coefficient for an arbitrary number of (integer or half-integer) angular momenta is expressed as a multiple sum over products of 6-j coefficients, including phase factors and square root factors. This summation formula can then be evaluated for given values of the angular momenta (for this purpose we use the program NJSUMMATION [4]).

Solution method:
A summation formula for a general recoupling coefficient is obtained by representing the coefficient by a Yutsis graph, and by performing a number of reduction rules valid for such graphs. Each reduction rule contributes to the final summation formula either just by a numerical factor, or else by an additional summation variable. The purpose is to find an optimal summation formula, i.e. with a minimum number of summation variables. With this in mind special attention is paid to implementing the graphical rules whereby N-cycles are reduced in the most optimal way.

Unusual features:
The program has been tested using the Linux [1] operating system. The compilers TURBO C++ [2], GNU CC [3] and SPARCompiler C were used.

Running time:
less than 0.1 s on a 486-based PC running Linux.

[1] Linux version 2.0.0 (Unix clone for 386/486-based PCs); publicly available via the Internet, see e.g. http://www.yahoo.com/Computers/Operating_Systems/Unix/Linux/.
[2] Turbo C++ version 1.01, User Guide (Borland, 1990).
[3] GNU CC version 2.5 (Free Software Foundation, Cambridge, MA, USA); publicly available via the Internet, see e.g. http://www.gnu.ai.mit.edu/home.html.
[4] V. Fack, S.N. Pitre, J. Van der Jeugt, Comput. Phys. Commun. 86(1995)105.