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Manuscript Title: New efficient programs to calculate general recoupling coefficients. Part I: generation of a summation formula.
Authors: V. Fack, S.N. Pitre, J. Van der Jeugt
Program title: NJFORMULA
Catalogue identifier: ACVV_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 83(1994)275
Programming language: C.
Computer: 386/486-based PCs.
Operating system: MS-DOS, Linux [11], Unix.
Keywords: General purpose, Rotation group, Atomic structure, Nuclear structure, Scattering, General recoupling Coefficient, Angular momentum, Racah coefficient, 3n-j coefficient, Coupling tree, Binary trees, Recursive search process.
Classification: 4.1.

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 will provide a program NJSUMMATION [5]).

Solution method:
A summation formula for a general recoupling coefficient is obtained by determining a path between the binary coupling trees corresponding to the state vectors, using so-called flop operations. Such a path consists of a number of 'successful flop sequences', each of which is found by a recursive search process. To obtain an optimal summation formula, i.e. with a minimal number of summation variables, the total number of flop operations must be minimal. Heuristic techniques are used to keep the length of the path as short as possible.

Unusual features:
Compilers used: Turbo C++ [2], GNU CC [3], SPARCompiler C, 3L Parallel C [4]

Running time:
For typical examples, obtaining single, double or triple summation formulae, the running time is of the order of 0.01 second on the Sun Sparc and on a 486-based PC. For more complicated examples, such as generating a 7-fold and a 9-fold summation formula, the program takes less than 0.5 second. On the whole we find our running times to be comparable with those of NJGRAF [6].

[1] Linus (Unix clone for 386/486-based PCs) version 1.0; publicly available via anonymous ftp to nic.funet.fi in directory /pub/OS/Linux.
[2] Turbo C++ (version 1.01) User Guide, Borland International Inc. (1990).
[3] GNU CC version 2.5, Free Software Foundation, Cambridge, MA, USA; publicly available via anonymous ftp to prep.ai.mit.edu in directory /pub/gnu.
[4] Parallel C (version 2.2.2) User guide, 3L Ltd., UK (1991).
[5] V. Fack, S.N. Pitre and J. Van der Jeugt, New efficient programs to calculate general recoupling coefficients. Part II: evaluation of a summation formula, Comput. Phys. Commun. 86(1995)105.
[6] A. Bar-Shalom and M. Klapisch, NJGRAF: an efficient program for calculation of general recoupling coefficients by graphical analysis, compatible with NJSYM, Comput. Phys. Commun. 50(1988)375.