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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_0Distribution 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]. | ||

References: | ||

[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. |

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