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Manuscript Title: A program to calculate a general recoupling coefficient.
Authors: P.G. Burke
Program title: NJSYM
Catalogue identifier: AAGD_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 1(1969)241
Programming language: Fortran.
Computer: ICL 1907 1900 SERIES.
Operating system: QUBE.
RAM: 13K words
Word size: 24
Keywords: General purpose, Structure, Scattering, Racah coefficient, Wigner coefficient, Fano coefficient, Rotation group, 3j-symbol, 6j-symbol, 9j-symbol, 12j-symbol, 15j-symbol, 18j-symbol, 21j-symbol, Angular momentum, Angular integral, Element, Recoupling coefficient, Representation of Three dimensional Rotation.
Classification: 4.1.

Revision history:
Type Tit le Reference
correction 000A CORRECTION 10/03/71 See below
adaptation 0001 ADAPT NJSYM FOR WEIGHTS See below
adaptation 0002 ADAPT TO INTEGER ARITHMETIC See below

Nature of problem:
A general recoupling coefficient for an arbitrary number of integer or half integer angular monenta is calculated. The result is given as a floating point number.

Solution method:
The recoupling coefficient is first expressed as a sum over products of Racah coefficients multiplied by (-1) factors and (2j+1)**1/2 factors. This summation is then evaluated.

Restrictions:
The program can be used to calculate a recoupling coefficient containing any number of angular momenta by modifying the dimensions of certain arrays.

Unusual features:
When the program has been used once to evaluate a given recoupling coefficient, it is possible to call the routine over and over again for the same coefficient with different angular momenta without re-express- ing the recoupling coefficient in terms of Racah coefficients.

Running time:
The test run, consisting of four recoupling coefficients with between 3 and 7 angular momenta, takes 4 seconds to execute on the I.C.L. 1907 this is approximately equivalent in speed to the IBM 7090).

CORRECTION SUMMARY
Manuscript Title: A program to calculate a general recoupling coefficient. (C.P.C. 1(1969)241).
Authors: P.G. Burke
Program title: 000A CORRECTION 10/03/71
Catalogue identifier: AAGD_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 2(1971)173
Classification: 4.1.

ADAPTATION SUMMARY
Manuscript Title: Adaptation of NJSYM and GENSUM for use with program WEIGHTS.
Authors: A. Hibbert
Program title: 0001 ADAPT NJSYM FOR WEIGHTS
Catalogue identifier: AAGD_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 2(1971)181
Programming language: Fortran.
Classification: 4.1.

Nature of problem:
The purpose of the program is to express the matrix elements of the two- electron interaction of the hamiltonian as a weighted sum of radial slater integrals.

Solution method:
The main difference between this code and the earlier version is that that the present code makes use of average energy expressions where possible.

Running time:
The six sets of configurations in the test data took 111 seconds on an ICL 1907. This should be compared with the time of 75 seconds for the first two sets of configurations, using the earlier version. The use of average energy contributions provides a varied improvement in time, but typically is of the order of 30%. Another factor which affects the comparison between these two times is a new compiler on our ICL 1907. This too reduces the execution time. The new compiler also appears to reduce the store required for programs of this sort of size by approximately 10%. Thus, the reduction in core storage from 30K to 28K is a result of the introduction of the new compiler, and the removal of four COMMON blocks (about 2k words), balanced by 500 extra cards.

ADAPTATION SUMMARY
Manuscript Title: A program to calculate a general recoupling coefficient.
Authors: I.P. Grant
Program title: 0002 ADAPT TO INTEGER ARITHMETIC
Catalogue identifier: AAGD_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 5(1973)161
Programming language: Fortran.
Computer: ICL 1906A.
Classification: 4.1.

Nature of problem:
The adaptation consists of an internal modification by which all manipulation involving quantum numbers and selection rules in calculating recoupling coefficients is handled using integer arithmetic. Only the final calculation of the answer now involves floating point instructions. A different Racah coefficient subroutine (due to Bessis) is included in the adaptation deck. It uses prime exponent arithmetic in order to minimize rounding errors due to floating point operations with large factorials, and works entirely with integer except in carrying out the final summation. It uses the standard formula.