New algorithms for calculating 3n-j symbols


  • Clemens C. J. Roothaan

    1. Department of Physics and Chemistry, University of Chicago, Chicago, Illinois 60637; and Hewlett-Packard Laboratories, 1501 Page Mill Road, Palo Alto, California 94304
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    • Research carried out in part during the author's stay as a visiting professor at the University of Delaware, Newark, DE, 1987-88.


Compact expressions are presented for the 3n-j symbols, where 1 ⩽ n ⩽ 4, which feature sums over products of binomial coefficients, and certain integer triangular coefficients. The triangular coefficients in turn can be expressed as products of binomial coefficients. Thus in the formulas presented for the 3n-j symbols, the dependence on numerous factorials, formally as well as computationally, has been completely eliminated. While formulas which incorporate summations over products of binomial coefficients have been known for the 3- j and 6- j symbols, the introduction of the triangular coefficients, and the application of the binomial/triangular scheme to 3n-j symbols with n > 2, provide important new results. The new formulas are simpler, and they permit more efficient computations of the 3n-j symbols, both in exact and in floating point format, than most schemes which are currently in use. © 1993 John Wiley & Sons, Inc.