Unified approach for exact calculation of angular momentum coupling and recoupling coefficients

We present schemes to reformulate all the 3j, 6j and 9j symbols in a form w hich is the product of two factors. One is a prefactor which is the square root of integer products and quotients. The other is the summation of the p roducts of binomial coefficients. In the calculation of these factors, we u tilize two types of number representation: the prime number representation for the prefactor, and the 32768-base number representation for the summati on terms. This makes it possible to tabulate or exactly calculate the coupl ing and recoupling coefficients for any large angular momenta. Instead of e valuating a large number of factorials of integers, we also compute the bin omial coefficients recursively at every stage, which dramatically increases the efficiency of calculation. Hence, a direct method for very fast and ex act calculation of coupling and recoupling coefficients for all range of qu antum angular moments is established. (C) 1999 Elsevier Science B.V. All ri ghts reserved.