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

We present schemes to reformulate all the 3j, 6j and 9j symbols in a form which 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 products of binomial coefficients. In the calculation of these factors, we utilize two types of number representation: the prime number representation for the prefactor, and the 32768-base number representation for the summation terms. This makes it possible to tabulate or exactly calculate the coupling and recoupling coefficients for any large angular momenta. Instead of evaluating a large number of factorials of integers, we also compute the binomial coefficients recursively at every stage, which dramatically increases the efficiency of calculation. Hence, a direct method for very fast and exact calculation of coupling and recoupling coefficients for all range of quantum angular momenta is established.