Accurate computation of individual and tables of 3-j and 6-j symbols

Abstract

By rewriting the formulas for 3-j and 6-j symbols in terms of several possible alternating binomial sums, it is possible to calculate these quantities quickly and accurately, often exactly, using floating point operations. The binomial sums can be calculated by direct summation or by recursion. A simple method for uniquely parameterizing the well-known Regge symmetries of the 3-j and 6-j symbols makes it possible to systematize the choice of the smallest magnitude binomial sum (which enhances the accuracy of floating point calculations and speeds up exact calculations using large integer routines). Formulas for special cases of the 3-j symbols enable the construction of recursion sequences which are often substantially faster than direct summation, especially for very large angular momentum arguments. For both 3-j and 6-j symbols, recursion offers several advantages over direct summation in exact calculations and for calculating tables.