New formula for 9-j symbols and their direct calculation

An algebraic expression for 9-j symbols in the form of a summation of the p roducts of binomial coefficients is obtained. An algorithm is also devised to calculate these binomial coefficients recursively. This avoids the evalu ation of factorials of integers, which is the main source of overflow in ca lculation of coupling coefficients for large angular momenta. Thus, the new formula permits accurate calculation of 9-j symbols. In addition, it has h igher symmetry and involves only a twofold summation. Therefore, a direct a pproach for accurate and efficient calculation of 9-j symbols for very larg e angular momenta is thereby established. (C) 1998 American Institute of Ph ysics. [S0894-1866(98)02006-9].