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Scholars Day 2006, Wednesday, April 12

Wigner 3n-j symbols: New Relations and Computational Search Methods for Non-trivial Zeros

Quantities known as 3n-j symbols, which arise in the quantum theory of angular momentum, are used extensively in such areas of chemistry and physics as scattering theory and electronic structure. The formulas for these quantities are written in the form of a square root factor multiplied by an alternating sum of products of binomial coefficients, and a 3n-j symbol is zero only if its corresponding binomial sum is zero. The pattern of occurrences of these zeros is of considerable theoretical and computational interest. The alternating sums can be evaluated with no loss of accuracy using large integer arithmetic; however, this is slow. Methods for searching for zeros while avoiding most of the large integer arithmetic are described. These methods considerably speed up the search process. A cumbersome but reliable way for evaluating some cases of the binomial sums without cancellation error is also described. These may make certain number-theorectical studies of the binomial sums easier. Similar methods may be applied to newly found classes of relations between certain products of 3n-j symbols that appear in molecular scattering calculations. The development of these new relations is a parallel area of research that will also be described.

Presenter: Robert Tuzun (Faculty)
Topic: Computational Science
Location: 204 Holmes
Time: 9:20 am (Session I)