Asymptotics of Clebsch-Gordan Coefficients
Matthias W. Reinsch, James J. Morehead
TL;DR
This paper derives asymptotic formulas for Clebsch-Gordan coefficients using integral representations, analyzing different regions and providing high-accuracy approximations for large quantum numbers.
Contribution
It introduces new asymptotic expressions for Clebsch-Gordan coefficients, including higher-order approximations with six-digit accuracy for large quantum numbers.
Findings
Asymptotic formulas derived from integral representations.
Analysis of classically allowed and forbidden regions.
High-accuracy approximations for quantum numbers in the hundreds.
Abstract
Asymptotic expressions for Clebsch-Gordan coefficients are derived from an exact integral representation. Both the classically allowed and forbidden regions are analyzed. Higher-order approximations are calculated. These give, for example, six digit accuracy when the quantum numbers are in the hundreds.
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