Improved recursive computation of clebsch-Gordan coefficients. (October 2020)

• Record Type: Journal Article
• Authors: Xu, Guanglang
• Is Part Of: Journal of quantitative spectroscopy & radiative transfer. Volume 254(2020)
• Publication Date: 2020-10
• Subjects: Clebsch-Gordan coefficients -- Recursive computation -- Light scattering -- Translation coefficients -- Multipole fields -- T-Matrix; Spectrum analysis -- Periodicals; Radiation -- Periodicals; Analyse spectrale -- Périodiques; Rayonnement -- Périodiques; Radiation; Spectrum analysis; Periodicals; 543.0858
• DOI: 10.1016/j.jqsrt.2020.107210
• Languages: English
• ISSNs: 0022-4073

Abstract

Highlights: The sign-exponent recurrence method is presented as an improved recursion method for computing Clebsch-Gordan Coefficients. The sign-exponent recurrence method is more stable than the widely applied three-term linear recurrence method, while having the same level of accuracy and efficiency. The accuracy and efficiency are demonstrated by comparing with Python library SymPy. Abstract: Fast, accurate, and stable computation of the Clebsch-Gordan (C-G) coefficients is always desirable, for example, in light scattering simulations, the translation of the multipole fields, quantum physics and chemistry. Current recursive methods for computing the C-G coefficients are often unstable for large quantum numbers due to numerical overflow or underflow. In this paper, we present an improved method, called the sign-exponent recurrence, for the recursive computation of C-G coefficients. The result shows that the proposed method can significantly improve the stability of the computation without losing its efficiency, producing accurate values for the C-G coefficients even with very large quantum numbers.