New orthogonality relationships of the Gaunt coefficients

Ozay S., Akdemir S., Öztekin E.

COMPUTER PHYSICS COMMUNICATIONS, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2024
  • Doi Number: 10.1016/j.cpc.2024.109118
  • Journal Name: COMPUTER PHYSICS COMMUNICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Chemical Abstracts Core, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

A new analytical formula for the Gaunt coefficients is derived using expressions of Clebsch Gordan coefficients in terms of the generalized hypergeometric functions of unit argument and binomial coefficients. In addition, new sum expressions and orthogonality relations containing the Gaunt coefficients are written. These expressions are used to test the accuracy of the numerical calculation for the Gaunt coefficients. These formulae are coded in the Mathematica programming language, and the Gaunt coefficients are calculated numerically and compared with the values from the literature.