A program for simplifying summation of Wigner 3j-symbols

Published: 23-04-2021| Version 1 | DOI: 10.17632/9zmx4b5sdd.1
Shaohui Xiang,
Liming Wang,
Zong-Chao Yan,
Haoxue Qiao


The program presented in this paper aims to simplify formulas involving products of a large amount of Wigner 3j-symbols summed over various magnetic quantum numbers. The algorithm used in our program is based on the graphical techniques originally developed by Yutsis, Levinson, and Vanagas, and later revised by some others. The output of our program is expressed as a weighted sum of products of 3j-, 6j- and 9j-symbols, with appropriate phase factors embedded. Compared with the previous literature, the present program is more flexible in a sense that it can deal with not only closed diagrams, such as the angular momentum recoupling coefficients, but also open diagrams. Our program is particularly useful to high precision atomic and molecular structure calculations using correlated electron–electron coordinates.