A C++ ensemble of functions to compute the Wigner 3j- and 6j- symbols. It reimplements the algorithm designed by Schulten and Gordon in C++, but also contains the original Fortran implementation. It can either compute an array of Wigner 3j or 6j symbols, or a single coefficient. It also computes the Clebsch-Gordan coefficients.

This library uses CMake to help the build process. First, download the source code. It is recommended to create a separate directory for building, i.e.

mkdir build/.

Then, run

cmake .. && make && sudo make install.

By default, the library is installed to /usr/lib/ and the include files are in /usr/include/. To install to another directory, say /usr/local/, use the command-line argument

cmake -DCMAKE_INSTALL_PREFIX:PATH=/usr/local && make && sudo make install.

We list the user-facing functions that compute the Wigner symbols. The functions are behind the namespace WignerSymbols.

• std::vector<double> wigner3j(double l2, double l3, double m1, double m2, double m3)
  Computes Wigner 3j symbols with all possible values of l1. Returns an std::vector<double> with the coefficients sorted by increasing values of l1.
• double wigner3j(double l1, double l2, double l3, double m1, double m2, double m3)
  Computes a specific Wigner 3j symbol.
• double clebschGordan(double l1, double l2, double l3, double m1, double m2, double m3)
  Computes a specific Clebch-Gordan coeffcient.
• std::vector<double> wigner6j(double l2, double l3, double l4, double l5, double l6)
  Computes Wigner 6j symbols with all possible values of l1. Returns an std::vector<double> with the coefficients sorted by increasing values of l1.
• double wigner6j(double l1, double l2, double l3, double l4, double l5, double l6)
  Computes a specific Wigner 6j symbol.

• double wigner3j_f(double l1, double l2, double l3, double m1, double m2, double m3)
  Computes a specific Wigner 3j symbol.
• double clebschGordan_f(double l1, double l2, double l3, double m1, double m2, double m3)
  Computes a specific Clebch-Gordan coeffcient.
• double wigner6j_f(double l1, double l2, double l3, double l4, double l5, double l6)
  Computes a specific Wigner 6j symbol.

• K. Schulten and R. G. Gordon, Recursive evaluation of 3j and 6j coefficients, Comput. Phys. Commun. 11, 269–278 (1976).
• K. Schulten, Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta, J. Math. Phys. 16, 1961 (1975).