triqs.operators.util.U_matrix.angular_matrix_element

triqs.operators.util.U_matrix.angular_matrix_element(l, k, m1, m2, m3, m4)

Calculate the angular Racah-Wigner matrix element.

\[\begin{split}(2l+1)^2 \begin{pmatrix} l & k & l \\ 0 & 0 & 0 \end{pmatrix}^2 \sum_{q=-k}^k (-1)^{m_1+m_2+q} \begin{pmatrix} l & k & l \\ -m_1 & q & m_3 \end{pmatrix} \begin{pmatrix} l & k & l \\ -m_2 & -q & m_4 \end{pmatrix}.\end{split}\]

Parameters:

lint

Orbital angular momentum of the shell.

kint

Order of the multipole expansion.

m1, m2, m3, m4int

Magnetic quantum numbers of the four orbitals.

Returns:

float

Value of the angular matrix element.