qspec.reduced_f_root  (  i ,  j_l ,  f_l ,  j_u ,  f_u ,  as_sympy = False  )[source]

The geometric coefficient $$\sqrt{f_F^{F^\prime}} = (-1)^{F + I + 1 + J_u}\sqrt{2F_l + 1}\sqrt{2F_u + 1}\begin{Bmatrix} J_u & J_l & 1 \\ F_l & F_u & I \end{Bmatrix},$$ as described in [R. C. Brown et al., Phys. Rev. A 87, 032504 (2013)].

Parameters:

isympy_expr | scalar

The nuclear spin quantum number $I$.

j_lsympy_expr | scalar

The electronic total angular momentum quantum number $J_l$ of the lower state.

f_lsympy_expr | scalar

The total angular momentum quantum number $F_l$ of the lower state.

j_usympy_expr | scalar

The electronic total angular momentum quantum number $J_u$ of the upper state.

f_usympy_expr | scalar

The total angular momentum quantum number $F_u$ of the upper state.

as_sympybool

Return the result as a symbol (True) or as a float (False).

Returns:

outsympy_expr | float

The geometric coefficient $\sqrt{f_F^{F^\prime}}$.