qspec.hyperfine  (  i ,  j ,  f ,  hyper_const = 0.0  )[source]

The hyperfine structure (HFS) shift of an atomic state $|IJF\rangle$ $$\begin{aligned} \Delta_\mathrm{hfs} &= A\frac{K}{2} + B\frac{\frac{3}{4}K(K + 1) - I(I + 1)J(J + 1)}{2I(2I - 1)J(2J - 1)}\\[1ex] &\quad + C\frac{\left[\splitdfrac{\frac{5}{4}K^3 + 5K^2 - 5I(I + 1)J(J + 1)} {+ K(I(I + 1) + J(J + 1) - 3I(I + 1)J(J + 1) + 3)}\right]}{I(I - 1)(2I - 1)J(J - 1)(2J - 1)}\\[3ex] K &= F(F + 1) - I(I + 1) - J(J + 1), \end{aligned}$$ with the HFS constants $A$, $B$ and $C$, specified as a list in hyper_const.

Parameters:

iquant_like

The nuclear spin quantum number $I$.

jquant_like

The electronic total angular momentum quantum number $J$.

fquant_like

The total angular momentum quantum number $F$.

hyper_constarray_like

The hyperfine structure constants $A = \mu_I \mathcal{B}_J / (IJ)$, $B = eQ_I (\partial^2 V_J / \partial z^2)$ and $C = \Omega_I T_J^{(3)}$ of the magnetic dipole, electric quadrupole and magnetic octupole order, respectively. If a scalar is given, only the $A$ constant is used (MHz if as_freq else eV).

Returns:

dnu_hfsndarray

The hyperfine structure shift $\Delta_\mathrm{hfs}$ ([a_hyper]).