qspec.hyperfine  (  i ,  j ,  f ,  a_hyper = 0.0 ,  b_hyper = 0.0 ,  c_hyper = 0.0  )[source]

The hyperfine structure shift of an atomic state (i, j, f) with the hyperfine constants a and b and c $$\begin{aligned} \Delta_\mathrm{hfs} &= A\frac{K}{2} + B\frac{\frac{3}{4}K(K + 1) - I(I + 1)J(J + 1)}{2I(2I - 1)J(2J - 1)}\\[1ex] &\quad + C\frac{\left[\splitdfrac{\frac{5}{4}K^3 + 5K^2 - 5I(I + 1)J(J + 1)} {+ K(I(I + 1) + J(J + 1) - 3I(I + 1)J(J + 1) + 3)}\right]}{I(I - 1)(2I - 1)J(J - 1)(2J - 1)}\\[3ex] K &= F(F + 1) - I(I + 1) - J(J + 1) \end{aligned}$$

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 $F$.

a_hyperarray_like

The magnetic dipole hyperfine constant $A = \mu_I \mathcal{B}_J / (IJ)$ (arb. units).

b_hyperarray_like

The electric quadrupole hyperfine constant $B = eQ_I (\partial^2 V_J / \partial z^2)$ ([a_hyper]).

c_hyperarray_like

The magnetic octupole hyperfine constant $C = \Omega_I T_J^{(3)}$ ([a_hyper])

Returns:

outndarray

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