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

The cartesian transition dipole element vector $$\vec{A}_{Fm}^{F^\prime m^\prime} = \begin{pmatrix} \frac{1}{\sqrt{2}}\left[(A_{Fm}^{F^\prime m^\prime})_{-1} - (A_{Fm}^{F^\prime m^\prime})_1\right]\\ \frac{i}{\sqrt{2}}\left[(A_{Fm}^{F^\prime m^\prime})_{-1} + (A_{Fm}^{F^\prime m^\prime})_1\right]\\ (A_{Fm}^{F^\prime m^\prime})_0 \end{pmatrix},$$ with $(A_{Fm}^{F^\prime m^\prime})_q$ as in a_dipole. See [R. C. Brown et al., Phys. Rev. A 87, 032504 (2013)].

Parameters:

isympy_quant

The nuclear spin quantum number $I$.

j_lsympy_quant

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

f_lsympy_quant

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

m_lsympy_quant

The magnetic quantum number $m_l$ of the total angular moment of the lower state.

j_usympy_quant

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

f_usympy_quant

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

m_usympy_quant

The magnetic quantum number $m_u$ of the total angular moment of the upper state.

as_sympybool

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

Returns:

a_dipole_cartsympy.vector.vector.Vector | ndarray

The cartesian transition dipole element vector $\vec{A}_{Fm}^{F^\prime m^\prime}$.