# arc.calculations_atom_single.AtomSurfaceVdW.getC3contribution#

AtomSurfaceVdW.getC3contribution(n1, l1, j1, n2, l2, j2, s=0.5)[source]#

Contribution to $$C_3$$ of $$|n_1, \ell_1, j_1\rangle$$ state due to dipole coupling to $$|n_2, \ell_2, j_2\rangle$$ state.

Calculates $$\frac{1}{4\pi\varepsilon_0}\ \frac{ n(\omega_{\rm ab})^2 - 1}{ n(\omega_{\rm ab})^2 + 1}\ \frac{ \left| \langle a| D_x | b \rangle \right|^2 \ + \left| \langle a | D_y | b \rangle \right|^2 + \ 2 \cdot \left|\langle a |D_z| b \rangle \right|^2}{16}$$

where $$|{\rm a}\rangle \equiv |n_1, \ell_1, j_1\rangle$$ , $$|{\rm b}\rangle \equiv |n_2, \ell_2, j_2\rangle$$, $$\mathbf{D} \equiv e \cdot \mathbf{r} \ \equiv \hat{x} D_x + \hat{y} D_y\ + \hat{z} D_z$$ is atomic dipole operator and $$n(\omega_{\rm ab})$$ is refractive index of the considered surface at transition frequency $$\omega_{\rm ab}$$ .

Parameters
• n1 (int) – principal quantum number of state 1

• l1 (int) – orbital angular momentum of state 1

• j1 (float) – total angular momentum of state 1

• n2 (int) – principal quantum number od state 2

• l2 (int) – orbital angular momentum of state 2

• j2 (float) – total angular momentum of state 2

• s (float) – optional, spin angular momentum of states. Default value of 0.5 is correct for AlkaliAtoms. For DivalentAtom it has to be explicitly stated

Returns

contribution to VdW coefficient $$C_3$$ ,estimated error $$\delta C_3$$ (in units of $${\rm J}\cdot{\rm m}^3$$), and refractive index $$n$$ of the surface material for the given transition.

Return type

Warning

This is just contribution of one transition to the level shift of a particular state. To calculate total level shift, check AtomSurfaceVdW.getStateC3