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