Electric dipole-dipole interaction

Electric dipole-dipole interaction between f electron atoms

Estimate of electric dipole moment:

According to Yen et al.[1], the electric dipole moment can be estimated as:
 
p~e<r>V_c/D,

where e is the elctronic charge, <r>~10^-10 m is the mean radius of the 4f electronic orbit, V_c~500 cm^-1 is the characteristic crystal field splitting, and D~60000 cm^-1 [2] is the energy separation between (4f)ⁿ and (4f)^n-1(5d)' configuration.

Then p~1.3e-31 C.m

Then the dipole-dipole interaction is

W=\frac{ p_1 p_2}{4\pi \epsilon_0 R^3}

For example, if R=0.42 nm, we get

W=1.2 e-5 eV, or 0.01 meV.

[1]    W. M. Yen et al., Physical Review 140, 1188 (1965).
[2]    G. H. Dieke, and H. M. Crosswhite, Applied Optics 2, 675 (1963).