# Reaction field - not Onsager

1. Jun 26, 2008

### joseph12

I am trying to understand the origin of the following expression for the reaction field (dipole $$\mu$$ in spherical cavity surrounded by medium of permittivity $$\epsilon$$):
$$\begin{equation*} R= \frac{2 \mu}{4\pi\epsilon_0\rho^3} f(\epsilon)$$
where f(\epsilon) is _not_ the Kirkwood function,
$$\begin{equation*} f(\epsilon)=\frac{\epsilon-1}{2\epsilon+1},$$
but the following:
$$\begin{equation*} f(\epsilon)=\frac{\epsilon-1}{2\epsilon+4}.$$
I simply can not figure out the idea behind the third expression. I have already considered $$\epsilon_i\ne1$$ for the interior of the spherical cavity, or a polarizable dipole taking as refractive index squared, $$n^2$$=2 or 4 arbitrarily. I got many similar expressions in this way but unfortunately not the desired one. Has somebody encountered this expression already and can shed some light on its origin?

Thanks,
Joseph