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Reaction field - not Onsager

  1. Jun 26, 2008 #1
    I am trying to understand the origin of the following expression for the reaction field (dipole [tex]\mu[/tex] in spherical cavity surrounded by medium of permittivity [tex]\epsilon[/tex]):
    [tex]
    \begin{equation*}
    R= \frac{2 \mu}{4\pi\epsilon_0\rho^3} f(\epsilon)
    \end{equation}
    [/tex]
    where f(\epsilon) is _not_ the Kirkwood function,
    [tex]
    \begin{equation*}
    f(\epsilon)=\frac{\epsilon-1}{2\epsilon+1},
    \end{equation}
    [/tex]
    but the following:
    [tex]
    \begin{equation*}
    f(\epsilon)=\frac{\epsilon-1}{2\epsilon+4}.
    \end{equation}
    [/tex]
    I simply can not figure out the idea behind the third expression. I have already considered [tex]\epsilon_i\ne1[/tex] for the interior of the spherical cavity, or a polarizable dipole taking as refractive index squared, [tex]n^2[/tex]=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
     
  2. jcsd
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