Isotropic electrostatic polarizability

To the extent that the polarization of physical atoms results in dipole moments of finite length, it can be argued that the shell model is more physically realistic (the section on Applications will examine this argument in more detail). Of course, both models include additional approximations that may be even more severe than ignoring the finite electronic displacement upon polarization. Among these approximations are (1) the representation of the electronic charge density with point charges and/or dipoles, (2) the assumption of an isotropic electrostatic polarizability, and (3) the assumption that the electrostatic interactions can be terminated after the dipole-dipole term. 

The field la then the same for all molecules and parallel to . as are the induced moments m taken to be given by m > o where o is a simple scalar polarizability The gist of the Lorentz argument (7) is that the resultant field at any one molecule i from all the other dipoles j in a sphere, surrounding the one vanishes as it is given by the sumr Tl - 3 cos (R j z)]a over lattice distances which is zero for cubic symmetry (or an isotropic continuum) leaving s the field of charges external to the sphere if it is in a vacuum. The macroscopic in the sphere from Eo and the macroscopic is by electrostatics - - (AtT/3) and the Lorentz field is... 

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