Limitations of the concept of polarizability density as applied to atoms and molecules

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Abstract
We point out that in general it is not possible to define a dipole or polarizability density to describe the polarization of an atom or molecule in an arbitrary, non-uniform electric field. Calculations based on the concept of a dipole density are shown to give incorrect results for all the multipole moments higher than the dipole moment, and the field created by the polarized atom is hence also given incorrectly by such theories. Exact calculations of all the multipole moments induced in a hydrogen atom in a weak field of arbitrary spatial dependence are used as an illustration of these points. Implications for recent theories of light scattering and of collisional polarizabilities based on the polarizability density concept are indicated.

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