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An electron is not in itself distorted. If the effective nuclear charge of the atom that the electron is part of is relatively low and the ionization energy of the atom that pulls the electron towards is relatively high -- then the electron is highly polarizable and thus distorted
Neutral nonpolar atoms have electron clouds with spherically symmetrical electron arrangements. These electron clouds can be distorted if in the presence of an electric field, and I believe this distortion is defined as the polarizability of the atom or molecule. This distortion allows originally nonpolar molecules or atoms to achieve a dipole moment.
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