Polarizability is the relative tendency of a charge distribution, like the electron cloud of an atom or molecule, to be distorted from its normal shape by an external electric field, which may be caused by the presence of a nearby ion or dipole.

The electronic polarizability alpha is defined as the ratio of the induced dipole moment boldsymbol{p} of an atom to the electric field boldsymbol{E} that produces this dipole moment.

boldsymbol{p} = alpha boldsymbol{E}

Polarizability has the SI units of C·m2·V-1 = A2·s4·kg-1 but is more often expressed as polarizability volume with units of cm3 or in Å3 = 10-24 cm3.

alpha boldsymbol{(cm^3) = } frac{10^6}{ 4 pi epsilon _0 }alpha boldsymbol{(C cdot m^2 cdot V^{-1})} where epsilon _0 is the vacuum permittivity.

The polarizability of individual particles is related to the average electric susceptibility of the medium by the Clausius-Mossotti relation.

Note that the polarizability alpha as defined above is a scalar quantity. This implies that the applied electric fields can only produce polarization components parallel to the field. For example, an electric field in the x-direction can only produce an x component in boldsymbol{p}. However, it can happen that an electric field in the x-direction, produces a y or z component in the vector boldsymbol{p}. In this case alpha is described as a tensor of rank 2, which is represented with respect to a given system of axes (frame of reference) by a 3times3 matrix.

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