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# Polarizability

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 α 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 polarizabilty 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 ε0 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 α 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 α is described as a tensor of rank 2, which is represented with respect to a given system of axes (frame of reference) by a 3$\times$3 matrix.