The electronic polarizability is defined as the ratio of the induced dipole moment of an atom to the electric field that produces this dipole moment.
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.
where is the vacuum permittivity.
Note that the polarizability 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 -direction can only produce an component in . However, it can happen that an electric field in the -direction, produces a or component in the vector . In this case is described as a tensor of rank 2, which is represented with respect to a given system of axes (frame of reference) by a 33 matrix.