Higher Polarizability of the Helium Atom

The electric dipole moment induced in a helium atom by a uniform electric field F can be expressed by αF+⅙γF3+···, where α is the well-known electric polarizability, and γ is a higher polarizability describing the initial deviation from a linear polarization law, and is sometimes called the hyperpolarizability. An experimental determination of γ has been made by observation of the Kerr electro-optical effect in helium. The result is γ = (2.6±0.4) × 10−38 esu. An analytic calculation has been carried out by a perturbation procedure, with the results γ = 1.57×10−38 esu, α = 0.2027 Å3. The observed value of α is 0.2051 Å3. Approximate calculations of the quadrupole moment of helium induced by an electric field and a field gradient are also described.