A theory of the quadratic Stark effect is presented. It is aimed at a description of the hyperfine structure of a free atom in a uniform electric field. A perturbation theory approach is adopted and extensive use is made of effective operators. In spherical tensor form these can be written as the sum of a scalar and a tensor of rank two. Associated scalar and tensor polarizabilities are defined and their properties are discussed. A variety of applications of the theory are given.
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