On the Theory of Shallow Impurity States

A theoretical investigation is made of the shallow states of an impurity interacting weakly with polar phonons. An effective mass equation is found containing besides usual terms corrections including the renormalization of the electron mass, deviations from the parabolic dispersion law (due to phonons), and a contact term arising from the interaction of the electron with the fluctuations of the phonon field. Physical interpretation of the contact interaction is given. Analogy between a polaron and an electronic polaron is recalled to draw some conclusions concerning electron‐electron correlation. The shift of the lowest energy level of a hydrogen‐like impurity is calculated.