CHARGE SCREENING IN CLASSICAL SPINOR ELECTRODYNAMICS

We study the problem of a fixed source of charge Z in electromagnetic interaction with a classical Dirac field. We find that partially screened solutions with energy less than the energy associated with pure Coulomb configurations (with zero spinor field) exist for Z > Z(c), where Z(c), is the usual value at which the eigenvalue from the (linear) Dirac equation reaches the lower continuum. In contrast with the corresponding problem of coupling to a scalar (Klein-Gordon) field, such solutions do not arise for Z0 < Z < Z(c), where Z0 is the value at which the Dirac equation has a zero eigenvalue, so that nonlinear effects of the kind considered here do not impair the usual interpretation of the Dirac equation as a single-particle equation for Z < Z(c).