Polarization of vacuum in a hydrogen-like relativistic atom: Hyperfine structure

Abstract

An analysis is made of the contribution of the polarization of vacuum to the hyperfine splitting of the ground state of a hydrogen-like atom. An expression for the correction to the energy is obtained as an explicit function of the parameter Zα. The final expression derived in terms of generalized hypergeometric functions and their derivatives is a function of the particle mass ratio in orbit and in a vacuum loop, and is therefore valid for both ordinary and muonic atoms. Various asymptotic forms are also given.