Microscopic Theory of the Photon Recoil of an Atom in a Dielectric

An atom recoils when it undergoes spontaneous decay. In this paper we present a microscopic calculation of the recoil of a source atom imbedded in a dielectric medium. We find that the source atom recoils with the canonical photon momentum $n\hbar k_{0,}$ where $n$ is the index of refraction and $\hbar k_{0}$ is the photon momentum calculated at the source atom atomic frequency $\omega_{0}$. We also show explicitly how the energy is conserved with the photon inside the medium.