The E1 & M1 Spontaneous Decay Rates for an Emitter Inside a Cavity Within a Medium

This short note is based on an early draft of a paper we wrote describing our measurement of the hyperfine quenching rate of the clock transition in Yb-171, see Phys. Rev. Lett. 113 033003 (2014) [1]. We discuss the E1 and M1 spontaneous decay rates of the an emitter residing inside of a real cavity carved out of a vast, uniform, homogenous, isotropic, linear, lossless, dispersionless, and continuous medium. The ratio of the medium rate to vacuum rate is given by Γm/Γ0 = [G(u)]2n3/u, where G(u) = 3u/(2u + 1) is the local field correction factor, n = √ μ/( 0μ0) is the index of refraction of the medium, ( 0) is the electric permitivity of the medium (vacuum), μ(μ0) is the magnetic permeability of the medium (vacuum), and u = / 0 for E1 transitions or u = μ0/μ for M1 transitions. ∗singhj AT nscl DOT msu DOT edu