Combining the equilibrium approximation (t → ∞ and the collective limit (N → ∞ and thus C 0 J→K → 1), the collective equilibrium FGR (E-FGR) rate constants can be obtained analytically. These E-FGR expressions can either be obtained from applying the two abovementioned approximations, or directly taking the t → ∞ limit of Eq. 29 (note that when 1/t → 0 the last line in Eq. 29 becomes the delta function), with the details provided in Appendix. C. The final expressions for these well-known E-FGR rate constants are