We report on the exciton formation and relaxation dynamics following photocarrier injection in a single-layer two-dimensional lead-iodide perovskite. We probe the time evolution of four distinct exciton resonances by means of time-resolved photoluminescence and transient absorption spectroscopies, and find that at 5,K a subset of excitons form on a $lesssim$ 1-ps timescale, and that these relax subsequently to lower-energy excitons on $sim$ 5--10,ps with a marked temperature dependence over $<$ 100,K. We implement a mode projection analysis that determines the relative contribution of all observed phonons with frequency $leq$50,cm$^{-1}$ to inter-exciton nonadiabatic coupling, which in turn determines the rate of exciton relaxation. This analysis ranks the relative contribution of the phonons that participate in polaronic lattice distortions to the exciton inter-conversion dynamics and thus establishes their role in the nonadiabatic mixing of exciton states, and this in the exciton relaxation rate.
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