Understanding how photoexcited electron dynamics depend on electron-electron (e-e) and electron-phonon (e-p) interaction strengths is important for many fields, e.g. ultrafast magnetism, photocatalysis, plasmonics, and others. Here, we report simple expressions that capture the interplay of e-e and e-p interactions on electron distribution relaxation times. We observe a dependence of the dynamics on e-e and e-p interaction strengths that is universal to most metals and is also counterintuitive. While only e-p interactions reduce the total energy stored by excited electrons, the time for energy to leave the electronic subsystem also depends on e-e interaction strengths because e-e interactions increase the number of electrons emitting phonons. The effect of e-e interactions on energy-relaxation is largest in metals with strong e-p interactions. Finally, the time high energy electron states remain occupied depends only on the strength of e-e interactions, even if e-p scattering rates are much greater than e-e scattering rates.
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