For the determination of the absolute scintillation yields –the number of scintillation photons per unit absorbed energy– for a variety of particles in liquid argon, a series of simultaneous ionization and scintillation measurements were performed. The results verified that scintillation yields for relativistic heavy particles from Ne to La are constant despite their extensive range of linear energy transfer. Such a constant level, called "flat top response" level, manifests the maximum absolute scintillation yield in liquid argon. The maximum absolute scintillation yield is defined by the average energy to produce a single photon, Wph(max) = 19.5±1.0 eV. In liquid xenon, the existence of the same flat top response level was also found by conducting scintillation measurements on relativistic heavy particles. The Wph(max) in liquid xenon was evaluated to be 13.8±0.9 eV using the Wph for 1 MeV electrons, obtained experimentally. The ratio between the two maximum scintillation yields at the flat top response level obtained in liquid argon and xenon is in good agreement with the estimation by way of the energy resolutions of scintillation due to alpha particles in both liquids.