We present a combined soft x-ray and high-resolution vacuum-ultraviolet angle-resolved photoemission spectroscopy study of the electron-overdoped cuprate Pr$_{1.3-x}$La$_{0.7}$Ce$_{x}$CuO$_4$ (PLCCO). Demonstration of its highly two-dimensional band structure enabled precise determination of the in-plane self-energy dominated by electron-electron scattering. Through analysis of this self-energy and the Fermi-liquid cut-off energy scale, we find -- in contrast to hole-doped cuprates -- a momentum isotropic and comparatively weak electron correlation in PLCCO. Yet, the self-energies extracted from multiple oxide systems combine to demonstrate a logarithmic divergent relation between the quasiparticle scattering rate and mass. This constitutes a spectroscopic version of the Kadowaki-Woods relation with an important merit -- the demonstration of Fermi liquid quasiparticle lifetime and mass being set by a single energy scale.
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