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We use the Z-V (distance-voltage) spectroscopy in scanning tunneling microscopy to detect the linewidths of empty quantum-well (QW) states acquired from a Pb island grown on the Cu(111) substrate. It is found that the continual broadening of the linewidth can extend to the electronic states near the vacuum level. We apply the Fermi-liquid theory with the Fabry–Pérot mode to analyze the linewidths of the QW states, and obtain the electron-phonon coupling constant, the electron-electron coupling factor, and the product of the electron reflectivities at the surface and interface of the Pb island.