We report on a novel approach to measure the phase relaxation length and fe
mtosecond lifetime of hot quasiparticles on metal surfaces. A 4 K scanning
tunneling microscope has been used to study the spatial decay of interferen
ce patterns in the local density of states for surface state electrons on A
g(111) and Cu(111). This decay is governed by inelastic; electron-electron
scattering. We find a (E - E-F)(-2) energy dependence of the lifetimes for
both Ag and Cu, and our values are comparable to the corresponding bulk ele
ctron lifetimes. This indicates that electron-electron interaction of hot s
urface state electrons with the Fermi sea is dominated by the underlying bu
lk electrons. [S0031-9007(99)09260-1].