Experimental studies of the positron annihilation induced Auger electron (PAES) spectra from the Fe-Cu alloy surfaces with quantum-dot like Cu nanoparticles embedded in Fe show that the PAES signal from Cu increase rapidly as the concentration of Cu is enhanced by vacuum annealing. These measurements indicate that almost 75% of positrons that annihilate with core electrons due so with Cu even though the surface concentration of Cu as measured by EAES is only 6%. This result suggests that positrons become localized at sites at the surface containing high concentration of Cu atoms before annihilation. These experimental results are investigated theoretically by performing calculations of the "image-potential" positron surface states and annih...