In this paper, we have proved that the non -magnetic doping can also produce pair-breaking effect in the Anderson lattice model of the high-Tc cuprate superconductorts due the energy dependence of the order parameter. In the case of dilute doping, we have obtained a linear decreasing behavior of Tc with the increasing of non-magnetic impurity concentration in agreement with experimental results. Furthermore, we have also calculated the influence of doping on the superconducting energy gap in the density of states. The results indicate that the decreasing of the gap at T = 0 is much slower than the dropping of Tc with the increasing of non-magnetic impurities. Therefore, the gapless region may not appear before the system transforms into the normal state in different from the conventional BCS superconductors with magnetic impurities.
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