Effect of Spinless Impurities on Reduction of $T_c$ in High $T_c$ Superconductors

The notion of a finite pairing interaction energy range suggested by Nam, results in some states at the Fermi level not participating in pairings when there are scattering centers such as impurities. The fact that not all states at the Fermi level participate in pairing is shown to suppress $T_c$ in an isotropic superconductor and destroy superconductivity. We have presented quantitative calculations of $T_c$ reduced via spinless impurities, in good agreements with data of Zn-doped YBCO and LSCO, respectively. It is not necessary to have the anisotropic order parameter, to account for the destruction of superconductivity via non-magnetic impurities.