Dependence of the energy gap on T_c: Absence of scaling in the copper oxide superconductors

High-resolution electron energy loss spectroscopy has been used to investigate the energy gap (2Δ) in a series of oxygen-doped Bi₂Sr₂CaCu₂O_8+δ single crystals with critical temperatures ranging from 71 to 94 K. Temperature dependent energy loss spectra demonstrate that 2Δ develops sharply for T<T_c in all of the samples, and that the magnitude of 2Δ exceeds significantly 3.5kT_c. Furthermore, 2Δ decreases only slightly as T_c is reduced from 94 to 71 K, and thus, 2Δ/kT_c increases systematically as T_c decreases. These results indicate that T_c may be reduced significantly by strong inelastic scattering in the current copper oxides.