Dependence of the energy gap on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">T</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>: Absence of scaling in the copper oxide superconductors

High-resolution electron energy loss spectroscopy has been used to investigate the energy gap (2\ensuremath{\Delta}) in a series of oxygen-doped ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ single crystals with critical temperatures ranging from 71 to 94 K. Temperature dependent energy loss spectra demonstrate that 2\ensuremath{\Delta} develops sharply for T${\mathit{T}}_{\mathit{c}}$ in all of the samples, and that the magnitude of 2\ensuremath{\Delta} exceeds significantly 3.5${\mathit{kT}}_{\mathit{c}}$. Furthermore, 2\ensuremath{\Delta} decreases only slightly as ${\mathit{T}}_{\mathit{c}}$ is reduced from 94 to 71 K, and thus, 2\ensuremath{\Delta}/${\mathit{kT}}_{\mathit{c}}$ increases systematically as ${\mathit{T}}_{\mathit{c}}$ decreases. These results indicate that ${\mathit{T}}_{\mathit{c}}$ may be reduced significantly by strong inelastic scattering in the current copper oxides.