Unusual Strong-Coupling Effects in the Tunneling Spectroscopy of Optimally Doped and Overdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{O}_{8+\mathit{\delta }}$

Tunneling spectroscopy measurements are reported on single crystals of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ using vacuum tunneling and point-contact methods. A reproducible dip feature in the tunneling conductance is found near $|\mathrm{eV}|=2\mathrm{}\Delta$, observed for both voltage polarities in the best resolved spectra. With overdoping the position of the dip continues to scale with $\Delta$, and its magnitude decreases as $\Delta$ decreases. These results indicate that the dip feature arises from a strong-coupling effect whereby the quasiparticle lifetime is decreased at a characteristic energy of $\mathrm{\sim }2\Delta$, consistent with an electron-electron pairing interaction.