Phonons and superconductivity in ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$

Detailed neutron scattering measurements have been made for selected phonons for ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$. The temperature dependence of the linewidths indicates large anharmonic effects particularly for the oxygen modes. The superconductivity induced change in width below ${\mathit{T}}_{\mathit{c}}$ of the two highest energy oxygen modes is found to be nearly 2% of the phonon energy suggesting a large electron phonon coupling.