Neutron scattering and the B-1g phonon in the cuprates

The momentum-dependent line shape of the out-of-phase oxygen vibration as m easured in recent neutron-scattering measurements is investigated. Starting from a microscopic coupling of the phonon vibration to a local crystal fie ld, the phonon line shift and broadening is calculated as a function of tra nsferred momentum in the superconducting state of YBa2Cu3O7. The absolute m agnitude of the shift is obtained as a function of momentum and is found to be in excellent agreement with experiment. It is shown that the anisotropy of the density of states, superconducting energy gap, and the electron-pho non coupling are all crucial in order to explain these experiments.