Coupling of Low Energy Electrons in Optimally Doped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+}$ δ to an Optical Phonon Mode Abstract J.D. Rameau, H.-B. Yang, G.D. Gu, and P.D. Johnson Condensed Matter Physics and Materials Science Department Brookhaven National Laboratory Upton, NY 11973 (Dated: December 6, 2018) Laser based photoemission with photons of energy 6 eV is used to examine the fine details of the very low energy electron dispersion and associated dynamics in the nodal region of optimally doped Bi2212. A ”kink” in the dispersion in the immediate vicinity of the Fermi energy is associated with scattering from an optical phonon previously identified in Raman studies. The identification of this phonon as the appropriate mode is confirmed by comparing the scattering rates observed experimentally with the results of calculated scattering rates based on the properties of the phonon mode. arXiv:1002.1990v1 [cond-mat.supr-con] 9 Feb 2010 1