In Part I we discuss accumulating experimental evidence related to thestructure and origin of the bosonic spectral function in high-temperaturesuperconducting (HTSC) cuprates at and near optimal doping. Some globalproperties of the spectral function, such as number and positions of peaks, areextracted by combining optics, neutron scattering, ARPES and tunnellingmeasurements. These methods give convincing evidence for strong electron-phononinteraction (EPI) with the coupling constant between 1-3 in cuprates nearoptimal doping. Here we clarify how these results are in favor of theEliashberg-like theory for HTSC cuprates near optimal doping. In Part II wediscuss some theoretical ingredients - such as strong EPI, strong correlations- which are necessary to explain the experimental results related to themechanism of d-wave pairing in optimally doped cuprates. These comprise theMigdal-Eliashberg theory for EPI in strongly correlated systems which give riseto the forward scattering peak. The latter is further supported by the weaklyscreened Madelung interaction in the ionic-metallic structure of layeredcuprates. In this approach EPI is responsible for the strength of pairing whilethe residual Coulomb interaction (by including spin fluctuations) triggers thed-wave pairing.
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