Neutron peak in the extended-saddle-point model of high-temperature superconductors

An explanation is proposed of the maximum at 41 meV in the inelastic spin-flip neutron scattering from ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }},$ based on the extended-saddle-point model developed by the author in his previous works. It is shown that for appearance of the maximum in the imaginary part of the spin susceptibility a close proximity of the Fermi energy to the extended saddle point is necessary. The energy of the maximum is then close to $2{\Delta }_{\max }$ in agreement with experiment. Theoretical and experimental evidence concerning the energy of the extended saddle point (flat region) is discussed. Different limiting cases are calculated. A proof is given within the present model that interaction in the final state is small, and hence, no collective modes are formed. A general discussion of the experimental situation is presented.