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An approach to considering systems with high concentration of correlated carriers and strong long-range electron-phonon interaction and to calculating the high-energy part of the angle-resolved photoemission spectroscopy (ARPES) spectra of such systems is suggested. Joint relaxation of strongly coupled fields - a field of correlated electrons and phonon field - after photoemission is studied to clarify the nature of characteristic features observed in high-energy part of ARPES spectra of cuprate superconductors. Such relaxation occurs in systems with strong predominantly long-range electron-phonon interaction at sufficiently high carrier concentration due to coexistence of autolocalized and delocalized carriers. A simple method to calculate analytically a high-energy part of the ARPES spectrum arising is proposed. It takes advantages of using the coherent states basis for the phonon field in the polaron and bipolaron states. The approach suggested yields all the high-energy spectral features like broad Gaussian band and regions of "vertical dispersion" being in good quantitative agreement with the experiments on cuprates at any doping with both types of carriers. Demonstrated coexistence of autolocalized and delocalized carriers in superconducting cuprates changes the idea about their ground state above the superconducting transition temperature that is important for understanding transport and magnetic properties. High density of large-radius autolocalized carriers revealed may be a key to explanation of charge ordering in doped cuprates.

Relaxation of strongly coupled electron and phonon fields after photoemission and high-energy part of ARPES spectra of cuprates