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The anisotropy of the electron scattering rate and lifetime$\Gamma_\mathbf{p}=1/\tau_\mathbf{p}$ observed by Angle Resolved PhotoemissionSpectroscopy (ARPES) is evaluated using $s$-$d$ Kondo-Zener exchangeHamiltonian used previously to describe superconducting properties ofhigh-$T_c$ cuprates; for correlation between critical temperature $T_c$ and BCScoupling constant, for example. The performed qualitative analysis reveals that"cold spots" correspond to nodal regions of the superconducting phase where thesuperconducting gap is zero, because the exchange interaction is annulled. Viceversa, "hot spots" and intensive scattering in the normal state correspond tothe regions with maximal gap in the superconducting phase. We have obtainedthat separable kernel postulated in the Fermi liquid approach to the normalphase is the same kernel which is exactly calculated in the framework of the$s$-$d$ approach in the Linear Combination of Atomic Orbital (LCAO)approximation for CuO$_2$ plane. In this sense, at least on the qualitativelevel, the superconducting cuprates are described by one and the sameHamiltonian applied to their superconducting and normal properties. For theoverdopedcuprates having conventional Fermi liquid behavior we derived thecorresponding Stoss-integral for the $s$-$d$ interaction in the framework ofLCAO approximation which is the central result of the present study. Repeatingthe thermodynamics we observed that for optimally doped cuprates$2\Delta_\mathrm{max}/T_c$ is in good agreement with Pokrovsky theory foranisotropic gap superconductors.

The Influence of $s$-$d$ Exchange Interaction on the Gap Anisotropy and  Anisotropy of the Lifetime of Normal State Charge Carriers of Layered  Cuprates