Pressure Physics,\
    Troitsk, Moscow region, 142092, Russia.
- |
    Institute for Materials Science,\
    Krjijanovskogo 3, Kiev, 252180, Ukraine
- |
    Russian Research Center, Kurchatov Institute,\
    Kurchatov sq.46, Moscow, 123182, Russia.
- |
    Institute for High Pressure Physics,\
    Troitsk, Moscow region, 142092, Russia.
author:
- 'A.F. Barabanov'
- 'R.O. Kuzian'
- 'L.A. Maksimov'
- 'E.Zasinas'
title: 'Dynamics of Small Spin Polaron in the Three-Band Model of Two-Dimensional Spherically Symmetric Antiferromagnet.'
---

Introduction
============

Up to date much theoretical work has been devoted to the problem of a hole motion in two dimensional (2D) s=1/2 quantum antiferromagnet (AFM) [@dago]. The important question is whether a hole injected in the undoped ground state behaves like a quasiparticle (QP). This problem is mainly investigated within the framework of self-consistent Born approximation (SCBA) for the $t-J$ model [@varm; @KLR; @horsch; @liu; @tj6; @plak] and Kondo-lattice [@Prel]. There are rather few works devoted to the three-band Hubbard model or the Emery model [@em; @emrei] that is more realistic for CuO$_2$ planes in high- $T_c$ superconductors (HTSC). For the $
t-J$ model it was shown that the spectral density function $A_h({\bf k}
,\omega )$ of a doped hole revealed a QP peak of intensity $Z_{{\bf k}
}\approx 