bare hole Green’s function, gives the minimum value of quasiparticle energy equal to $\omega _{h,\min }=-2.6\tau $ [@kab], for a typical value of copper-copper AFM exchange constant $J=0.7\tau $. Here $\tau $ is a constant of the effective oxygen-oxygen hopping via an intervening copper site (note that our unit of energy is twice that of Ref. [@kab] $\tau =2t$). As to the value of the small polaron mean field band bottom it turns out to be substantially lower than $\omega _{h,\min }$, $\Omega _{{\bf k}}=-3.17\tau $, for the same value of $J/\tau $. So we may conclude that important local correlations are lost in SCBA when we start from the bare hole operators.

Secondly, we shall show that a small polaron represents the elementary hole excitation much more better than a bare hole dressed by magnons within the framework of SCBA. This will be manifested by a relatively great intensity of a quasiparticle peak in our calculation.

Finally, the mean field spectrum $\Omega _{{\bf k}}$ of the simplest small spin polaron explicitly depends on the state of the antiferromagnetic background . In the case of long range order state, $\Omega _{{\bf k}}$ demonstrates a flat band region close to the 