  We derive an effective Hamiltonian for spin polarons forming in weakly doped
antiferromagnets and demonstrate that the system becomes superconducting at
finite doping. We argue that the driving mechanism which gives rise to
superconductivity is lowering of the kinetic energy by formation of mobile
antiferromagnetic spin bipolarons. That source of attraction between holes is
by definition effective if the antiferromagnetic correlation length is longer
than the radius of forming polarons. Notwithstanding that the attraction is
strongest in the undoped system with long range order, the superconducting
order parameter vanishes when the doping parameter decreases which should be
attributed to emptying the spin polaron band and approaching the Mott insulator
phase. Since the hypothetical normal phase of low density gas of fermions is
unstable against formation of bound hole pairs the intensity of low energy
excitations is suppressed and the pseudogap forms in the underdoped region.
