  We develop a theory of superconducting pairing in low-density Strontium
titanate due to quadratic coupling of electron density to soft transverse
optical phonons. It leads to static attractive potential between electrons
which decay length scales inversely with soft optical gap. For low electron
densities attraction between electrons is local and transition temperature Tc
was found. The Tc(n) dependence in agreement with experimental data for low
doping was calculated. Next, we show that suppression of Tc by hydrostatic
pressure and strong increase of Tc due to isotop substitution are explained
within our theory.
