  The linear growth rate of the Rayleigh-Taylor instability (RTI) at ionization
fronts is investigated via perturbation analysis in the limit of incompressible
fluids. In agreement with previous numerical studies is found that absorption
of ionizing radiation inside the HII region due to hydrogen recombinations
suppresses the growth of instabilities. In the limit of a large density
contrast at the ionization front the RTI growth rate has the simple analytical
solution n=-nur+(nur^2+gk)^(1/2), where nur is the hydrogen recombination rate
inside the HII region, k is the perturbation's wavenumber and g is the
effective acceleration in the frame of reference of the front. Therefore, the
growth of surface perturbations with wavelengths lambda >> lambda_{cr} = 2\pi
g/nur^2 is suppressed by a factor (lambda_{cr}/4lambda)^(1/2) with respect to
the non-radiative incompressible RTI. Implications on stellar and black hole
feedback are briefly discussed.
