  We study the thermal evolution of UV-irradiated atomic cooling haloes using
high-resolution three-dimensional hydrodynamic simulations. We consider the
effect of H^- photodetachment by Ly{\alpha} cooling radiation trapped in the
optically-thick cores of three such haloes, a process which has not been
included in previous simulations. H^- is a precursor of molecular hydrogen, and
therefore, its destruction can diminish the H2 abundance and cooling. Using a
simple high-end estimate for the trapped Ly{\alpha} energy density, we find
that H^- photodetachment by Ly{\alpha} decreases the critical UV flux for
suppressing H2-cooling by up to a factor of \approx 5. With a more conservative
estimate of the Ly{\alpha} energy density, we find the critical flux is
decreased only by ~15-50 percent. Our results suggest that Ly{\alpha} radiation
may have an important effect on the thermal evolution of UV-irradiated haloes,
and therefore on the potential for massive black hole formation.
