  High redshift quasars at z>6 have masses up to ~$10^9$ M$_\odot$. One of the
pathways to their formation includes direct collapse of gas, forming a
supermassive star, precursor of the black hole seed. The conditions for direct
collapse are more easily achievable in metal-free haloes, where atomic hydrogen
cooling operates and molecular hydrogen (H2) formation is inhibited by a strong
external UV flux. Above a certain value of UV flux (J_crit), the gas in a halo
collapses isothermally at ~$10^4$ K and provides the conditions for
supermassive star formation. However, H2 can self-shield, reducing the effect
of photodissociation. So far, most numerical studies used the local Jeans
length to calculate the column densities for self-shielding. We implement an
improved method for the determination of column densities in 3D simulations and
analyse its effect on the value of J_crit. This new method captures the gas
geometry and velocity field and enables us to properly determine the
direction-dependent self-shielding factor of H2 against photodissociating
radiation. We find a value of J_crit that is a factor of two smaller than with
the Jeans approach (~2000 J_21 vs. ~4000 J_21). The main reason for this
difference is the strong directional dependence of the H2 column density. With
this lower value of J_crit, the number of haloes exposed to a flux >J_crit is
larger by more than an order of magnitude compared to previous studies. This
may translate into a similar enhancement in the predicted number density of
black hole seeds.
