  We investigate the effect of including diffuse field radiation when modelling
the radiatively driven implosion of a Bonnor-Ebert sphere (BES).
Radiation-hydrodynamical calculations are performed by using operator splitting
to combine Monte Carlo photoionization with grid-based Eulerian hydrodynamics
that includes self-gravity. It is found that the diffuse field has a
significant effect on the nature of radiatively driven collapse which is
strongly coupled to the strength of the driving shock that is established
before impacting the BES. This can result in either slower or more rapid star
formation than expected using the on-the-spot approximation depending on the
distance of the BES from the source object. As well as directly compressing the
BES, stronger shocks increase the thickness and density in the shell of
accumulated material, which leads to short, strong, photo-evaporative ejections
that reinforce the compression whenever it slows. This happens particularly
effectively when the diffuse field is included as rocket motion is induced over
a larger area of the shell surface. The formation and evolution of 'elephant
trunks' via instability is also found to vary significantly when the diffuse
field is included. Since the perturbations that seed instabilities are smeared
out elephant trunks form less readily and, once formed, are exposed to enhanced
thermal compression.
