  The atomic-to-molecular hydrogen (H/H2) transition has been extensively
studied as it controls the fraction of gas in a molecular state in an
interstellar cloud. This fraction is linked to star-formation by the
Schmidt-Kennicutt law. While theoretical estimates of the column density of the
H I layer have been proposed for static photodissociation regions (PDRs),
Herschel and well-resolved ALMA (Atacama Large Millimeter Array) observations
have revealed dynamical effects in star forming regions, caused by the process
of photoevaporation. We extend the analytic study of the H/H2 transition to
include the effects of the propagation of the ionization front, in particular
in the presence of photoevaporation at the walls of blister H II regions, and
we find its consequences on the total atomic hydrogen column density at the
surface of clouds in the presence of an ultraviolet field, and on the
properties of the H/H2 transition. We solved semi-analytically the differential
equation giving the H2 column density profile by taking into account H2
formation on grains, H2 photodissociation, and the ionization front propagation
dynamics modeled as advection of the gas through the ionization front. Taking
this advection into account reduces the width of the atomic region compared to
static models. The atomic region may disappear if the ionization front velocity
exceeds a certain value, leading the H/H2 transition and the ionization front
to merge. For both dissociated and merged configurations, we provide analytical
expressions to determine the total H I column density. Our results take the
metallicity into account. Finally, we compared our results to observations of
PDRs illuminated by O-stars, for which we conclude that the dynamical effects
are strong, especially for low-excitation PDRs.
