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.
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