  Understanding the molecular content of galaxies is a critical problem in star
formation and galactic evolution. Here we present a new method, based on a
Stromgren-type analysis, to calculate the amount of HI that surrounds a
molecular cloud irradiated by an isotropic radiation field. We consider both
planar and spherical clouds, and H_2 formation either in the gas phase or
catalyzed by dust grains. Under the assumption that the transition from atomic
to molecular gas is sharp, our method gives the solution without any reference
to the photodissociation cross section. We test our results for the planar case
against those of a PDR code, and find typical accuracies of about 10%. Our
results are also consistent with the scaling relations found in Paper I of this
series, but they apply to a wider range of physical conditions. We present
simple, accurate analytic fits to our results that are suitable for comparison
to observations and to implementation in numerical and semi-analytic models.
