  We present new analytic theory and radiative transfer computations for the
atomic to molecular (HI-to-H2) transitions, and the build-up of atomic-hydrogen
(HI) gas columns, in optically thick interstellar clouds, irradiated by
far-ultraviolet photodissociating radiation fields. We derive analytic
expressions for the total HI column densities for (1D) planar slabs, for beamed
or isotropic radiation fields, from the weak- to strong-field limits, for
gradual or sharp atomic to molecular transitions, and for arbitrary
metallicity. Our expressions may be used to evaluate the HI column densities as
functions of the radiation field intensity and the H2-dust-limited dissociation
flux, the hydrogen gas density, and the metallicity-dependent H2 formation
rate-coefficient and far-UV dust-grain absorption cross-section. We make the
distinction between "HI-dust" and "H2-dust" opacity, and we present
computations for the "universal H2-dust-limited effective dissociation
bandwidth". We validate our analytic formulae with Meudon PDR code computations
for the HI-to-H2 density profiles, and total HI column densities. We show that
our general 1D formulae predict HI columns and H2 mass fractions that are
essentially identical to those found in more complicated (and approximate)
spherical (shell/core) models. We apply our theory to compute H2 mass fractions
and star-formation thresholds for individual clouds in self-regulated galaxy
disks, for a wide range of metallicities. Our formulae for the HI columns and
H2 mass fractions may be incorporated into hydrodynamics simulations for galaxy
evolution.
