The HI Probability Distribution Function and the Atomic-to-Molecular
  Transition in Molecular Clouds
  We characterize the column density probability distributions functions (PDFs)
of the atomic hydrogen gas, HI, associated with seven Galactic molecular clouds
(MCs). We use 21 cm observations from the Leiden/Argentine/Bonn Galactic HI
Survey to derive column density maps and PDFs. We find that the peaks of the HI
PDFs occur at column densities ranging from ~1-2$\times 10^{21}$ cm$^2$
(equivalently, ~0.5-1 mag). The PDFs are uniformly narrow, with a mean
dispersion of $\sigma_{HI}\approx 10^{20}$ cm$^2$ (~0.1 mag). We also
investigate the HI-to-H$_2$ transition towards the cloud complexes and estimate
HI surface densities ranging from 7-16 $M_\odot$ pc$^{-2}$ at the transition.
We propose that the HI PDF is a fitting tool for identifying the HI-to-H$_2$
transition column in Galactic MCs.
