Molecular clouds form from the atomic phase of the interstellar medium. However, characterizing the transition between the atomic and the molecular interstellar medium (ISM) is a difficult observational task. Here we address cloud formation processes by combining HSIA with molecular line data. One scenario proposed by numerical simulations is that the column density probability density functions (N-PDF) evolves from a log-normal shape at early times to a power-law-like shape at later times. In this paper, we study the cold atomic component of the giant molecular filament GMF38a (d=3.4 kpc, length$sim230$ pc). We identify an extended HISA feature, which is partly correlated with the 13CO emission. The peak velocities of the HISA and 13CO observations agree well on the eastern side of the filament, whereas a velocity offset of approximately 4 km s$^{-1}$ is found on the western side. The sonic Mach number we derive from the linewidth measurements shows that a large fraction of the HISA, which is ascribed to the cold neutral medium (CNM), is at subsonic and transonic velocities. The column density of the CNM is on the order of 10$^{20}$ to 10$^{21}$ cm$^{-2}$. The column density of molecular hydrogen is an order of magnitude higher. The N-PDFs from HISA (CNM), HI emission (WNM+CNM), and 13CO (molecular component) are well described by log-normal functions, which is in agreement with turbulent motions being the main driver of cloud dynamics. The N-PDF of the molecular component also shows a power law in the high column-density region, indicating self-gravity. We suggest that we are witnessing two different evolutionary stages within the filament. The eastern subregion seems to be forming a molecular cloud out of the atomic gas, whereas the western subregion already shows high column density peaks, active star formation and evidence of related feedback processes.
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