  We have observed 12CO J = 2-1 and J = 1-0, and 13CO J = 1-0 emission in two
regions of HI Self-Absorption (HISA) in Perseus: a small, isolated HISA feature
called the globule and a more extended HISA cloud called the complex. Using
both Large Velocity Gradient and Monte Carlo radiative transfer codes we found
that, in the globule, N(12CO) < 6.0x10^15 cm-2 which, using PDR models, implies
that N(H_2) < 9.9x10^20 cm-2. In the complex we found that the H_2 column
densities ranged from 1.2 - 2.2 x 10^21 cm-2. By comparing the HISA and CO
observations we are able to constrain the physical conditions and atomic gas
fraction (f). In the globule, 8 K < T_spin < 22 K and 0.02 < f < 0.2 depending
on whether the (unknown) gas density is 10^2, 10^3, or 10^4 cm-3. In the
complex, 12 K < T_spin < 24 K, 0.02 < f < 0.05, and we were also able to
constrain the gas density (100 < n < 1200 cm-3). These results imply that the
gas in the HISA clouds is colder and denser than that usually associated with
the atomic ISM and, indeed, is similar to that seen in molecular clouds. The
small atomic gas fractions also imply that there is a significant molecular
component in these HISA clouds, even when little or no 12CO is detected. The
level of 12CO detected and the visual extinction due to dust is consistent with
the idea that these HISA clouds are undergoing a transition from the atomic to
molecular phase.
