On the other hand, for lower values of $T_{ex}$, values of $R$ as large as 65 are excluded, and the range of acceptable solutions gradually shifts from $R$ $\leq$ 50 at $T_{ex}$ = 7.5 K to values of $R$ $\leq$ 30 at $T_{ex}$ = 4.5 K. Correspondingly, the allowable solutions for the gas density and CO column density per unit line width decrease with decreasing excitation temperature. This trend again is consistent with increasing fractionation in the less well–shielded regions at the periphery of the clouds (see Liszt 2007) for a discussion of this effect in diffuse clouds). These regions dominate the positions found within our mask 1. This result agrees with the behavior found in previous observational studies [e.g. @goldsmith1980; @langer1980; @young1982; @langer1989; @goldsmith2005; @kainulainen2006].

It is not possible to model the mask 1 observations with a fixed value of the [*in situ*]{} carbon monoxide isotopic ratio but rather require that the value of $R$ vary significantly with excitation temperature. We have chosen solutions such that $R$ varies smoothly from a value of 65 at $T_{ex}$ $\geq$ 12.5 K to a value of 30 for $T_{ex}$ = 4.5 K. With this choice of $R$, we find that the gas 