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Millimeter observations of ^12^CO and ^ 13^CO in the diffuse region around ζ Ophiuchi. Using the 15-m SEST submillimeter telescope, we have observed ^12^CO and^13^CO in the diffuse molecular cloud lying close to ζ Oph, andsearched for C^18^O, CS, CN and HCO^+^ at 2 particular positions. The^12^CO(1-0) measurements show lines of the order of a few Kelvins inregions where the ^13^CO data seem to indicate diffuse material. Wemeasure ^12^CO(1-0)/^13^CO(1-0) ratios of the order of 30 toward thepositions of peak CO emission and lower limits of this ratio up to 65 inmore diffuse regions. We compare these data with the predictions of achemical model which solves consistently the thermal and chemicalequilibrium of an interstellar cloud and computes the submillimeter andmillimeter emergent line intensities of various atomic and moleculartransitions. For the positions of peak CO emission, the model andobservations agree satisfactorily for an isobaric cloud of pressurep=7.5x10^4^Kcm^-3^ or an isochoric cloud of density n(H_2_)=2500cm^-3^permeated by an UV radiation field enhanced by a factor of 5 compared tothe standard interstellar radiation field (ISRF) of Mathis et al. (???).The excitation properties of CO are consistent with a visual magnitudeof the order of 1.2. The upper limit found for CS is also reproduced ifthe gas phase sulfur abundance is lower than the recent HSTdeterminations.
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