We present an analysis of moderately high resolution optical spectra obtained for the sight line to CD-23 13777, an O9 supergiant that probes high velocity interstellar gas associated with the supernova remnant W28. Absorption components at both high positive and high negative velocity are seen in the interstellar Na I D and Ca II H and K lines toward CD-23 13777. The high velocity components exhibit low Na I/Ca II ratios, suggesting efficient grain destruction by shock sputtering. High column densities of CH+, and high CH+/CH ratios, for the components seen at lower velocity may be indicative of enhanced turbulence in the clouds interacting with W28. The highest positive and negative velocities of the components seen in Na I and Ca II absorption toward CD-23 13777 imply that the velocity of the blast wave associated with W28 is at least 150 km/s, a value that is significantly higher than most previous estimates. The line of sight to CD-23 13777 passes very close to a well-known site of interaction between the SNR and a molecular cloud to the northeast. The northeast molecular cloud exhibits broad molecular line emission, OH maser emission from numerous locations, and bright extended GeV and TeV gamma-ray emission. The sight line to CD-23 13777 is thus a unique and valuable probe of the interaction between W28 and dense molecular gas in its environs. Future observations at UV and visible wavelengths will help to better constrain the abundances, kinematics, and physical conditions in the shocked and quiescent gas along this line of sight.
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