Spectrum syntheses for three elements (Mg, Na, and Eu) in high-resolution integrated light spectra of the Galactic globular clusters 47 Tuc, M3, M13, NGC 7006, and M15 are presented, along with calibration syntheses of the Solar and Arcturus spectra. Iron abundances in the target clusters are also derived from integrated light equivalent width analyses. Line profiles in the spectra of these five globular clusters are well fit after careful consideration of the atomic and molecular spectral features, providing levels of precision that are better than equivalent width analyses of the same integrated light spectra, and that are comparable to the precision in individual stellar analyses. The integrated light abundances from the 5528 and 5711 A Mg I lines, the 6154 and 6160 A Na I lines, and the 6645 A Eu II line fall within the observed ranges from individual stars; however, these integrated light abundances do not always agree with the average literature abundances. Tests with the second parameter clusters M3, M13, and NGC 7006 show that assuming an incorrect horizontal branch morphology is likely to have only a small (< 0.06 dex) effect on these Mg, Na, and Eu abundances. These tests therefore show that integrated light spectrum syntheses can be applied to unresolved globular clusters over a wide range of metallicities and horizontal branch morphologies. Such high precision in integrated light spectrum syntheses is valuable for interpreting the chemical abundances of globular cluster systems around other galaxies.
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