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Yes, but not much. And it does not hang around.
Very tenuous atmospheres are hard to see. They are usually observed via emission of atoms or molecules. In the case of the Moon the easiest gas to observe is atomic Sodium (Na) which is a very efficient scatterer of sunlight - that same yellow glow of street lights.
The following "images" were taken during a lunar eclipse - the Earth blocking the brightest sunlight that would be reflected by the Moon so that the weaker, scattered sunlight from Na atoms can be seen. These measurements were made by Michael Mendillo, Jeffrey Baumgardner, and Jody Wilson (a CU PhD) at the Center for Space Physics, Boston University.
The sodium atmosphere of the Moon as captured during four lunar eclipses.
Average pattern of the Moon’s extended sodium atmosphere at the time of full Moon as observed during four eclipses. The irregular shaped dark area is the sum of the regions close to the Moon not observed during any of the eclipse events shown in the 4 images above. To create an average image, the four events were normalized to the average extrapolated near-surface brightness of 1145 Rayleighs (a crazy unit of intensity used by planetary scientists).
So - what are we looking at here? How does this IMAGE relate to COLUMN DENSITY? See bottom of presentation for reminder of relationships between column density, column mass, surface pressure, etc.
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on image to see larger version
Mendillo's group then fit the average profile of intensity vs. radial distance with a simple power-law function:
And from this then derived the total column density (along a line-of-sight at the limb) of Na atoms in the Moons atmosphere, the surface density n0 and the power-law for the density profile:
Column density - Nlos(limb)= 1.4 x 109 atoms cm-2
Surface density - n = n0r-a where n0= 3 atoms cm-3 ( compare with 1025 cm-3 for Earth's atmosphere) and a=2.4 (that's a little steeper than r squared).
Images of Mercury’s Na emission taken at the McMath-Pierce solar telescope, Kitt Peak National Observatory, Arizona, on three consecutive days: July 20, 21, and 22, 1994. The maximum emission (red) is 4.1 MRayleighs. On these dates the Na is concentrated in high-latitude enhancements and can be detected to a planetary radius above the poles. The morphology changed dramatically from one night to the next.
Comparison of the elements detected in the atmospheres of theMoon and Mercury - Top table has surface densities of the observed gases. In the second table the Cosmic abundance is relative to Hydrogen (fixed at a value of 1012). The Moon and Mercury numbers are column densities and the ratio is the ratio of these column densities.
These are SURFACE NUMBER DENSITIES n0
Below are COLUMN DENSITIES

Note -
Ganymede - UV auroral emission from atomic oxygen (HST) - excited by charged particles bombarding the atmosphere.
Europa - UV emission from atomic oxygen (HST) - again, particle bombardment exciting the atoms.

Yes, Callisto seems to have a carbon dioxide atmosphere. Plus some mystery compound(s) on the surface.
