Within the deeper craters of the dark side of the moon, would it be possible to have an 'atmosphere' of any gas within this crater?

There is no such thing as the dark side of the Moon, or at least there is no area that is always dark. The Moon has a side that always faces Earth. When we see a full moon, the far side is dark, but when we have a new moon, the far side is fully illuminated by the sun. In other words, one lunar day is equal to approximately one Earth month.

Supposing that part of a crater was always in the dark, there might be a very thin atmosphere, but not much since the Moon’s gravity is fairly weak.

From my research the moon already has a an extremely thin atmosphere, which contributes to it moon glow. If one goes deeper inside a crater on the dark side of the moon, atmospheric pressures may possibly increase, especially with the “outgassing” phenomenon, allowing other gasses that favor higher pressures to remain within these craters. Presumably Earth formed it’s atmosphere in a similar way? Unlike the Moon, Earth was able to develop a strong enough magnetic field to protect its growth.

http://www.space.com/18067-moon-atmosphere.html

Brian Ghilliotti

I agree with @jwalt Their is no dark side of the moon , but there is a far side of the moon that is always not looking at Earth. There might be H3 and water at the poles in a hole.

You could maintain an atmosphere in a moon crater by building a dome over it. Otherwise any gases will escape into space.

No. As far as we know, the deeper craters on the moon are filled with strawberry jam, which does not qualify as atmosphere.