What is the issue you’re trying to solve or the thing you’re hoping to improve?
If you’re dealing with a wandering POI from day to day, or when it sustains a little bump or that sort of thing, a barrel band is probably what you want to try.
If instead you are looking to make some improvement to group size, stiffening the barrel with carbon fiber to reduce vibration may be beneficial. For best results, you want to seat the carbon fiber into the receiver if possible but it looks like many folks are seeing improvements by just sleeving the exposed portion.
To bond it, Loctite 638 bearing compound works great if the gap is less than 0.010” (0.020” difference on the diameter), or a 2-part epoxy if the gap is larger.