RTV, silicone caulk, "Shoe Goo", possibly bonding using a piece of fabric and a solvent to "weld" the crack, epoxy, Gorilla Glue, or any combination of the above. Without knowing what the barrel is made of (ABS, PVC, etc), it's hard to make a definitive recommendation. The surface you are going to repair needs to be squeaky clean. Get some sandpaper and rough up the surface around the crack before you start, otherwise anything you put on it will have a hard time bonding to the plastic.

Usually, the way to keep a crack from getting worse is to "stop drill" it. That is, drill a very small hole at the exact end of the crack (at each end). This removes the concentration of stress and reduces (but not eliminates) the chance that the crack will get bigger just by normal flexing. Of course, if your goal is to seal the crack, stop-drilling just means you have two holes you have to seal as well.

Thank you, pianojuggler! I'll give it a try; maybe even two layers of the glue/fabric patch combo will be good.
Hillsidedinah