If you want to do this the correct way, you should put the barrel in the lathe and machine the part where you are going to install the sleeve, machine it down to the diameter where it is grooved, probably around .500”. Then make a tight fitting sleeve slightly larger then the outside of the diameter of the barrel it self and slightly longer then the barrel. Then press fit the sleeve on the end of the barrel. Then put the barrel back in the lathe, and machine the sleeve to the size of the barrel.