Well, not sure a bb gun will do it for you. I've had issues with a hawk recently. I pelted him with my son's bb gun. I know i hit him because he jumped. He eventually left, but came back the next day. Hubby hit him with a 12-gauge. We actually saw him flip over backwards. We immediately went to find the body and make sure he was dead and wasn't suffering. Can you believe it - there was no body! About a week later he - or someone who looks exactly like him - was back again. Dang hawk got 3 of my birds. Haven't seen him since, though.
BTW, I did check with DNR before bringing out the big gun. I was told it is legal to shoot a hawk if he is killing livestock. I have a photo of him on top of a dead chicken - so if there is ever a question I have proof. Hawks are beautiful and I hate to shoot at them, but I'm also not a chicken restaurant for them.
I have read suggestions of using those plastic owls also - haven't tried it yet though.