I don't see why that makes a difference. To catch the atom you have to damp its new accelerated momentum, not its original momentum. So the ship will be transla

I don't see why that makes a difference. To catch the atom you have to damp its new accelerated momentum, not its original momentum. So the ship will be translated backwards by a correspondingly accelerated amount. All you're doing is converting a slow relativistic acceleration into an equal and opposite fast relativistic deceleration.