The Epicurean Argument for Fear of Death

The Epicureans are notorious for thinking that death is nothing to fear. They have several arguments for this but could you maybe tell us at least one of the arguments they give and talk about whether it's a good argument or not? Well they think, yes you're quite right, they think that the fear of death is something that affects a large majority of people and they think it's a painful fear like other kinds of fears. But fortunately death isn't something we should worry about. Why not? Because when we die there isn't such a thing as a non-physical immortal soul that hangs around somewhere. So our death is the absolute end of our existence. That seems like it should