How Many Megasieverts to Kill Goat heads and Other Satanic Weeds?

If you have ever stepped on one of these that migrated into the house on your shoes,  you know why my wife calls them Satan's weed.  More realistically, I need a soil sterilizer that is to KillzAll  what the cat and the mouse in Mouse Hunt were to a real cat and mouse.  Something that kills for years on end. Nerve gas for weeds.