There isn't one. It varies from airfield to airfield but you won't clear the departure to line up unless the arrival is a set distance from touchdown, eg 2 miles, then only if the departure advises he is ready for an immediate. There is no written minimum separation distance between arrival and departure. Separation is only lost if arrival and departure are on the runway at the same time or if a go around is mis managed
Minimum safe distance between airborne aircraft varies depending on airspace. 3nm in TMA, 5nm enroute, 10 mins in procedural for example...