Well at work in the last month alone, we've quoted or rebuilt 5
My own 3800 is included too.
All were diagnosed with excessive oil bearing clearance. A couple were because of the oil pump, most were because of a conn rod bearing spinning though. My own was diagnosed with a conn rod bearing noise due to using too light (thin/slippery) of an oil for the oil pump to handle!
First thing to do is to have the oil pressure sender checked (or replaced).
Secondly, switch to a slightly heavier oil to see if noise goes away. If it does, either the oil pump is weak or you've got conn rod bearing problems.