Benzo dying out

[bpeesy]

I have a 300e 160k miles. I just replaced the alternator. I've just replaced the alternator, but for some reason it doesn't seem to charge the battery. When I jump start it, it starts fine, but once i unhook the jumper cables, I can see the head lights start to dim. Question: Once it's started, shouldnt the alternator keep all lights bright even if the battery is dead? Please help!! Thank you