Visions of the Fog

First, head to The Nucleus, the Children of Atom's base of operations. The first time you visit, you'll find Richter executing two members due to an “issue of loyalty”. Talk to him and if you showed interest in joining the cult, the quest Visions in the Fog will start.

He will then send you to Atom's Spring, a highly-irradiated spring to the west. After drinking, you'll start to hallucinate and see a ghostly figure. Follow the figure until you reach the Children of Atom Shrine. This location will only appear in your map during this sequence. Head to the building and interact with the terminal. Check the side of the nearby locker to find some writings scribbled on it. Examine the terminal again and you'll be able to open the security door. Collect the Mother Idol on the table then travel back to The Nucleus to report to Richter. You can ask him questions. If you agree to take the next step (Longfellow will dislike this decision), tell Richter you and the quest will be complete. You'll also receive the Robes of Atom's Devoted. The next quest for this faction will automatically start as well.

Radioactive Tripping