Visions in the Fog

Visions in the Fog is a main quest $$==Quick walkthrough==

Detailed walkthrough
Upon speaking with Grand Zealot Richter outside of the Nucleus. He explains that to join the Children of Atom, the Sole Survivor must drink water from the sacred spring.

Journey to the spring and drink the water by interacting with it. One will then enter a hallucinatory state and a ghostly, dark figure (known as the Mother of the Fog) covered in black smoke will appear. Following the figure will eventually lead the player character to a shrine, which is guarded by feral ghouls.

After eliminating the feral ghouls, enter the shrine. The marker will point to an icon located behind a maglocked security door that can only be opened with a password-protected terminal. To get the terminal's password, read the note on the shelf, which hints at the password's location on the side of a locker near a periodic table. Retrieve the icon and bring it back to Richter, who will allow the Survivor to join the Children of Atom and enter the Nucleus.