To Prime the Pump by A. Bertram Chandler

The provided text details Lieutenant John Grimes' experiences as an officer aboard the Survey Service cruiser Aries, initially on a routine deep-space mission. His journey takes an unexpected turn when the ship is diverted to El Dorado, an exclusive and highly automated planet inhabited by an elite class of "aristocrats." Grimes becomes entangled with Princess Marlene von Stolzberg, a powerful figure on El Dorado, and discovers the planet's shocking secret: its inhabitants are unable to reproduce naturally. The narrative then follows Grimes as he navigates the complex social dynamics of El Dorado, participating in their unusual customs and rituals, including a violent hunt and a bizarre voodoo ceremony. Ultimately, the ship's Surgeon Commander provides an explanation for El Dorado's fertility issues, hinting that the "Old Religion" practiced by some inhabitants, involving sacrifice, may be the key to their reproductive success, which is confirmed at the story's conclusion with news of widespread births after the Aries's visit.