Calculations show how the mysterious “magic numbers” that stabilize nuclear structures emerge naturally from nuclear forces—once these are described with appropriate spatial resolution.

Atomic nuclei have been studied for over a century, yet some of nuclear physics’ most basic questions remain unanswered: How many bound combinations of protons and neutrons, or isotopes, can exist? Where do the limits of nuclear existence lie? How are chemical elements synthetized in the Universe? Clues to solving these puzzles lie in the vast phenomenology of nuclear structure—the measured properties of tens of thousands of nuclear states, their decays, and their reactions. In this bedlam of information, patterns and irregularities in data provide crucial hints. One such irregularity was spotted as early as 1934 [1]: Nuclei containing specific numbers of protons and neutrons (2, 8, 20, 28, 50, 82…) are unexpectedly stable. These “magic numbers” (Fig.