concept

magic number

A number of protons or neutrons that fills a nuclear shell, making the nucleus especially stable.
14 related articles

Description

Magic numbers are specific counts of protons or neutrons in an atomic nucleus that result in particularly stable configurations. These numbers — 2, 8, 20, 28, 50, 82, 126 — correspond to completely filled nuclear shells, analogous to the closed electron shells that make noble gases chemically inert. Nuclei with magic numbers have higher binding energies per nucleon, are more abundant in nature, and are more resistant to radioactive decay.

History

The concept of magic numbers was introduced by Maria Goeppert-Mayer and J. Hans D. Jensen in 1949, who independently developed the nuclear shell model and were awarded the Nobel Prize in Physics in 1963 for this work.

How it works

The nuclear shell model describes protons and neutrons as occupying discrete energy levels, or shells, within the nucleus. When a shell is completely filled, the nucleus gains extra stability because the nucleons are tightly bound and the energy gap to the next shell is large. This stability is observed experimentally as a sudden drop in the energy required to remove a nucleon, and as an increase in the abundance of such nuclei in stellar nucleosynthesis.

In practice

Magic numbers are used to predict the stability of superheavy elements, to understand the synthesis of elements in stars, and in nuclear medicine for selecting isotopes with desirable decay properties.

Fun fact

The magic number 32 has been recently observed in experiments with titanium isotopes, suggesting that the traditional shell model may need revision for exotic nuclei far from stability.

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Related articles · 14

Nuclear Theory2026-08-121 minarXiv:2608.12120express
The Quantum Thread Between Nuclear Fragments
When a heavy atomic nucleus splits into two fragments, an invisible quantum thread remains between them. This thread is entanglement: the state of one fragment is instantly linked to the state of the other, as if they were still a single whole. For the first time, physicists have precisely calculated how long and strong such a thread can be, tracing the fission process step by step.
Nuclear Theory2026-08-112 minarXiv:2608.10943express
Calcium-53: One Neutron Changes Everything
The atomic nucleus is not a bag of marbles but an ordered structure where protons and neutrons fill shells, much like electrons in an atom. When a shell is filled, the nucleus becomes especially stable, and the number of particles is called magic. For calcium with 20 protons, the classic magic neutron numbers are 20 and 28.
Nuclear Theory2026-07-312 minarXiv:2607.29081express
Why Technetium and Promethium Are Outcasts of the Periodic Table
In nuclear physics, a puzzle has long been nagging: why among elements lighter than bismuth, only technetium (No. 43) and promethium (No. 61) have no stable isotope at all? All their neighbors in the periodic table can boast at least one long-lived variant, but these two seem to fall out of the general pattern.
Nuclear Experiment2026-07-122 minarXiv:2607.10894express
Lead's Nuclear Shell Gets Stronger
At the center of every atom lies a nucleus — a dense ball of protons and neutrons. These particles don't just crowd together randomly; they fill strict energy levels, much like floors in a skyscraper. When a floor is completely filled, the nucleus becomes especially stable — physicists call this a magic number.
Nuclear Experiment2026-07-101 minarXiv:2607.09551express
Tin-116 Hides Three Shapes in One Nucleus
An atomic nucleus is not just a ball of protons and neutrons. It has a shape, and that shape can change. The tin-116 nucleus was long considered almost perfectly spherical: it has 50 protons — a 'magic' number that usually gives a nucleus spherical symmetry. But a new ultra-precise measurement showed otherwise.
Nuclear Theory2026-07-101 minarXiv:2607.09897express
Is the Shell Closed in Tin-140?
The atomic nucleus is not just a jumble of protons and neutrons. The particles inside arrange themselves in layers, like spectators in a stadium: the lower rows are filled, and each new proton or neutron looks for a spot on a higher tier. When a row is completely filled, the nucleus becomes especially stable — physicists call this a magic number.
Nuclear Theory2026-05-021 minarXiv:2605.01573express
Why the Periodic Table Ends with Lead
The atomic nucleus is not a solid ball but a dense swarm of tiny particles called quarks, glued together by a special glue (the strong force). In light nuclei, such as calcium, this swarm is simply arranged: the numbers of the two quark types, up and down, are almost equal, like the white and black keys in an octave.
Nuclear Theory2026-04-032 minarXiv:2604.02612express
Ghost Nuclei: When Neutrons Run Free
An ordinary atomic nucleus is like a tight ball: protons and neutrons are packed closely together. But some light nuclei, such as helium-6, are different. Two neutrons seem to step aside and form a dilute cloud around the nucleus — called a halo.
Nuclear Theory2026-03-072 minarXiv:2603.07069express
The Magic Number 32: How Nuclear Halves Give Away Their Secret
Inside an atom's nucleus, protons and neutrons stack in layers, like spectators in a packed hall. When a layer is full, the nucleus becomes especially stable — physicists call these 'full rows' magic numbers. One of them, 32, has long been elusive: in nuclei with 32 neutrons, its effect is weak, and in some neighbors it seems absent altogether.
Nuclear Experiment2026-02-271 minarXiv:2602.23776express
Precision Scales for a Stellar Explosion
When matter accumulates on the surface of a neutron star, the ultra-dense remnant of a dead star, an explosion occurs, akin to a giant thermonuclear bomb. In this inferno, nuclei of elements not found on Earth are born within seconds. To understand which ones, their masses must be known with great precision.
Nuclear Experiment2026-01-262 minarXiv:2601.18688express
Bell-Shaped Nucleus: How Niobium-104 Vibrates
A bell doesn't ring with a single note — after being struck, it sounds with several harmonics at once. An atomic nucleus vibrates in much the same way: after a collision, it can oscillate, and these oscillations show up in the emitted gamma rays.
High Energy2017-03-231 minarXiv:1703.08204express
Cosmic Nuclei: What They Tell Us About Their Stars
Like long-distance runners, atomic nuclei, from light helium to heavy iron, race toward us across the Galaxy. At the finish line, in a detector on a high-altitude balloon, we see that heavy nuclei arrive a bit more exhausted than light ones. The difference is small, but it repeats from flight to flight.
High Energy2017-02-081 minarXiv:1702.02352express
Cosmic Rays Break a Simple Law
High above Earth, a satellite flies, and inside it is an instrument the size of a small wardrobe. It catches particles that have been racing through the galaxy for billions of years and finally slam into the detector. Such particles are called cosmic rays, and they bring news of distant stellar explosions.
High Energy2011-01-171 minarXiv:1101.3246express
Cosmic nuclei reveal their energies
High above the Antarctic ice sheet, a balloon with a detector floated for twenty days. It caught tiny particles that had been traveling toward us for millions of years from distant stellar explosions. Now scientists have sorted through the catch and reported how much energy the protons and nuclei of different elements carried.