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





