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The term “magic” is rarely associated with science, yet it found a significant context in the early 1930s when researchers began to identify specific atomic nuclei that exhibited remarkable stability. These nuclei, characterized by particular counts of protons and neutrons—dubbed “magic numbers” after the insightful physicist Eugene Wigner—led to an intriguing pursuit among scientists to unravel the enigma of their stability.
This quest was driven by the understanding that grasping the nature of these magic numbers could enable scientists to predict various properties of atomic nuclei, including their mass and longevity, and explain which proton-neutron combinations yield successful nuclei formations.
In 1949, two independent breakthroughs emerged concurrently. In the United States, physicist Maria Goeppert Mayer unveiled a theoretical model, while in Germany, a group led by J. Hans D. Jensen reached a similar conclusion. Their findings unveiled the underlying principles of nuclear stability, earning both physicists a notable share of the 1963 Nobel Prize in Physics.
As contemporary nuclear scientists, we build upon the seminal work of Mayer and Jensen, investigating the properties of nuclei that exist for mere fractions of a second, continuing the legacy of exploring these magic numbers.
Understanding Atomic Stability
The atom is composed of a nucleus at its center, made up of protons and neutrons—collectively termed nucleons—and surrounded by electrons that orbit this nucleus. Nobel laureate Niels Bohr contributed significantly to this understanding by conceptualizing electron arrangements in specific energy levels or “shells,” with each shell capable of holding a limited number of electrons.
Chemical reactivity arises from interactions between these electrons; according to Bohr’s model, if an electron shell is not fully occupied, the likelihood increases for atoms to engage in sharing or exchanging electrons, thus spurring chemical reactions.
Elements known as noble gases are exceptional in this regard, as their fully filled electron shells render them largely non-reactive. This led to speculation in the 1930s about whether protons and neutrons similarly occupy organized shells within the nucleus. However, a conclusive demonstration of this remained elusive for over a decade, leaving scientists to simplify their models of nuclei as a uniform system rather than as discrete protons and neutrons.
The Emergence of Magic Numbers
The pivotal moment arrived in 1949 when Goeppert Mayer and Jensen introduced the nuclear shell model. Their framework posited that protons and neutrons occupy defined orbits, akin to electrons, with an additional characteristic known as spin—a phenomenon similar to that of a spinning top. By incorporating these elements into their calculations, they successfully aligned their models with empirical observations.
Through experimentation, they discerned that nuclei featuring certain magic numbers of protons or neutrons demonstrated unusual stability, adhering to their nucleons more firmly than previously anticipated, echoing the inertness of noble gases with electrons.
Scientists have identified magic numbers as 2, 8, 20, 28, 50, 82, and 126 for both protons and neutrons. A nucleus exhibiting a magic number is characterized by a full orbit, rendering it less reactive. Take the element tin, for instance, which possesses a magic number of 50 protons and commonly manifests with 70 neutrons in its most prevalent isotope. This unique status affords tin the distinction of having the largest number of stable isotopes.
Helium, with its two protons and two neutrons, ranks as the lightest “doubly magic” nucleus. Its neutron and proton counts align with magic numbers, resulting in exceedingly strong binding forces that prevent the addition of further nucleons, leading to instability. Similarly, lead-208 represents the heaviest stable nucleus, bearing magic numbers of 82 protons and 126 neutrons.
Natural Stability of Nuclei
The nuclear shell structure imparts insights into the distribution and abundance of elements both on Earth and throughout the cosmos. Oxygen, especially the isotope oxygen-16—present in significant abundance in the human body—is a prime example.
Oxygen-16, with its eight protons and eight neutrons, possesses a stable nucleus forged in nuclear processes within stars prior to the formation of the solar system. Its status as a doubly magic nucleus allowed it to remain relatively unreactive, thus enhancing its availability as a key component for life as we know it.
In her Nobel lecture, Maria Goeppert Mayer discussed research she underwent with physicist Edward Teller, seeking to elucidate the variation in element formation in stars. They identified that the disparities in elemental abundances traced back to nuclei with magic numbers of neutrons, leading to the publication of findings on stellar nucleosynthesis in 1957.
Current researchers continue to apply the concepts derived from the nuclear shell model as they explore new phenomena in nuclear science. Facilities such as the Facility for Rare Isotope Beams are at the forefront of generating exotic nuclei to investigate their properties in relation to their stable counterparts.
At these institutions, scientists create new isotopes by accelerating stable isotopes at impressive speeds and bombarding them against targets, meticulously selecting the rarest fragments for study. Interestingly, recent discoveries suggest that the magic numbers may differ in exotic nuclei, indicating that the exploration of these mysterious numbers persists, even after this groundbreaking work from 75 years ago.
Source
phys.org