# Islands of insight in the nuclear chart (2022)

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B. Alex Brown

• Michigan State University, East Lansing, MI 48824, USA

&bullet; Physics 3, 104

A one of a kind radioactive beam experiment yields new insight for neutron-rich nuclei.

Like the shell model for atoms, which identifies which elements are volatile and which are inert, the nuclear shell model has guided our understanding of nuclear properties. Certain “magic number” landmarks associated with “inert” nuclei have dominated the nuclear landscape for over 50 years. As the more exotic neutron-rich nuclei are being studied, however, one finds that nuclear properties associated with the traditional landmarks can suddenly disappear. The reason is that both the relative importance of the average (“mean field”) and residual nuclear interactions, as well as the mean field itself, change.

One of the regions of the chart of nuclides where this breakdown occurs is at $N=20$ ( $N$ is the number of neutrons) and it is called the “island of inversion” (Fig. 1). The island of inversion is now known to be part of an archipelago of “islands of shell breaking” associated with the magic neutron numbers $8$, $14$, $20$, $28$, and $40$. In order to accurately account for the effects of interactions and understand how the shell model breaks down, theorists need high-precision spectroscopic data for the isotopes in these regions. Now, in a paper appearing in Physical Review Letters, an international collaboration (Wimmer et al.) presents precise spectroscopic measurements of the neutron-rich element magnesium- $32$, which lies in the much explored island of inversion at $N=20$ [1]. The measurements, which are the first of their kind and were performed at the REX-ISOLDE radioactive beam facility at CERN, address a long standing question about the low-lying energy spectrum of this nucleus and provide important information about the collective effects of nuclear interactions.

A Google search for “island of inversion” yields about $1000$ results, almost all of which refer to a group of neutron-rich nuclei in a region of the nuclear chart centered around sodium- $31$, which has $11$ protons and $20$ neutrons (stable sodium has $12$ neutrons). The term goes back to a paper by Warburton, Becker, and Brown [2] in which they studied the unusual features for nuclei in this mass region with the nuclear shell model. The magic numbers quoted above are derived from the nuclear shell model, the foundation of which is the appearance of gaps in the spectrum of single-particle energies that arise from the average (mean-field) interaction of one nucleon with all of the other nucleons. To draw an analogy with atomic physics, like the highly stable elements with closed electronic orbitals, the single-particle energy levels of “magic number” nuclei are filled with protons or neutrons (fermions that obey the Pauli principle) up to an energy just below the gaps. The energies of the first excited states in the nuclei with magic numbers are relatively high compared with those of neighboring nuclei since a proton or neutron must be excited to states across the gap. In contrast, inside the “islands of shell breaking” the energy of the first excited state drops and no longer shows any indication of the magic numbers found for the nuclei closer to stability. This archipelago holds the secret to many puzzling microscopic features of nuclear structure.

Current experiments with radioactive beams of isotopes are concentrated on studying the properties of neutron-rich nuclei out to the neutron drip line (the bottom-right edge of the chart of nuclei), where the islands of inversion lie. Inside the neutron drip line, the nuclei beta decay toward stability with lifetimes characteristic of the weak interaction, on the order of $10-3$ seconds. With this long lifetime, the masses, excited states, and decay properties of these nuclei can be studied in some detail when they can be produced. Beyond the neutron drip line, the nuclei are unstable to neutron decay and have a lifetime characteristic of the strong interaction, on the order of $10-20$ seconds. The experimental study of these nuclei is limited to observation of the neutrons from their decay.

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With these general remarks in mind, one can look at the region of the nuclear chart probed by the REX-ISOLDE experiment. Two configurations for magnesium- $32$ are displayed for $20$ neutrons (Fig. 1, upper left); the closed-shell configuration A, and configuration B consisting of two neutrons excited from the $0d3/2$ and $1s1/2$ orbitals into the $0f7/2$ and $1p3/2$ orbitals across the $N=20$ shell gap, making a two-particle, two-hole state. Near the shell gaps, configurations of type B usually appear as excited states and are sometimes called pairing vibrations. The energy of these states is lower than twice the shell gap due to the pairing correlations between the particles and between the holes.

In this island of inversion, configurations of the type B become the ground state rather than the excited state. This change is sudden, with B forming an excited state in silicon- $34$ ( $20$ neutrons and $14$ protons) and then becoming the ground state for magnesium- $32$ ( $20$ neutrons and $12$ protons). Two factors contribute to this sudden change: a gradual reduction in the spherical $N=20$ shell gap as one approaches the neutron drip line at fluorine ( $9$ protons), and the configuration for the protons suddenly changing from “closed shell” in silicon- $34$ to “open shell” in magnesium- $32$, which leads to stronger proton-neutron correlations and deformation.

Many experiments have studied the states in the island of inversion with configurations similar to B. The work at REX-ISOLDE provides the first confirmation that the predicted coexisting excited state A exists and shows some of its properties, providing a much sought after example of an explicit disappearance of shell closure. It is the first experiment of its type where a radioactive beam of magnesium-30 reacts with a target loaded with radioactive tritium. Two neutrons from the tritium target are transferred to magnesium- $30$, leaving magnesium- $32$ and a proton that is detected. The shell-model configuration of magnesium- $30$ is shown in Fig 1. When two neutrons are added to make a final state with spin and parity $Jπ=0+$, they can go into the $0d3/2,1s1/2$ orbitals, making state A, or into the $0f7/2,1p3/2$ orbitals, making state B. (The labels $nℓj$ here are those associated with a wave function from a spherical potential with radial quantum number $n$, orbital quantum number $ℓ$, and total angular momentum $j$). The REX-ISOLDE team observed two $0+$ states: the ground state and an excited state at $1.06MeV$. The energy of the excited state, which is presumed to correspond to configuration A, is lower than any of the theoretical predictions discussed in this paper. The simplest estimate based on the theoretical extrapolation for the energy of A together with the measured energy of the ground state B is $2.3MeV$ [3]. Understanding the reason for this disagreement with theory will be crucial for improving the many-body models as they are used to predict the properties of nuclei in even more neutron-rich nuclei.

The cross sections for the population of these two states give indirect information on the details of their structure. It is inferred that there is mixing between A and B, and that the $1p3/2$ component of B is larger than expected. This may be a signal that the single-particle energy of the $1p3/2$ orbital, which is about one $MeV$ above that of the $0f7/2$ orbital in $34Si$, is dropping relative to $0f7/2$ as one approaches the neutron drip line. This is a feature of loosely bound orbitals with $ℓ=1$ [4] and may be important for understanding why the neutron drip line suddenly changes from $1$6 neutrons for the oxygen isotopes ( $8$ protons) to greater than $22$ neutrons for the fluorine isotopes ( $9$ protons).

With the advent of experiments like the one reported by the REX-ISOLDE collaboration, the likes of which were inconceivable even a few years ago, we are beginning to gain a deeper understanding of the complexity of the collective effects that shape the nuclear landscape. The reasons for the existence of the islands of shell breaking are complex, and much needs to be explored. In addition, new magic numbers may appear near the neutron drip line [5] (for example, $24O$ shows evidence that $N=16$ is a magic number). Apart from problems of intrinsic interest to nuclear physics, several questions in astrophysics also hinge crucially on our understanding of nuclear stability. Ultimately, an important goal is to be able to confidently predict the properties of neutron-rich nuclei and their role in the stellar nucleo-synthesis of elements. Such an objective will require a coherent program of theoretical, computational, and experimental advances.

## References

1. K. Wimmer et al., Phys. Rev. Lett. 105, 252501 (2010)
2. E. K. Warburton, J. A. Becker, and B. A. Brown, Phys. Rev. C 41, 1147 (1990)
3. B. A. Brown and W. A. Richter, Phys. Rev. C 74, 034315 (2006)
4. I. Hamamoto, Phys. Rev. C 76, 054319 (2007)
5. T. Otsuka, R. Fujimoto, Y. Utsuno, B. A. Brown, M. Honma, and T. Mizusaki, Phys. Rev. Lett. 87, 082502 (2001)

Alex Brown is a Professor in the Department of Physics and Astronomy at Michigan State University and a member of the nuclear theory group at the National Superconducting Cyclotron Laboratory. His research focuses on theoretical models for nuclear structure and their applications to experiments with rare isotope beams, nuclear astrophysics, and fundamental symmetries in the nucleus. He received his Ph.D. in 1974 from Stony Brook University. In 2008 he was recognized as an Outstanding Referee by the American Physical Society.

#### Discovery of the Shape Coexisting ${0}^{+}$ State in ${}^{32}\mathrm{Mg}$ by a Two Neutron Transfer Reaction

K. Wimmer et al.

Phys. Rev. Lett. 105, 252501 (2010)

Published December 13, 2010

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## FAQs

### What is an island in physics? ›

In nuclear physics, the island of stability is a predicted set of isotopes of superheavy elements that may have considerably longer half-lives than known isotopes of these elements. It is predicted to appear as an "island" in the chart of nuclides, separated from known stable and long-lived primordial radionuclides.

### How do you read a chart of nuclides? ›

So potassium has 19 protons. And then calcium has 20 and scandium is another one 21 protons and so

### What is the line of stability? ›

The line of stable nuclides down the center of the valley of stability is known as the line of beta stability. The sides of the valley correspond to increasing instability to beta decay (β or β+). The decay of a nuclide becomes more energetically favorable the further it is from the line of beta stability.

### How many nuclides are there? ›

252 stable and about 87 unstable (radioactive) nuclides exist naturally on Earth, for a total of about 339 naturally occurring nuclides on Earth.

### How do islands work? ›

When the tops of the volcanoes appear above the water, an island is formed. While the volcano is still beneath the ocean surface, it is called a seamount. Oceanic islands can form from different types of volcanoes. One type forms in subduction zones, where one tectonic plate is shifting under another.

### How does an island get power? ›

Most islands are well endowed with one or more renewable energy source — rivers, waterfalls, wind, sunshine, biomass, wave power, geothermal deposits — yet virtually all remain heavily or entirely reliant on imported fossil fuels to produce electricity and power transport.

### What is Fe on chart? ›

Iron is a chemical element with symbol Fe and atomic number 26.

### How do you read binding energy graphs? ›

Binding energy graph | Nuclei | Physics | Khan Academy - YouTube

### What are the 3 types of stability explain? ›

• Stable Equilibrium.
• Unstable Equilibrium.
• Metastable Equilibrium.

### What are the 3 states of stability? ›

States of stability
• Stable equilibrium.
• Neutral buoyancy.
• Unstable equilibrium.
23 Sept 2020

### Why is the island of stability important? ›

Elements in this so-called island of stability could act as powerful nuclear fuel for future fission-propelled space missions. They might also be exhibit useful new chemical properties.

### What is the largest atom possible? ›

Atomic radii vary in a predictable way across the periodic table. As can be seen in the figures below, the atomic radius increases from top to bottom in a group, and decreases from left to right across a period. Thus, helium is the smallest element, and francium is the largest.

### Is there a limit to the size of an atom? ›

Under most definitions the radii of isolated neutral atoms range between 30 and 300 pm (trillionths of a meter), or between 0.3 and 3 ångströms. Therefore, the radius of an atom is more than 10,000 times the radius of its nucleus (1–10 fm), and less than 1/1000 of the wavelength of visible light (400–700 nm).

### Why are the islands important? ›

Islands are threatened hotspots of diversity that concentrate unique cultural, biological and geophysical values, and they form the basis of the livelihoods of millions of islanders. Second, islands are paradigmatic places of human–environment relationships.

### Why is Australia not an island? ›

According to Britannica, an island is a mass of land that is both “entirely surrounded by water” and also “smaller than a continent.” By that definition, Australia can't be an island because it's already a continent.

### What are the types of islands? ›

The six primary types of islands include the following: continental, tidal, barrier, oceanic, coral, and artificial. Each type varies in terms of how they are formed. These islands are formed and shaped by different processes, such as volcanic eruptions, sediment deposition, or glacial retreats.

### How do private islands get water? ›

Reverse osmosis is the most common method of water desalination on private islands. Purification is done with the help of semi-permeable membranes, through which water molecules can flow, but not the salt. The membrane in good condition will remove up to 99% of the brine.

### Where does Hawaii get their electricity? ›

Electricity can be generated from a variety of resources. Some are fossil fuels such as oil and coal. Over 80 percent of all the energy used in Hawaii for electricity, surface and air transportation comes from imported fossil fuels, mostly oil and some coal.

### Is it expensive to own an island? ›

Prices can range from approximately US \$500,000 for a 0.5 to 1 acre undeveloped private island up to US \$10 to \$12 million for larger 60 to 70 acre islands, often with some infrastructure and development in place such as existing homes, docks, roads and airstrips.

### What is an island answer in short? ›

island, any area of land smaller than a continent and entirely surrounded by water. Islands may occur in oceans, seas, lakes, or rivers. A group of islands is called an archipelago.

### Is an island a tectonic plate? ›

When tectonic plates are pushed and pulled apart, they form volcanoes, causing eruptions when the plates are pulled apart. As hot magma rises from the crevasses created, it eventually builds up to form islands.

### What is a Magnetic island physics? ›

A magnetic island is a closed magnetic flux tube (cf. Flux surface), bounded by a separatrix, isolating it from the rest of space. Its topology is toroidal.

### What is the island Class 9? ›

The two major island groups in India are the Lakshadweep islands and the Andaman and Nicobar islands. The Andaman and Nicobar islands are present in the Bay of Bengal and are an India archipelago. In this group of islands there are around 300 islands.

### Why is Australia not an island? ›

According to Britannica, an island is a mass of land that is both “entirely surrounded by water” and also “smaller than a continent.” By that definition, Australia can't be an island because it's already a continent.

### Is America an island? ›

North America is a continent in the Northern Hemisphere and almost entirely within the Western Hemisphere. It is bordered to the north by the Arctic Ocean, to the east by the Atlantic Ocean, to the southeast by South America and the Caribbean Sea, and to the west and south by the Pacific Ocean.

### Was Hawaii created from a volcano? ›

The Hawaiian Islands were formed by volcanic activity.

The Hawaiian Emperor seamount chain is a well-known example of a large seamount and island chain created by hot-spot volcanism. Each island or submerged seamount in the chain is successively older toward the northwest.

### Is Iceland going to split? ›

No, it will not. Only because if it could happen, it probably would have occurred in those millions of years since it was formed. Iceland is being pulled apart at a rate of about 2.5 cm each year, which is quite a bit, but our volcanic eruptions help by filling up the gaps that could form.

### Are islands floating? ›

No they do not float, islands are the tops of underwater mountains. The base is at the bottom of the ocean. They may be the result of a volcano, or just an accumulation of coral or the remainder of an ancient mountain around which the sea level rose.

### What are the 4 types of magnetic? ›

There are four basic types of magnetism that a material can have: superconducting, diamagnetic, paramagnetic, and lastly ferromagnetic. Superconducting materials are strongly repelled from permanent magnets. Diamagnetic materials are weakly repelled by permanent magnets.

### What are the 3 types of magnetic? ›

There are three types of magnets: permanent magnets, temporary magnets, and electromagnets. Permanent magnets emit a magnetic field without the need for any external source of magnetism or electrical power.

### What are the 3 main magnetic elements? ›

Since then only three elements on the periodic table have been found to be ferromagnetic at room temperature—iron (Fe), cobalt (Co), and nickel (Ni).

### What are the 2 islands of India? ›

The Andaman and Nicobar Islands lie to the South-East of the Indian mainland in the Bay of Bengal.

### Why is the island important? ›

Islands are key foundations for coral reef ecosystems. Wherever there is a land mass in the open ocean, ocean circulation patterns change. Nutrients from the deeper, colder water rise up to the surface, creating the conditions for sea life to thrive. This is known as the Island Mass Effect.

### Which is the largest island in the world class 4? ›

The Largest Islands in the World
• Greenland (836,330 sq miles/2,166,086 sq km) ...
• New Guinea (317,150 sq miles/821,400 sq km) ...
• Borneo (288,869 sq miles/748,168 sq km) ...
• Madagascar (226,756 sq miles/587,295 sq km) ...
• Baffin (195,928 sq miles/507,451 sq km) ...
• Sumatra (171,069 sq miles/443,066 sq km)

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