Island of stability

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. Its theoretical existence is attributed to stabilizing effects of predicted "magic numbers" of protons and neutrons in the superheavy mass region.
Several predictions have been made regarding the exact location of the island of stability, though it is generally thought to center near copernicium and flerovium isotopes in the vicinity of the predicted closed neutron shell at N = 184. These models strongly suggest that the closed shell will confer further stability towards fission and alpha decay. While these effects are expected to be greatest near atomic number Z = 114 and N = 184, the region of increased stability is expected to encompass several neighboring elements, and there may also be additional islands of stability around heavier nuclei that are doubly magic. Estimates of the stability of the nuclides within the island are usually around a half-life of minutes or days; some optimists propose half-lives on the order of millions of years.
Although the nuclear shell model predicting magic numbers has existed since the 1940s, the existence of long-lived superheavy nuclides has not been definitively demonstrated. Like the rest of the superheavy elements, the nuclides within the island of stability have never been found in nature; thus, they must be created artificially in a nuclear reaction to be studied. Scientists have not found a way to carry out such a reaction, for it is likely that new types of reactions will be needed to populate nuclei near the center of the island. Nevertheless, the successful synthesis of superheavy elements up to Z = 118 with up to 177 neutrons demonstrates a slight stabilizing effect around elements 110 to 114 that may continue in heavier isotopes, consistent with the existence of the island of stability.

Introduction

Nuclide stability

The composition of a nuclide is defined by the number of protons Z and the number of neutrons N, which sum to mass number A. Proton number Z, also named the atomic number, determines the position of an element in the periodic table. The approximately 3300 known nuclides are commonly represented in a chart with Z and N for its axes and the half-life for radioactive decay indicated for each unstable nuclide., 251 nuclides are observed to be stable ; generally, as the number of protons increases, stable nuclei have a higher neutron–proton ratio. The last element in the periodic table that has a stable isotope is lead, with stability generally decreasing in heavier elements, especially beyond curium. The half-lives of nuclei also decrease when there is a lopsided neutron–proton ratio, such that the resulting nuclei have too few or too many neutrons to be stable.
The stability of a nucleus is determined by its binding energy, higher binding energy conferring greater stability. The binding energy per nucleon increases with atomic number to a broad plateau around A = 60, then declines. If a nucleus can be split into two parts that have a lower total energy, it is unstable. The nucleus can hold together for a finite time because there is a potential barrier opposing the split, but this barrier can be crossed by quantum tunneling. The lower the barrier and the masses of the fragments, the greater the probability per unit time of a split.
Protons in a nucleus are bound together by the strong force, which counterbalances the Coulomb repulsion between positively charged protons. In heavier nuclei, larger numbers of uncharged neutrons are needed to reduce repulsion and confer additional stability. Even so, as physicists started to synthesize elements that are not found in nature, they found the stability decreased as the nuclei became heavier. Thus, they speculated that the periodic table might come to an end. The discoverers of plutonium considered naming it "ultimium", thinking it was the last. Following the discoveries of heavier elements, of which some decayed in microseconds, it then seemed that instability with respect to spontaneous fission would limit the existence of heavier elements. In 1939, an upper limit of potential element synthesis was estimated around element 104, and following the first discoveries of transactinide elements in the early 1960s, this upper limit prediction was extended to element 108.

Magic numbers

As early as 1914, the possible existence of superheavy elements with atomic numbers well beyond that of uranium—then the heaviest known element—was suggested, when German physicist Richard Swinne proposed that superheavy elements around Z = 108 were a source of radiation in cosmic rays. Although he did not make any definitive observations, he hypothesized in 1931 that transuranium elements around Z = 100 or Z = 108 may be relatively long-lived and possibly exist in nature. In 1955, American physicist John Archibald Wheeler also proposed the existence of these elements; he is credited with the first usage of the term "superheavy element" in a 1958 paper published with Frederick Werner. This idea did not attract wide interest until a decade later, after improvements in the nuclear shell model. In this model, the atomic nucleus is built up in "shells", analogous to electron shells in atoms. Independently of each other, neutrons and protons have energy levels that are normally close together, but after a given shell is filled, it takes substantially more energy to start filling the next. Thus, the binding energy per nucleon reaches a local maximum and nuclei with filled shells are more stable than those without. This theory of a nuclear shell model originates in the 1930s, but it was not until 1949 that German physicists Maria Goeppert Mayer and Johannes Hans Daniel Jensen et al. independently devised the correct formulation.
The numbers of nucleons for which shells are filled are called magic numbers. Magic numbers of 2, 8, 20, 28, 50, 82 and 126 have been observed for neutrons, and the next number is predicted to be 184. Protons share the first six of these magic numbers, and 126 has been predicted as a magic proton number since the 1940s. Nuclides with a magic number of each—such as ¹⁶O, ¹³²Sn, and ²⁰⁸Pb —are referred to as "doubly magic" and are more stable than nearby nuclides as a result of greater binding energies.
In the late 1960s, more sophisticated shell models were formulated by American physicist William Myers and Polish physicist Władysław Świątecki, and independently by German physicist Heiner Meldner. With these models, taking into account Coulomb repulsion, Meldner predicted that the next proton magic number may be 114 instead of 126. Myers and Świątecki appear to have coined the term "island of stability", and American chemist Glenn Seaborg, later a discoverer of many of the superheavy elements, quickly adopted the term and promoted it. Myers and Świątecki also proposed that some superheavy nuclei would be longer-lived as a consequence of higher fission barriers. Further improvements in the nuclear shell model by Soviet physicist Vilen Strutinsky led to the emergence of the macroscopic–microscopic method, a nuclear mass model that takes into consideration both smooth trends characteristic of the liquid-drop model and local fluctuations such as shell effects. This approach enabled Swedish physicist Sven Nilsson et al., as well as other groups, to make the first detailed calculations of the stability of nuclei within the island. With the emergence of this model, Strutinsky, Nilsson, and other groups argued for the existence of the doubly magic nuclide , rather than ³¹⁰Ubh which was predicted to be doubly magic as early as 1957. Subsequently, estimates of the proton magic number have ranged from 114 to 126, and there is still no consensus.

Discoveries

Interest in a possible island of stability grew throughout the 1960s, as some calculations suggested that it might contain nuclides with half-lives of billions of years. They were also predicted to be especially stable against spontaneous fission in spite of their high atomic mass. It was thought that if such elements exist and are sufficiently long-lived, there may be several novel applications as a consequence of their nuclear and chemical properties. These include use in particle accelerators as neutron sources, in nuclear weapons as a consequence of their predicted low critical masses and high number of neutrons emitted per fission, and as nuclear fuel to power space missions. These speculations led many researchers to conduct searches for superheavy elements in the 1960s and 1970s, both in nature and through nucleosynthesis in particle accelerators.
During the 1970s, many searches for long-lived superheavy nuclei were conducted. Experiments aimed at synthesizing elements ranging in atomic number from 110 to 127 were conducted at laboratories around the world. These elements were sought in fusion-evaporation reactions, in which a heavy target made of one nuclide is irradiated by accelerated ions of another in a cyclotron, and new nuclides are produced after these nuclei fuse and the resulting excited system releases energy by evaporating several particles. These reactions are divided into "cold" and "hot" fusion, which respectively create systems with lower and higher excitation energies; this affects the yield of the reaction. For example, the reaction between ²⁴⁸Cm and ⁴⁰Ar was expected to yield isotopes of element 114, and that between ²³²Th and ⁸⁴Kr was expected to yield isotopes of element 126. None of these attempts were successful, indicating that such experiments may have been insufficiently sensitive if reaction cross sections were low—resulting in lower yields—or that any nuclei reachable via such fusion-evaporation reactions might be too short-lived for detection. Subsequent successful experiments reveal that half-lives and cross sections indeed decrease with increasing atomic number, resulting in the synthesis of only a few short-lived atoms of the heaviest elements in each experiment; as of 2022, the highest reported cross section for a superheavy nuclide near the island of stability is for ²⁸⁸Mc in the reaction between ²⁴³Am and ⁴⁸Ca.
Similar searches in nature were also unsuccessful, suggesting that if superheavy elements do exist in nature, their abundance is less than 10⁻¹⁴ moles of superheavy elements per mole of ore. Despite these unsuccessful attempts to observe long-lived superheavy nuclei, new superheavy elements were synthesized every few years in laboratories through light-ion bombardment and cold fusion reactions; rutherfordium, the first transactinide, was discovered in 1969, and copernicium, eight protons closer to the island of stability predicted at Z = 114, was reached by 1996. Even though the half-lives of these nuclei are very short, the very existence of elements heavier than rutherfordium is indicative of stabilizing effects thought to be caused by closed shells; a model not considering such effects would forbid the existence of these elements due to rapid spontaneous fission.
Flerovium, with the expected magic 114 protons, was first synthesized in 1998 at the Joint Institute for Nuclear Research in Dubna, Russia, by a group of physicists led by Yuri Oganessian. A single atom of element 114 was detected, with a lifetime of 30.4 seconds, and its decay products had half-lives measurable in minutes. Because the produced nuclei underwent alpha decay rather than fission, and the half-lives were several orders of magnitude longer than those previously predicted or observed for superheavy elements, this event was seen as a "textbook example" of a decay chain characteristic of the island of stability, providing strong evidence for the existence of the island of stability in this region. Even though the original 1998 chain was not observed again, and its assignment remains uncertain, further successful experiments in the next two decades led to the discovery of all elements up to oganesson, whose half-lives were found to exceed initially predicted values; these decay properties further support the presence of the island of stability. However, a 2021 study on the decay chains of flerovium isotopes suggests that there is no strong stabilizing effect from Z = 114 in the region of known nuclei, and that extra stability would be predominantly a consequence of the neutron shell closure. Although known nuclei still fall several neutrons short of N = 184 where maximum stability is expected, and the exact location of the center of the island remains unknown, the trend of increasing stability closer to N = 184 has been demonstrated. For example, the isotope ²⁸⁵Cn, with eight more neutrons than ²⁷⁷Cn, has a half-life almost five orders of magnitude longer. This trend is expected to continue into unknown heavier isotopes in the vicinity of the shell closure.