Calculations for atomic nuclei up to a mass number of ten
“It was in 1935 that Dr Yukawa unveiled the original idea for his ‘meson theory’. In his theory, the positively charged protons and uncharged neutrons that constitute an atomic nucleus are held together by strong ‘nuclear forces’ produced when ‘mesons’ are exchanged between the protons and neutrons. The basic theory that explains what constitutes a nucleus or what kinds of forces exist in the nucleus has been known for more than 70 years. However, no-one has been successful in deriving an equation that can accurately calculate all the characteristics of nuclei on the basis of the basic theory of nuclear forces,” says Nakatsukasa.
The basic theory of nuclear forces is still based on the Yukawa model. The complexity of calculations based on the basic theory, however, increases rapidly with increasing mass number — the total number of protons and neutrons constituting a nucleus. For example, a deuterium nucleus, which has a mass number of two (one proton and one neutron), can be simulated using basic theory for the nuclear forces with parameters such as lifetime, mass, shape, hardness and how the nucleus splits or fuses. “The calculation becomes extremely difficult, however, when the number increases to three, because the amount of calculation increases dramatically every time the number increases,” says Nakatsukasa.
Why is simulation of the nucleus so complex? “There are three main reasons. Firstly, the atomic nucleus must be modeled on the basis of the quantum mechanics used to describe the microscopic world. Secondly, the calculations involve ‘anti-symmetrization’ of the wave function, because protons and neutrons belong to the group of particles known as ‘Fermi’ particles. Thirdly, the long-range Coulomb force acts only on positively charged protons, and the nuclear forces act as an attractive force when atomic particles come within a distance of 10–15 m and a repulsive force when they get closer. In other words, the forces in the nucleus are a complex mixture of long-range, short-range, attractive and repulsive forces, so the calculation of forces in the nucleus becomes very complex.”
A research group from the US recently succeeded in deriving the characteristics of dozens of atomic nuclei up to a mass number of ten, using a supercomputer to compute the basic theory of nuclear forces. “Theory predicts the existence of about 10,000 kinds of nucleus. The calculation based on the conventional theory, however, is available for only 1% or less of these nuclei.” RIKEN’s Next-Generation Supercomputer scheduled for completion by 2012 and capable of an incredible 1016 calculations per second could greatly assist these calculations. “Even using the Next-Generation Supercomputer, however, only a relatively few new nuclei can be calculated.”
In search of the equation that explains all atomic nuclei
There is another obstacle to Nakatsukasa’s goal: the current equations based on the basic theory of nuclear forces are unable to explain the characteristics of all nuclei. “To make this possible, we need another calculation approach. Thus, we started developing a calculation method based on the ‘density functional equation’. We can accurately calculate all the characteristics of nuclei using a functional equation that describes the distribution of protons and neutrons. The density functional equation has been proved mathematically, but has yet to be established with high accuracy. Thus, many researchers working on the theory of the atomic nucleus around the world are working hard to find a rigorous functional equation.”
The current equation is still useful, however, and can be used to derive at least some of the characteristics of nuclei. “The equation can predict the mass of a nucleus with an accuracy of 0.1%. But to predict the structure and reaction accurately, the accuracy of the mass prediction must be refined by an order of magnitude.”
Nakatsukasa and the members of his laboratory are endeavoring to derive an equation with this level of prediction accuracy. “In addition to an experimental approach, we can use a purely theoretical approach. We can use an equation based on the basic theory of nuclear forces to calculate the characteristics of the nuclei up to a mass number of about ten. We can create a virtual nucleus using a supercomputer and deform the nucleus by applying an external force to create various nuclei with various density distributions and then calculate their characteristics. Thus, we are striving to derive a density functional equation that can completely describe the relationship between the density distribution of nuclei and their characteristics.”
Predicted by theory and verified using RIKEN’s Radioactive Isotope Beam Factory
“The substances around us are composed of atoms with basically stable nuclei. A stable nucleus consists of almost the same number of protons and neutrons. About 300 stable nuclei are known to us, and conventional nuclear theory has been established mainly on the basis of experimental data on these stable nuclei. Yet about 10,000 atomic nuclei are predicted to exist theoretically. Most, however, are unstable, consisting of different numbers of protons and neutrons, and they decay, emitting radiation.”
In the 1980s, scientists successfully created beams of unstable nuclei using particle accelerators, allowing experiments to be conducted to examine the characteristics of unstable nuclei. Over time, scientists discovered various phenomena that could not be explained by the conventional theory. For example, the atomic nucleus, which had been accepted as being spherical by conventional theory, is in fact shaped more like a rugby ball. Scientists also found nuclei consisting of protons and neutrons with different density distributions, and discovered a new type of radiation involving the emission of multiple kinds of particle.
So far, about 3,000 nuclei have been created using accelerators. In 2007, RIKEN started operating its Radioactive Isotope Beam Factory (RIBF), which is capable of creating the world’s most intense beam of any of about 4,000 unstable nuclei ranging from hydrogen to uranium. Most conventional facilities are able to create only a limited range of nuclear beams and therefore do not provide sufficient information to derive general characteristics. The RIBF, however, is capable of creating a beam of any nucleus, and thus provides detailed information. Although scientists in Europe and the US are planning to develop a new generation of accelerators, it will be at least seven or eight years before they can conduct experiments similar to those being performed today at the RIBF.
“Conducting research in collaboration with the experimental group at the RIBF has many advantages. We obtain the latest experimental data, which can be used for theoretical research; conversely, we can propose experiments based on theoretical approaches. I want to use the density functional equation to predict in advance the characteristics of the thousand or so unknown atomic nuclei that could be created by the RIBF in the future. I would like to make suggestions to the experimental groups, such as ‘This nucleus seems to have these interesting characteristics.’”
Using the density functional equation, Nakatsukasa predicts that the dysprosium-160 nucleus, consisting of 66 protons and 94 neutrons, and similar nuclei become mango-shaped when revolving at high speed. Another theoretical group in Japan predicts that zirconium-80, consisting of 40 protons and 40 neutrons, will become rice-ball-shaped in a quasi-stable state. These theoretical predictions have not yet been verified experimentally, but the RIBF provides the means to do so.
Pursuing supernova explosions and the origin of elements
A major goal for research using the RIBF is to probe the origins of matter and elements. Most elements, from iron (atomic number 26) to uranium (atomic number 92), are considered to have been created when a supernova, the final explosive stage of a star, expels huge amounts of unstable heavy elements, which then decay into lighter and lighter elements.
Scientists are planning to use the RIBF to create such heavy unstable elements for the first time to examine their characteristics. “In collaboration with researchers in astrophysics, we are planning to theoretically predict the characteristics of nuclei with high accuracy, thereby reproducing the processes in a supernova and the creation of elements.”
Although the mechanism of supernovae has yet to be properly clarified, the mechanism of creation and the origin of elements appear to be well understood through experiments in astronomy and at the RIBF, and through theoretical studies on the nucleus and astrophysics. Studies in these fields will lead to the verification of new theories using experimental and astronomical observation data, and to improvements in the accuracy of the density functional equation.
“Our ultimate goal is to predict the characteristics of all atomic nuclei; that is, to find a way to calculate all of their characteristics based on the numbers of protons and neutrons that constitute the nucleus.”
Generating energy from unused atomic nuclei
“Within ten years, I think we will discover a density functional equation that allows us to predict the characteristics of all atomic nuclei with accuracy ten times higher than that of the conventional equation. I think a more accurate prediction of the mechanism of how an atomic nucleus splits into fragments will greatly contribute to solving energy and resource problems,” says Nakatsukasa.
Current atomic power plants use uranium-235 (235U) as a fuel source because it is readily fissile. However, 235U is a limited resource, accounting for only 0.7% of all naturally occurring uranium. The remainder is primarily uranium-238 (238U), which contains three more neutrons than 235U. “The nuclei of 238U and other heavy elements around it in the periodic table are fissile, but we do not yet know how to use them effectively as a fuel source.”
In modern nuclear power plants, low-energy neutrons are forced to collide with 235U nuclei to cause nuclear fission. Other heavy elements, such as 238U, have not yet been used as a fuel source in this way. Yet these heavy nuclei can also undergo nuclear fission when bombarded with high-energy neutrons. For example, some scientists are proposing a new type of nuclear power plant in which fission is induced by bombardment of high-energy neutrons produced by an accelerator. There are great hopes for this new type of nuclear power plant because it has several advantages, including the ability to use previously unused heavy elements as a fuel source, and its high safety because nuclear fission ceases when the accelerator is stopped. Unfortunately, these proposals have yet to be put into practice.
“Various experiments have been conducted with 238U to examine the conditions required for the fuel to be used and the energy level of the bombarding neutrons required to cause the nuclei of the fuel atoms to split effectively. A mere theoretical approach seems unable to provide new data. However, we may be able to propose a new type of nuclear fission reactor by taking advantage of nuclear theory to accurately predict the mechanism of the nuclear fission in atomic nuclei produced in nuclear reactors, such as neptunium, americium and curium, which have so far been disregarded.”
Is it feasible to convert high-level radioactive waste to stable nuclei to produce rare-earth elements?
Some of the nuclei produced by the nuclear fission of 235U in nuclear reactors have very long half-lives—the period over which half of a sample undergoes radioactive decay. As a result, the inclusion of such nuclei in high-level radioactive waste poses a major problem for disposal. “If these unstable, long-life radioactive nuclei are bombarded by protons or neutrons, or even light (photons) of a specific energy, they may split into smaller nuclei that have a shorter half-life, or into stable nuclei that do not emit radiation.”
Even now, some reactions are known to be able to convert long-life radioactive nuclei into short half-life species. “However, the probability of the occurrence of the reactions is so small that disposing of all high-level radioactive waste in this way is too costly and time-consuming to be practical. Furthermore, experimental attempts to find a reaction with a higher probability of occurrence are also costly and time-intensive. I think nuclear theory will help to find a reaction with a higher probability in the near future. We may be able to find a reaction that creates rare-earth elements as well as convert high-level radioactive nuclei into stable species.” Rare-earth elements are essential materials for light-emitting diodes, fuel cells and high-tech equipment. Thus, the creation of rare-earth elements in this way could be good news not only for resource-poor Japan, but also for the entire world.
Advancing nuclear physics by leaps and bounds using the RIBF
Nakatsukasa believes that a new nuclear theory with high accuracy will be established within ten years, and that the theory will contribute to technological development in various areas, but he is also excited about a completely different scenario.
“Experiments based on the RIBF might provide experimental data that could be completely different from the results predicted by the latest nuclear theory. This could be of great benefit even to theoreticians, because theories are refined and reformulated whenever new phenomena that existing theories fail to explain are found. Thus, physics has developed by leaps and bounds. I think the theoretician’s main work is to refine and reformulate conventional theories. Quantum dynamics, the basics of nuclear theory, was established in the 1920s. In the more than 80 years since then, no data has been found that suggests some error in the theory. If the RIBF contributes to finding such data, it will bring about a great innovation in physics.”
In either event, RIKEN with its RIBF is very well positioned to achieve major breakthroughs in nuclear physics and become a world research base in the field over the coming years.
Takashi Nakatsukasa was born in Tokyo, Japan, in 1967. He graduated from the Faculty of Science, Kyoto University, in 1989, and obtained his PhD in 1994 from the same university. He spent more than 4 years as a postdoctoral researcher at Atomic Energy, Canada Limited in Chalk River, Canada, and at the University of Manchester Institute of Science and Technology in Manchester, UK. He returned to Japan as a special postdoctoral researcher at RIKEN in 1999, then became an assistant professor at Tohoku University in 2001 and a lecturer at the University of Tsukuba in 2003. Since 2007, he has acted as associate chief scientist at the RIKEN Nishina Center for Accelerator-Based Science. His current research focuses on computational nuclear physics using density functional theory.
Saeko Okada | Research asia research news
Further reports about: > Accelerator-Based > Isotop > Next-Generation Supercomputer > Next-generation > Nuclear Physics > RIBF > RIKEN > Radioactive > Science TV > Supercomputer > atomic nuclei > light-emitting diode > nuclear power > nuclear reactor > power plant > radioactive nuclei > supernova explosion
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