UNIVERSAL NUCLEAR ENERGY DENSITY FUNCTIONAL Computing ATOMIC NUCLEI Petascale computing helps disentangle the nuclear puzzle. The goal of the Universal Nuclear Energy Density Functional (UNEDF) collaboration is to provide a comprehensive description of all nuclei and their reactions based on the most accurate knowledge of the nuclear interaction, the most reliable theoretical approaches, and the massive use of computer power. Science of Nuclei the Hamiltonian matrix. Coupled cluster (CC) Nuclei comprise 99.9% of all baryonic matter in techniques, which were formulated by nuclear sci- the Universe and are the fuel that burns in stars. entists in the 1950s, are essential techniques in The rather complex nature of the nuclear forces chemistry today and have recently been resurgent among protons and neutrons generates a broad in nuclear structure. Quantum Monte Carlo tech- range and diversity in the nuclear phenomena that niques dominate studies of phase transitions in can be observed. As shown during the last decade, spin systems and nuclei. These methods are used developing a comprehensive description of all to understand both the nuclear and electronic nuclei and their reactions requires theoretical and equations of state in condensed systems, and they experimental investigations of rare isotopes with are used to investigate the excitation spectra in unusual neutron-to-proton ratios. These nuclei nuclei, atoms, and molecules. are labeled exotic, or rare, because they are not When applied to systems with many active par- typically found on Earth. They are difficult to pro- ticles, ab initio and configuration interaction duce experimentally because they usually have methods present computational challenges as the extremely short lifetimes. The goal of a compre- configuration space explodes rapidly. Thus other hensive description and reliable modeling of all models are needed in which the most important nuclei—light, heavy, and superheavy—represents degrees of freedom are identified and retained so one of the great intellectual opportunities for that a full treatment of all interactions among the physics in the twenty-first century. active particles can be avoided. This kind of The nuclear many-body problem is of broad approach to many-body quantum physics can be intrinsic interest. The phenomena that arise— found in many other fields, such as condensed shell structure, superfluidity, collective motion, matter physics, atomic and molecular physics, phase transitions—and the connections with and quantum chemistry. Density functional the- many-body symmetries, are also fundamental to ory (DFT), a tool of choice for complex nuclei, is fields such as atomic physics, condensed matter built on theorems showing the existence of uni- physics, and quantum chemistry. Although the versal energy functionals for many-body systems, interactions of nuclear physics differ from the elec- which include, in principle, all many-body corre- The rather complex tromagnetic interactions that dominate chemistry, lations. DFT has been spectacularly successful in nature of the nuclear materials, and biological molecules, the theoreti- condensed matter physics and chemistry, as was forces among protons cal methods and many of the computational tech- recognized by the 1998 Nobel Prize in chemistry, and neutrons generates niques to solve the quantum many-body awarded to Walter Kohn. In fact, it was the com- a broad range and problems are shared (figure 1). All basis expansion bined work of many dedicated researchers that diversity in the nuclear methods—configuration interaction in chemistry, culminated in finding remarkably accurate func- phenomena that can be interacting shell model in nuclear physics—use tionals for use in chemistry. A concerted effort observed. exactly the same technique, that of diagonalizing rooted in a fundamental understanding of inter- 42 S CIDAC REVIEW W INTER 2007 WWW. SCIDACREVIEW. ORG U N E D F C O L L A Nuclear Landscape B O R A T I O N Ab Initio Configuration Interaction Density Functional Theory 82 s 50 n o t o r P 28 20 82 8 50 2 28 20 2 8 Figure 1. The theoretical methods and computational techniques used to solve the nuclear many-body problem. On this chart of the nuclides in the (N,Z)-plane, the black squares represent stable nuclei and the yellow squares indicate unstable nuclei that have been produced and studied in the laboratory. The many thousands of these unstable nuclei yet to be explored are indicated in green (terra incognita). Except for the lightest nuclei, where it has been reached experimentally, the neutron drip line (the rightmost border of the nuclear landscape) has to be estimated on the basis of nuclear models—hence it is very uncertain due to the dramatic extrapolations involved. The red vertical and horizontal lines show the magic numbers, reflecting regions where nuclei are expected to be more tightly bound and have longer half-lives. The anticipated path of the astrophysical r-process responsible for nucleosynthesis of heavy elements is also shown (purple line). The thick dotted lines indicate domains of major theoretical approaches to the nuclear many-body problem. For the lightest nuclei, ab initio calculations (Green’s function Monte Carlo, no-core shell model, coupled cluster method), based on the bare nucleon–nucleon interaction, are possible (red). Medium-mass nuclei can be treated by configuration interaction techniques (interacting shell model, in green). For heavy nuclei, the density functional theory based on self-consistent/mean field theory (blue) is the tool of choice. By investigating the intersections between these theoretical strategies, one aims at nothing less than developing a unified description of the nucleus. nucleon interactions offers promise to achieve Practical Applications corresponding qualitative improvements in the Applications of nuclear physics in today’s global accuracy and applicability for nuclear physics. economy and national security are numerous. Recognizing that the nucleus is composed of They include the nuclear power industry and fermions, neutrons, and protons, DFT is the only nuclear medicine, as well as national defense. As tractable theory that can be applied across the has been illustrated many times in all fields of sci- Density functional theory entire table of nuclides. The new challenges faced ence, improved understanding of the microworld is built on theorems by the nuclear DFT are the presence of two kinds benefits society. Fusion and fission are excellent showing the existence of of fermions, the essential role of pairing, and the examples. The description of these fundamental universal energy need for symmetry restoration in finite, self- nuclear processes is still very schematic, yet nuclear functionals for many- bound systems. fission powers reactors that produce energy for the body systems. S CIDAC REVIEW W INTER 2007 WWW. SCIDACREVIEW. ORG 43 UNIVERSAL NUCLEAR ENERGY DENSITY FUNCTIONAL A . T O V Experimental Evidence that Challenges Theory E Y While only about 300 combinations of protons and neutrons in nuclei are stable enough to exist in nature, several thousand nuclei can be synthe- sized in the laboratory, and even more can be cre- ated in stars. The chart of nuclei (figure 1, p43) shows all possible nuclei in the plane of the neu- tron number N and the proton (or atomic) num- ber Z. In this landscape, the stable nuclei are bunched along the valley of beta-stability. The ensemble of the heaviest isotopes of each element forms a broken line in the nuclear chart, called the neutron drip line, to the right of beta stability. Universities Atomic nuclei beyond that line are unbound with Laboratories respect to neutron radioactivity. Coulomb repul- sion limits the existence on the proton-rich side Figure 2. The UNEDF collaboration includes researchers from six national laboratories of the nuclear landscape. and eight U.S. universities. These include Ames Laboratory, ANL, LBNL, LLNL, LANL, In 1963 Maria Goeppert-Mayer and J. Hans D. ORNL, Central Michigan University, Iowa State University, Michigan State University, Jensen received the Nobel Prize in physics for Ohio State University, San Diego State Univesity, the University of North Carolina, the explaining why nuclei containing certain num- University of Tennessee–Knoxville, and the University of Washington. bers of protons and neutrons (2, 8, 20, 28, 50, 82, and 126, for example) are extremely stable. These nation, and fusion, which is responsible for energy numbers are called “magic numbers.” This discov- production in stars, has the promise of providing ery had led to an extremely successful tool used a clean alternative source of energy. in describing nuclei called the “shell model.” In There is little question that the nuclear many- this model, the protons and neutrons—collec- body problem has high societal relevance. In the tively called the nucleons—move and mutually area of national defense, for instance, developing interact within a given subset of the shells that are a comprehensive description of nuclei aligns well well separated in energy from other shells in an with the goals of the National Nuclear Security average mean field generated by the remaining Administration (NNSA) Stockpile Stewardship particles. This separation means a nucleus can be Program, which entails an accurate and complete modeled as a core, representing the magic modeling of the behavior and performance of nucleus, and valence nucleons. This simple pic- devices in the nation’s aging nuclear weapons ture works well in many nuclei near the valley of stockpile. Improving the accuracy of that under- stability. standing is central to the continuing process of However, a significant new theme concerns certifying both the safety and the reliability of the shell structure near the particle drip lines and in stockpile without a resumption of nuclear test- the superheavy nuclei. Theoretical predictions ing. In short, understanding of nuclei and their and experimental discoveries in the last decade reactions is critical to providing a more secure indicate that nucleonic shell structure is being rec- homeland. ognized now as a more local concept.