A unified theory of atomic and nuclear shell structure

Nuclear structure theory is a domain of physics faced at present with great challenges and opportunities. A larger and larger body of high-precision experimental data has been and continues to be accumulated. Experiments on very exotic short-lived isotopes are the backbone of activity at numerous large-scale facilities. Over the years, tremendous progress has been made in understanding the basic features of nuclei. However, the theoretical description of nuclear systems is still far from being complete and is often not very precise. Many questions, both basic and practical, remain unanswered.The goal of publishing this special focus issue of Journal of Physics G: Nuclear and Particle Physics on Open Problems in Nuclear Structure Theory (OPeNST) is to construct a fundamental inventory thereof, so that the tasks and available options become more clearly exposed and that this will help to stimulate a boost in theoretical activity, commensurate with the experimental progress. The requested format and scope of the articles on OPeNST was quite flexible. The journal simply offered the possibility to provide a forum for the material, which is very often discussed at conferences during the coffee breaks but does not normally have sufficient substance to form regular publications. Nonetheless, very often formulating a problem provides a major step towards its solution, and it may constitute a scientific achievement on its own.Prospective authors were therefore invited to find their own balance between the two extremes of very general problems on the one hand (for example, to solve exactly the many-body equations for a hundred particles) and very specific problems on the other hand (for example, those that one could put in one's own grant proposal). The authors were also asked not to cover results already obtained, nor to limit their presentations to giving a review of the subject, although some elements of those could be included to properly introduce the subject matter.The focus of these collected articles is therefore on the discussion of topics that are not yet understood, or that are poorly understood. We very much welcomed presentations on: (i) contradictory approaches, models, or theories that are, at present, difficult to reconcile,(ii) unsolved theoretical problems that hamper applications of existing methods, (iii) limitations of current approaches, (iv) difficulties in deriving and justifying models and theories, (v) generic problems in understanding or describing specific experimental data,and even (vi) all possible, wildest speculations and/or conjectures. The main idea behind the focus issue was to stimulate creative, unbounded thinking and provide young, but not only young, researchers with ideas that would promote further progress in this domain of science.The community of nuclear structure theorists enthusiastically responded to the idea of publishing the volume on OPeNST. It seemed that the idea struck the right chord and many colleagues were willing to share their observations on what research directions to follow and which problems to attack. The volume turned out to be a snapshot of the domain, revealing the burning questions that the community wants to address. All the articles also have a very interesting personal touch. They sometimes even present opposing or conflicting points of view, which is exactly what one would expect within a vibrant scientific discussion. All in all, the Editors of Journal of Physics G are very happy to offer you this unique collection, which will constitute very interesting reading for all those working in nuclear structure theory.

The Tenth International Spring Seminar on Nuclear Physics was held in Vietri sul Mare from May 21 to May 25, 2010. This Seminar was the tenth in a series of topical meetings held every two or three years in the Naples area. The series began with the Sorrento meeting in 1986 and continued with the Capri meeting in 1988, the Ischia meeting in 1990, the Amalfi meeting in 1992, the Ravello meeting in 1995, the S. Agata meeting in 1998, the Maiori meeting in 2001, the Paestum meeting in 2004, and the Vico Equense meeting in 2007.For this tenth meeting we returned to Salerno Bay and met in the small town of Vietri. While the location of the Conference has never been the same, what remained invariant is the aim of these meetings, which is to discuss recent advances and new perspectives in nuclear structure experiments and theory in a pleasant and friendly atmosphere.It is by now well established that we have entered a new era in Nuclear Physics research with the advent of radioactive ion beam facilities. While nuclear structure studies are currently being performed in several laboratories where RIBs are available, the development of new facilities, which will provide high-intensity beams, is in progress or under discussion in Europe, Asia and North America. At this meeting we had a comprehensive overview of this fascinating field and of future scenarios thanks to the participation of leaders of the most important projects.The results that are becoming available for nuclei far from stability are highlighting new themes of research, such as the evolution of the shell structure when moving towards the particle drip lines, and stimulating a proficuous interplay between experiment and theory. On the other hand, new ideas and the development of more powerful computational tools promise a deeper understanding of the structure of nuclei in terms of the basic interactions between their constituents.As usual, the program of the meeting consisted of general talks and of more specialized seminars, the latter including most of the contributions submitted by participants. The speakers covered five main topics: i) Nuclear Structure far from Stability: New Advances and Perspectives; ii) From Nuclear Forces to Nuclear Structure; iii) Exploring Nuclear Shell Structure: Experiment and Theory; iv) New Aspects of Collective Nuclear Motion; and v) Special Topics.We received 63 manuscripts out of the 77 invited papers and contributions presented at the Seminar. All of these have been peer reviewed and are collected in this volume. We would like to thank all the anonymous colleagues who have acted as referees to assess the suitability of the various articles for publication in the Journal of Physics: Conference Series. We are confident that the high quality of both invited and contributed papers contained in these Proceedings will be appreciated by the nuclear physics community.As was the case for most of the previous Seminars, the Vietri Seminar also ended with a Round Table Discussion on the theme ‘Trends and Perspectives in Nuclear Structure’. N Benczer-Koller, B A Brown, A Faessler, B Fornal, O Sorlin, and I Talmi kindly agreed to be on the panel and their remarks were essential in bringing about the active involvement of the audience.The Conference had about 100 participants from some 20 countries (please see PDF for list of participants). This is well in line with the tradition of these meetings, as is the fact that about 50% of the present participants attended one or more of the previous Seminars.We gratefully acknowledge the financial support of the Istituto Nazionale di Fisica Nucleare and the University of Naples Federico II who helped make the Seminar possible. We also acknowledge the support provided in various ways by the Dipartimento di Scienze Fisiche which acted as host to the Seminar.Aldo Covello Angela Gargano Editors LOCAL ORGANIZING COMMITTEEA Covello (Chair) A Gargano (Co-Chair) L Coraggio (Scientific Secretary) F Andreozzi N Itaco G La Rana N Lo Iudice A. Porrino INTERNATIONAL ADVISORY COMMITTEE J Äystö (Jyväskylä)D Morrissey (Michigan) A B Balantekin (Wisconsin)W Nazarewicz (Oak Ridge) B R Barrett (Tucson)P von Neumann-Cosel (Darmstadt) P G Bizzeti (Firenze)R Okamoto (Kyushu) Y Blumenfeld (CERN and IPN Orsay)A V Ramayya (Vanderbilt) J Dobaczewski (Warsaw)J Schiffer (Argonne) G Fiorentini (Ferrara)A C Shotter (Edinburgh) B Fornal (Kraków)Ch Stoyanov (Sofia) S Gales (GANIL)I Talmi (Rehovot) F Iachello (Yale)P van Duppen (Leuven) R Jolos (Dubna)A Vitturi (Padova) M Lattuada (Catania) SPONSORS OF THE SEMINARDipartimento di Scienze Fisiche, Università di Napoli "Federico II" Istituto Nazionale di Fisica Nucleare Università di Napoli Federico II

The nuclear shell structure, which originates in the nearly independent motion of nucleons in an average potential, provides an important guide for our understanding of nuclear structure and the underlying nuclear forces. Its most remarkable fingerprint is the existence of the so-called magic numbers of protons and neutrons associated with extra stability. Although the introduction of a phenomenological spin–orbit (SO) coupling force in 1949 helped in explaining the magic numbers, its origins are still open questions. Here, we present experimental evidence for the smallest SO-originated magic number (subshell closure) at the proton number six in 13–20C obtained from systematic analysis of point-proton distribution radii, electromagnetic transition rates and atomic masses of light nuclei. Performing ab initio calculations on 14,15C, we show that the observed proton distribution radii and subshell closure can be explained by the state-of-the-art nuclear theory with chiral nucleon–nucleon and three-nucleon forces, which are rooted in the quantum chromodynamics.

Background: Single-charge-exchange reactions are appropriate tools to study the nuclear response to one-particle/one-hole isospin probes, gaining additional interest from the connection to beta decay. This analogy has been recently extended to second order, connecting double-charge-exchange reactions and double beta decays. Nowadays, the availability of powerful experimental setups and advanced nuclear theories and models allows one to access precious information on key nuclear structure aspects embedded in the widely sought neutrinoless double beta decay.Purpose: We intend to bring to light the main nuclear structure and reaction features involved in the $^{18}\mathrm{O}+^{12}\mathrm{C}$ collision at 275 MeV incident energy. In this paper, the main focus is on the role of the initial- and final-state interactions in the overall reaction dynamics and on the single-particle nuclear structure properties accessed via the study of single-nucleon transfer reactions. Forthcoming articles will be devoted to go into the details of the response to one- and two-particle/hole isospin probes.Methods: Cross-section energy spectra and angular distributions were measured in a unique experimental setup for the $^{12}\mathrm{C}(^{18}\mathrm{O},^{18}\mathrm{O})^{12}\mathrm{C}$ elastic and inelastic scattering, the $^{12}\mathrm{C}(^{18}\mathrm{O},^{17}\mathrm{O})^{13}\mathrm{C}$ one-neutron stripping, the $^{12}\mathrm{C}(^{18}\mathrm{O},^{19}\mathrm{F})^{11}\mathrm{B}$ one-proton pickup, and the $^{12}\mathrm{C}(^{18}\mathrm{O},^{18}\mathrm{F})^{12}\mathrm{B}$ single-charge-exchange nuclear reactions. A unique comprehensive and coherent theoretical calculation, able to describe the whole network of direct reactions using state-of-the-art nuclear structure and reaction theories, was performed, and it is presented for the first time in this article. This holistic approach, applied both to the experimental and theoretical analysis, is the main feature and worth of the work here presented.Results: The energy and angular resolutions achieved in each reaction channel allowed us to isolate specific transitions and to map the diffraction patterns in the angular distributions. The cross-section calculations describe well the experimental data, both in terms of the absolute values and diffraction patterns. Although the distorted wave Born approximation (DWBA) calculations prove to be accurate in describing all the studied channels, better results are achieved when the couplings to inelastic transitions in both the incoming and outgoing partitions are introduced, as done in the coupled channels Born approximation (CCBA) calculations. Otherwise, no real improvement is found when the coupling effects among different partitions are explicitly taken into account in the coupled reaction channels (CRC) calculations.Conclusions: The multichannel approach proposed in this paper is a promising method for accurate investigations of direct reactions originating in heavy-ion collisions. This is quite appealing for the precise spectroscopy of heavy nuclei proposed in many areas of nuclear physics. An example is the NUMEN project with its challenging commitment to provide valuable information on neutrinoless double beta decay nuclear matrix elements from single- and double-charge-exchange cross-section measurements.

Work in nuclear structure and reaction theory, specifically, the relation of reactions to the nuclear structure. Other work was in intermediate energy physics, few-body problems, and computational physics that heavy ions can be used to measure simultaneously both neutron and proton multipole matrix elements of the target nucleus has added new interest to this area of nuclear structure. Considerable attention to the is therefore paid to the to the methods for calculating multiple matrix elements.

The present contribution does not aim at replacing the huge and often excellent literature on DFT for atomic nuclei, but tries to provide an updated introduction to this topic. The goal would be, ideally, to help a fresh this http URL. or Ph.D. student (or a researcher from other fields) to become acquainted with some basic concepts, and then move to the specialized textbooks or papers with some ability for orienteering. We first introduce the basics of DFT, and show the difference with the naive mean-field theory, that is doomed to fail as a model even in the simple case of uniform nuclear matter. We introduce the Energy Density Functionals (EDFs) that are used in nuclear structure, with few examples of their applications. The concepts of symmetry breaking and restoration are briefly discussed. We also include an introduction to the time-dependent extension of DFT that, so far, has been implemented essentially only in the adiabatic approximation and has been applied mainly to the study of nuclear vibrations. With this material, we hope that any reader is able to deal with the texts that go deeper into each of the topics, having understood that DFT is probably the best compromise in nuclear structure theory between simplicity, accuracy, and broad range of applicability.

Three-nucleon forces: Implementation and applications to atomic nuclei and dense matter

Deformed shell structures in nuclear mean-field potentials are systematically investigated as functions of deformation and surface diffuseness. As the mean-field model to investigate nuclear shell structures in a wide range of mass numbers, we propose the radial power-law potential model, V \propto r^\alpha, which enables a simple semiclassical analysis by the use of its scaling property. We find that remarkable shell structures emerge at certain combinations of deformation and diffuseness parameters, and they are closely related to the periodic-orbit bifurcations. In particular, significant roles of the "bridge orbit bifurcations" for normal and superdeformed shell structures are pointed out. It is shown that the prolate-oblate asymmetry in deformed shell structures is clearly understood from the contribution of the bridge orbit to the semiclassical level density. The roles of bridge orbit bifurcations in the emergence of superdeformed shell structures are also discussed.

The central focus of this research was the interplay between three generic classes of degrees of freedom relevant to nuclear structure theory: single-particle degrees of freedom, collective degrees of freedom, and statistical degrees of freedom, which can be thought of as an incoherent mean field or a thermal bath.

The nuclear shell model is a benchmark for the description of the structure of atomic nuclei. The magic numbers associated with closed shells have long been assumed to be valid across the whole nuclear chart. Investigations in recent years of nuclei far away from nuclear stability at facilities for radioactive ion beams have revealed that the magic numbers may change locally in those exotic nuclei leading to the disappearance of classic shell gaps and the appearance of new magic numbers. These changes in shell structure also have important implications for the synthesis of heavy elements in stars and stellar explosions. In this review a brief overview of the basics of the nuclear shell model will be given together with a summary of recent theoretical and experimental activities investigating these changes in the nuclear shell structure.

To investigate whether the spin-orbit force in the theory of nuclear shell structure is due to the tensor force of the pion-theoretical potential, the doublet splitting of the pphase shifts in low energy n-He/sup 4/ scattering was analyzed. It is concluded that the major pant of the experimental doublet splitting can be reproduced by the strong tensor force of the pion-theoretical potential. It is shown qualitatively which features of the pton-theoretical potential are important to the binding energy of He/sup 4/ and the discontinuity of the binding energies between He/sup 4/ and the system of He/sup 4/ plus one nucleon. (auth)

The systematics of beta-decay, alpha-emission, and spontaneous fission will be investigated in order: first, to determine the theoretical limits to the periodic table, and secondly, to examine the effects of nuclear shell structure on the end of the periodic table. Curves of beta-stability and lifetimes against alpha-emission and spontaneous fission will be drawn for the heaviest elements and will be extrapolated in order to yield information about the stability or form of instability of the transuranic elements. Nuclear shell structure will be seen to be responsible for the stability of ${\mathrm{Th}}^{222}$ and ${\mathrm{U}}^{238}$ as well as the instability of the group of highly radioactive elements beginning with polonium.

The relation between nuclear shell structure and nuclear shapes is brought out in diverse mass regions. Thus certain nuclear orbitals, shown to be responsible for the development of mass-asymmetric distortions, are here followed in more detail for large and realistic shape changes. The same holds for axial asymmetries. The study is applied to actinide and superheavy nuclei as as well as very light ones, among the latter 24Mg, which is shown to exhibit a deep octupole-shape second minimum.

A material (ZIF-8@SiO2) with a nuclear shell structure was synthesized to improve the flame retardancy and smoke suppression of epoxy resin (EP) through a synergetic catalytic effect. Zeolitic imidazolate framework-8 (ZIF-8) was synthesized and its surface was coated with SiO2 by hydrolyzing tetraethyl orthosilicate. Core–shell structured ZIF-8@SiO2 was obtained. Then ZIF-8@SiO2 was added to EP to explore its effect of flame retardancy and smoke suppression on the EP composite. The results of a cone calorimeter test showed that the peak heat release rate, total heat release, smoke production rate and total smoke production of the material were decreased by 75.9%, 38.9%, 51.1% and 39.8%, respectively, after 2 wt% ZIF-8@SiO2 was added to EP. Besides, through the analysis of char residue, the mechanism of ZIF-8@SiO2/EP's flame retardancy and smoke suppression was determined to be due to the physical barrier effect of SiO2 and the co-effect of SiO2 and ZnO decomposition by ZIF-8.

Nuclear shell structure at very high angular momentum