Ebook: Nuclear Structure far from Stability: New Physics and New Technology

The purpose of the CLXIX Course of the “Enrico Fermi” Varenna School was to give an account of recent advances and new perspectives in the study of nuclei far from stability both from the experimental and the theoretical point of view.

Experimental studies of exotic nuclei are currently being performed in several laboratories and new facilities with high-intensity beams are either just completed, or approved and under construction or in their planning stages. At the School an overview of several facilities, RIKEN-RIBF, CERN-ISOLDE, GANIL-SPIRAL2 and GSI-FAIR was given, as well as of the planned FRIB facility in the U.S., with the aim of presenting to the students what will be the experimental scenario in the next 10 years.

The bulk of the School was devoted to nuclear structure models and their derivation from the basic nucleon-nucleon interaction. Three models were extensively discussed: the shell model, the interacting boson model and the cluster model.

In recent years, considerable advance has been made in ab initio theories of nuclei, especially of light nuclei. These were also presented at the School thus providing a comprehensive view of the present status of nuclear structure theory.

Another aspect that was discussed was the occurrence of dynamic symmetries and super-symmetries in nuclei, including the newly suggested “critical” symmetries which occur in transitional nuclei when the shape changes from spherical to deformed.

Nuclei far from stability are of particular importance for astrophysics, especially for the r-process. Nuclear Astrophysics was reviewed in detail, including a discussion of energy generation in stars and nucleo-synthesis of elements.

Another aspect of nuclear structure physics is its role in understanding fundamental processes, such as electroweak processes. For example, nuclei offer the opportunity of measuring the neutrino mass through the observation of neutrinoless double-beta decay. A review of the experimental and theoretical situation for double-beta decay both with and without neutrinos was presented at the School.

The main lectures were complemented by seminars on issues of current interest in nuclear structure, some of them being given by students. The students were also given the opportunity to make use of some of the computer programs needed in nuclear structure model calculations.

This CLXIX Course was dedicated to Renato Angelo Ricci on the occasion of his 80th birthday. It was a pleasure to celebrate this joyful event, which gave us the opportunity to recognize the many contributions of Renato to the field of Nuclear Physics, especially those to the structure of fp-shell nuclei.

We gratefully acknowledge the financial support of the Istituto Nazionale di Fisica Nucleare (INFN). We also express our special thanks to Barbara Alzani, Lorenzo Corengia, and Marta Pigazzini for their very efficient and friendly help during the whole School.

A. Covello and F. Iachello

Three of the fundamental concepts that can be tested at radioactive beam facilities: a) dynamic symmetries and supersymmetries; b) quantum shape phase transitions; c) critical symmetries; are briefly discussed.

The problem of production and study of superheavy elements is discussed in this paper. Different nuclear reactions leading to formation of superheavy nuclei are analyzed. Collisions of transactinide nuclei are investigated as an alternative way for production of neutron-rich superheavy elements. In many events lifetime of the composite giant nuclear system consisting of two touching nuclei turns out to be rather long (≥10⁻²⁰s); sufficient for observing line structure in spontaneous positron emission from super-strong electric fields, a fundamental QED process.

A survey of the nuclear-structure studies through the nuclear-spectroscopy investigations as performed by different tools and techniques is presented. Starting from the simple radioactive decay studies and the associated γ-ray spectroscopy, since the pioneering work with the first scintillation devices, the review will cover the investigation of disintegration schemes and the scintillation spectra analysis performed in the 50's and the early 60's either by radioactive decays or with direct reactions such as stripping and pick-up and inelastic and quasi-free scattering. Examples are the results obtained for determining single particle and collective states in light and medium heavy nuclei. The selection of nuclear states from the first revolution in nuclear spectroscopy given by the scintillation detectors to the second revolution which allowed a more appropriate selection of nuclear states due to the advent of in-beam γ-ray spectroscopy and heavy-ion nuclear reactions is reviewed. The third and fourth revolution in nuclear spectroscopy given by the advent of more sophisticated γ-arrays and by the possibility of accelerating radioactive beams are also accounted for. In this context as a typical nuclear spectroscopy investigation the revival of the 1f_7/2 spectroscopy is reported with the aim to show the still attractive future of important aspects of nuclear physics.

The international Facility for Antiproton and Ion Research (FAIR) will provide a combination of accelerators and storage rings for a multidisciplinary scientific program. The FAIR accelerator complex constitutes a substantial extension of the present GSI systems and will use the existing accelerators after several upgrades as an injector. This new facility comprises as an integral part a next-generation rare-isotope beam facility based on the production and separation of secondary beams produced by fragmentation or fission of energetic high-intensity primary ion beams. An advanced experimental program including new and unique concepts promises a new quality in investigations of nuclei far away from stability. A brief overview on the facility is presented with emphasis on the radioactive-beam facility. The experimental program and its related instrumentation is discussed briefly.

During the last two decades, RIB has allowed the investigation of a new territory of nuclei with extreme N/Z called “terra incognita”. Due to technical limitations, existing facilities were able to cover some part of the light mass region of this “terra incognita”. The main goal of SPIRAL2 is clearly to extend our knowledge of the limit of existence and the structure of nuclei deeply in the medium and heavy mass region (A=60 to 140) which is to day an almost unexplored continent. SPIRAL2 is based on a high power, CW, superconducting driver LINAC, delivering 5 mA of deuteron beams at 40 MeV (200 KW) directed on a C converter+ Uranium target and producing therefore more 10¹³ fissions/s. The expected radioactive beams intensities for exotic species in the mass range from A=60 to A=140, of the order of 10⁶ to 10¹⁰ pps will surpass by two orders of magnitude any existing facilities in the world. These unstable atoms will be available at energies between few keV/n to 15 MeV/n. The same driver will accelerate high intensity (100 μA to 1 mA), heavier ions up to Ar at 14 MeV/n producing also proton-rich exotic nuclei. In applied areas SPIRAL2 is considered as a powerful variable energy neutron source, a must to study the impact of nuclear fission and fusion on materials. The intensities of these unstable species are excellent opportunities for new tracers and diagnostics either for solid state, material or for radiobiological science and medicine. The “Go” decision has been taken in May 2005. The investments and personnel costs amount to 190 M euro, for the construction period 2006-2012. The project group has been completed in 2006, the construction of the accelerator started in the beginning of 2007 whereas detail design of the RIB production processes are underway. Construction of the SPIRAL2 facility is shared by ten French laboratories and a network of international partners. Under the 7FP program of European Union called “Preparatory phase for the construction of new facilities”, the SPIRAL2 project has been granted a budget of about 4 M euro to build up an international consortium around this new venture. Regarding the future physics program a call for Letter of intents has been launched in Oct 2006. A very positive and enthusiastic response is the basis of new large international collaborations. Proposals for innovative new instrumentation and methods for the for SPIRAL2 facility are being examined by an International Scientific Advisory Committee. The status of the construction of SPIRAL2 accelerator and technical R&D programs for physics instrumentation (detectors, spectrometers) in collaboration with EU and International partners will be presented.

Nuclear structure physics has been revitalized by the new experimental information obtained with radioactive beams. The high level of activity is reflected in many overview papers, a brief introduction to radioactive-beam research can be found in 1. The ISOLDE radioactive beam facility at CERN has been operating for close to 40 years and has played a key role in many of the developments in the ISOL (Isotope Separation On-Line) field. This paper describes the present ISOLDE facility and gives selected examples that illustrate the present physics possibilities. Many different projects exist for construction of new facilities to bring the field of radioactive beams even further. The upgrade plans for ISOLDE, the HIE-ISOLDE project, will be discussed at the end.

RIKEN RI Beam Factory (RIBF) is one of the new-generation facilities for Radioactive Isotope (RI) beam, which are dedicated to provide various nuclei very far from the stability valley served as beam with high-power driver accelerators. The RIKEN RIBF is their first realization. The accelerator complex has already started operation, and the first result of new isotope production has been performed. Research opportunities with RI beams, especially for the ones with intermediate energies, are discussed.

During the last 15 years, there has been much progress in defining the nuclear Hamiltonian and applying quantum Monte Carlo methods to the calculation of light nuclei. I describe both aspects of this work and some recent results.

An overview of the ab initio no-core shell model is presented. Recent results for light nuclei obtained with the chiral two-nucleon and three-nucleon interactions are highlighted. Cross-section calculations of capture reactions important for astrophysics are discussed. The extension of the ab initio no-core shell model to the description of nuclear reactions by the resonating group method technique is outlined.

The nuclear many-body problem is discussed. Starting from realistic nuclear forces the problem of induced short-range correlations is treated with the unitary correlation operator method. Fermionic molecular dynamics many-body states are used to describe phenomena such as clustering of nucleons inside light nuclei, weakly bound two-neutron halos and nucleus-nucleus reactions at low energies.

Starting from the earliest ideas of clustering in light nuclei, the signatures traditionally supporting the existence of clusters will be discussed. In particular the procedure to perform an angular correlation analysis in order to infer a dominant angular momentum to a resonance will be shown. Then, moving from the α-chains in ⁸Be and ¹²C, the nuclear dimers and polymers will be introduced. Moreover, applications of cluster physics to nuclear astrophysics by means of quasi-free scattering and reactions will be considered.

Halo nuclei exhibit a new type of structure found in extremely neutron-rich light nuclei, at the limits of nuclear existence. Of particular interest are Borromean nuclei, where none of the binary substructures can bind, demonstrating features of universality. Nuclear physics has in recent years taken further steps to explore the nature of the halo continuum, this being in fact the major part of the spectrum since halo nuclei support only one or a few bound states. Since 3 → 3 scattering is prohibitively difficult to perform, the halo continuum has so far been excited in binary collisions, proceeding via the exotic ground state which to various degrees puts its imprint on the result. We discuss via examples how to disentangle continuum structures, comparing with recent correlation data, and the challenges of linking reaction theory and modern structure calculations.

A basic introduction to the nuclear shell model is presented, with illustrative explanations of shell-model concepts and procedures. All details of many-body theories are avoided. First, we explain how magic numbers and shell structures appear from fundamental properties of nuclei such as the short-range attractive interaction and density saturation. Some concepts needed to understand the shell model are explained from scratch. The process of the shell model calculation is sketched also in a visual way. After the introduction, one of the recent topics, the evolution of shell structure in exotic nuclei, is briefly discussed, mentioning the importance of the tensor force.

In this paper, I first give a brief survey of the theoretical framework for microscopic shell-model calculations starting from the free nucleon-nucleon (NN) potential. In this context, I discuss the use of the low-momentum NN potential V_low-k in the derivation of the two-body effective interaction and emphasize its practical value as an alternative to the Brueckner G-matrix method. Then, I present some results of a recent shell-model study of exotic nuclei beyond ¹³²Sn, which we have obtained starting from the CD-Bonn potential renormalized by use of the V_low-k approach. Comparison shows that they are in very good agreement with the available experimental data.

The study of differences in excitation energy between analogue states in isobaric multiplets allows to verify the validity of isospin symmetry and independence as a function of the angular momentum. These differences are of the order of tens of keV and can be well reproduced by state-of-the-art shell model calculations. Several nuclear-structure properties can be deduced from these data, such as the alignment of nucleons along rotational bands, the evolution of the nuclear radius and the identification of pure single-particle excitations across two main shells. In addition, the isospin breaking of the nuclear interaction is suggested by the systematic comparison with data. The different ingredients that enter the calculation of the Coulomb energy differences between mirror nuclei are introduced and shown in different examples of mirror nuclei in the f_7/2 and the sd shell.

These lectures discuss selected topics in nuclear astrophysics. They include hydrogen burning, solar neutrinos, advanced stellar burning stages, the final fate of massive stars as core-collapse supernovae and the associated explosive nucleosynthesis. The emphasis is on the nuclear ingredients, which determine the evolution and dynamics of the astrophysical objects.

These lectures notes give an introduction to the use of algebraic techniques for obtaining analytic eigensolutions of quantum-mechanical systems consisting of many particles in interaction. The notions of symmetry and dynamical symmetry in quantum physics are introduced and subsequently illustrated with the example of the interacting boson model of atomic nuclei. Some recent applications of this model to exotic nuclei are discussed.

The Interacting Boson Approximation (IBA) model is discussed in the context of microscopic and macroscopic approaches to nuclear collectivity. The Hamiltonian, group theoretical structure, dynamical symmetries, the Consistent Q Formalism (CQF and ECQF), the technique of Orthogonal Crossing Contours (OCC), and practical calculations with the model are discussed.

A survey of algebraic approaches to various problems in nuclear physics is given. Examples are chosen from pairing of many-nucleon systems, nuclear structure, fusion reactions below the Coulomb barrier, and supernova neutrino physics to illustrate the utility of group-theoretical and related algebraic methods in nuclear physics.

A quantum-statistical analysis of the regular and chaotic dynamics of medium-mass even-even nuclei within the framework of the interacting boson model-2 (IBM-2) has been carried out. In particular, in the SU_π+ν(3)→U_π+ν(5) transition a broad nearly regular region has been observed, while the SU_π+ν(3)^*→U_π+ν(5) one shows an unexpected completely regular behavior. These results confirm and extend the observations previously made by other authors in the frame of IBM-1, strengthening the hypothesis of the basic role played by the partial dynamical symmetries in preserving regular motion patterns even far from the usual dynamical limits of IBM-2. A new important feature of the SU_π+ν(3)^* limit has also been found, confirming the importance of the SU(3) symmetry of IBM in studying nuclear-structure properties.

A few examples will be given of the essential role played by low-energy nuclear physics in the fundaments of elementary particles and in particle astrophysics. The crucial impact in weak-interaction physics by the discovery of parity violation, which is now fifty years old, and the corresponding experiments will be summarized. A brief discussion will be devoted to the recent experiments on neutrino oscillations which prove that the difference between the square masses of two neutrinos of different flavour is different from zero. As a consequence the mass of at least one neutrino has to be finite, but oscillations cannot provide a direct indication of its value. Stimulated by these exciting results a vast series of experiments aiming to determine directly the neutrino mass has been carried out and is running or planned.

Experiments on the gamma decay of the giant dipole resonance, addressing three different aspects of nuclear structure are here discussed. The three aspects are: i) the problem of the damping mechanisms at finite temperature, ii) the dipole radiation emitted by a dynamic dipole formed in the process leading to compound nuclei, and iii) the search of the pygmy strength in neutron-rich exotic nuclei. The experiments addressing the first two points were carried out at LNL using the beams of the Tandem-ALPI complex and the GARFIELD set-up including the HECTOR array. The compound nucleus mass region investigated was A=130 at T>2 MeV. The problem of searching the pygmy resonance was addressed with the Coulomb excitation technique at relativistic energies for the nucleus ⁶⁸Ni. The experiment was carried out at GSI using the RISING set-up. The experimental results in all cases are compared with the available predictions.

1. Introduction 2. Collective modes in Tamm-Dancoff and random phase approximation 3. A well-established multiphonon approach: The quasi-particle–phonon model 4. A new multiphonon approach: An equation-of-motion phonon method 5. A numerical implementation of the method 6. Conclusions

Following an introduction on the general properties of E0 transitions and their significance in nuclear structure, an experiment is described in which the branching ratio between the E0 and E2 decays of the 0⁺₂ state in ¹⁵⁶Dy was measured.