Ebook: Nuclear Physics with Stable and Radioactive Ion Beams

The 201st International School of Physics “Enrico Fermi” addressed the fundamental features associated with the study of nuclear systems far from the valley of stability. Studies performed with stable beams and with radioactive ion beams produced at first generation facilities hint to a number of new insight in the way nuclei are built from their constituents. By studying the properties of the so-called exotic nuclei that possess an unbalanced number of protons to number of neutrons ratio, hidden aspects of the strong and weak force acting in the nuclear medium can be uncovered.

The field of radioactive ion beam research has evolved over the last three decades and several medium and large size facilities are currently undergoing a major upgrade or are under construction. In Europe, these include ISOLDE - CERN (Switzerland), SPIRAL2 - GANIL (France)FAIR - GSI (Germany)SPES (Italy) while RIBF - RIKEN (Japan)TRIUMF (Canada)FRIB - MSU (USA) are the major undertakings elsewhere. These facilities will create unprecedented opportunities to extend our knowledge in so far unexplored regions of the nuclear chart and to address key questions in nuclear physics, fundamental interactions and astrophysics, but also link to other fields of science including life science.

The lectures and seminars of the school focused on the structural and dynamical aspects from both a theoretical and experimental point of view. Recent advances in theoretical and experimental approaches were discussed. The former included advanced shell-model, density functional applications, and symmetry-based methods as well as cluster and reaction models. The latter dealt with state-of-the-art experimental themes covering reaction, decay and laser spectroscopy studies and Coulomb excitation experiments. On the occasion of the 90th birthday of Professor R.A. Ricci, a dedicated session was organized including a number of topical seminars. During this session, the pioneer work of Prof. Ricci in nuclear structure was recalled, together with his important contribution in the evolution of nuclear physics in Italy. He was especially one of the founders of heavy-ion-induced reaction studies in Italy devoted to deepen the knowledge on nuclear structure and dynamics coordinating the efforts at the Legnaro National Laboratory for the advent of the Tandem XTU in the 80’s and suggesting the development and installation of the LINAC ALPI in the 90’s.

The organization of the school with participants from ten different countries was a success thanks to the excellent lecturers and seminar speakers and to the highly appreciated work of the school’s administrative staff. The directors would like to express on behalf of all participants their sincere gratitude.

F. Gramegna, P. Van Duppen, A. Vitturi and S. Pirrone

An introduction and recent developments in the nuclear shell model are presented. The basic concepts are explained starting from the work of Mayer and Jensen. The conventional and Monte Carlo Shell Model are illustrated in a pedagogical way. Some important points of the Monte Carlo Shell Model are explained to some details. The monopole interaction and the shell evolution are discussed. The shape evolutions are also discussed with Type-II shell evolution. Finally the quantum self-organization is presented.

A brief account of the algebraic cluster model (ACM) is given. Applications to cluster structures composed of k α-particles with k = 2 (Z₂ symmetry), k = 3 (D_3h symmetry) and k = 4 (T_d symmetry) are presented. Experimental evidence for the occurrence of these symmetries in ⁸Be (Z₂), ¹²C (D_3h), and ¹⁶O (T_d) is shown.

Nuclear clustering is one of the essential features of nuclear systems. Various rich cluster phenomena have been discovered in a wide region of nuclear chart as functions of proton and neutron numbers and excitation energy. Examples are cluster formation/breaking at nuclear surface in low-lying states, cluster excitation and resonances in highly excited states, molecular orbital structures in neutron-rich Be and Ne, cluster gas and linear chain structures in multi-cluster systems. To make systematic study of such cluster phenomena, we apply a method of antisymmetrized molecular dynamics (AMD) and its extended versions. The method is a useful approach applicable to the ground and excited states of general nuclei. One of the advantages of the method is that it is able to describe various cluster phenomena including cluster formation and breaking as well as shell-model like structures. In this paper, we discuss some topics of cluster phenomena in light nuclei based on AMD calculations.

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 M.Sc. 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 “naïve” 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.

In this contribution, I present a short overview of the theory of direct nuclear reactions, with special emphasis on the case of reactions induced by weakly bound nuclei. After introducing some general results of quantum scattering theory, I present specific applications to elastic, inelastic, transfer and breakup reactions. For each of them, I first introduce the most standard framework, followed by some alternative models or extensions suitable for the case of weakly bound nuclei. A short discussion on semiclassical theory of Coulomb excitation and its application to breakup of halo nuclei is also provided.

These notes summarise the lectures given at the International School of Physics “Enrico Fermi”, in July 2017 at Varenna (Italy), about the use of transfer reactions to extract spectroscopic information on nuclei far from the valley of stability. Transfer reactions as a probe of nuclear structure have re-gained importance in the last 20 years with the development of good-quality beams of unstable nuclei, and thus the possibility of carrying out reaction studies in inverse kinematics. After a short introduction about the general properties of nuclear reactions and transfer reactions in particular, the notes discuss the experimental challenges related to the use of radioactive ion beams. The main part is then dedicated to the presentation of a number of selected experimental studies. The focus lies on the impact of those studies on our understanding of the nuclear structure and the features of the underlying nucleon-nucleon interaction. The topics touched upon are: shell evolution in light nuclei at N = 8, the disappearance of the N = 20 shell closure and the emergence of another shell gap at N = 16; the spin-orbit term of the nucleon-nucleon interaction and the changes in its strength in exotic nuclei; the microscopic origin of shape coexistence in low-lying 0⁺ states, in the neutron rich Mg and Ni regions. We conclude with a brief reflection on the present developments and challenges for experiments and theory in this field.

Radioactive decay occurs in unstable nuclei, being β decay the dominant process. The exotic nuclei encountered when going further away from the valley of stability are useful test benches for nuclear models at the limits of the existence of the nucleus. The properties of these exotic systems are of fundamental importance when describing the formation of the elements in the universe through stellar nucleosynthesis processes. The most recent techniques to study β decays in exotic systems and an overview of their specific properties are discussed in these lecture notes.

The optical spectrum of ions and atoms exhibits a nuclear fingerprint. With sufficient resolution and the choice of appropriate atomic transitions, nuclear properties like the spin, nuclear magnetic dipole moments, electric quadrupole moments and the change in the mean-square charge radius can be determined. During the last decade, progress in this field towards higher sensitivity and accuracy has allowed to study new regions of the nuclear chart.

The gamma decay of the giant dipole resonance (including its low-energy tail region) is an important tool to probe the properties of these states, and thus to test in detail the existing predictions. This paper focuses on two main aspects concerning the electric dipole excitation in nuclei. One is the study of the isospin character of the low-energy tail of the Giant Dipole Resonance (GDR), the so-called pygmy resonance, and the other is the isospin mixing of nuclear systems at finite temperature. In the first case, the pygmy resonance was populated using the inelastic-scattering reaction induced by ¹⁷O beams at 20 MeV/u. Comparison is made with data obtained with (α, α′γ) and (γ, γ′) reactions. In the second case, the gamma decay of the GDR in thermalized nuclear systems, formed in fusion-evaporation reactions, was used to investigate the isospin mixing in ⁸⁰Zr. For this work the reactions ⁴⁰Ca + ⁴⁰Ca at 3.4 MeV/u and ³⁷Cl + ⁴⁴Ca at 2.6 MeV/u were employed.

The f_7/2 shell constitutes an ideal benchmark to investigate different nuclear-structure properties that can be studied in detail by means of the large-scale shell model. In particular, the systematic study of differences in excitation energy in isobaric nuclei has allowed to develop a theoretical method to deduce from the data, changes in the shape of the nuclei along a rotational band, the mechanism of the backbending, and the need to include an isospin-symmetry-breaking term in the nuclear interaction. Recently, these studies have been extended to other mass regions. In particular, I show here some results obtained in the sd shell where the method deduced for the f_7/2 nuclei seems to work well. A new approach based on a charge-dependent realistic nucleon-nucleon interaction is introduced. It allows to deduce the neutron skin at every excited state from the mirror energy differences. Moreover, a strong correlation between the skin and the difference of occupation numbers of neutrons and protons in the s_1/2 orbit is found.

We explore the role of intrinsic and collective modes in the evaporation spectra of particles emitted by a compound nucleus. Collective effects are found to determine the gross features of the spectra, dramatically distorting the exit channel phase space of the free particle. We are also trying to determine whether the spectra retain information on the preformation of the particle inside the compound nucleus. Alpha particle evaporation spectra are analyzed and interesting modulations at the level of 1% are observed.

This lecture is aimed at reviewing recent results on the study of fission dynamics. It is well established that fission is a slow process dominated by nuclear viscosity. This is demonstrated by many experimental observations, mainly based on measurements of fission fragment Total Kinetic Energy (TKE), pre-scission light particle, GDR γ-ray multiplicities and energy spectra. Fission time-scale as well as the nature of energy dissipation during the process and its dependence on the nuclear shape and the temperature are the main aspects which have been addressed. In spite of the extensive work, there are still many open questions on the dynamics of the process, mainly due to the lack of constraints on the models and to the different probes used. Intermediate fissily systems are particularly suited for this study as they present comparable cross sections in the fusion-fission and fusion-evaporation channels, allowing to measure observables in both channels, and therefore to further constrain the models. Furthermore, for these systems the path from equilibrium to saddle configuration is expected to dominate with respect to saddle-to-scission one, reducing the complexity of the physical process to be studied. As a case study, we present the study performed on the nucleus ¹³²Ce, which shows the limits of the Statistical Model in accounting for the whole set of observables. We further present the analysis of the data with a 3D Langevin dynamical approach which proves to be capable of reproducing the values of a large set of observables. Our analysis reinforces the fact that extended data sets are essential to achieve reliable simulations to address the open questions on fission dynamics and strongly suggests the use of setups of high efficiency.

Important progresses in Heavy Ion (HI) physics at medium energies have been achieved in the field of nuclear structure and reaction mechanism over the last three decades. The ultimate goal of such studies was to pin down basic properties of the effective in-medium interaction. In particular, large efforts have been devoted to understand dynamical and thermal instabilities versus isospin asymmetries of nuclei. In this scenario, a prominent role has been played by the design of innovative devices covering a large part of the available phase space. In this lecture, the contribution of the 4π detector CHIMERA is emphasized with respect to the relevant case of the time scale in neck fragmentation around 40 MeV/nucleon of beam energy.

An excursus along the 65 years of a scientific activity mostly dedicated to Nuclear Physics is presented. The overwiew goes back to the first experiments on radioactivity and nuclear decays employing extensively the scintillation spectometry (Turin, Amsterdam, 1952–1957) and to the foundation of the experimental Nuclear Spectrscopy in Italy starting from the systematic researches in Naples in the ’60s of the last century. The extension to Florence and Padua and to the just founded Legnaro Laboratory which could become in the ’70s a national center for nuclear physics research with the institution by the INFN of the LNL (Laboratori Nazionali di Legnaro) is outlined. The domain of the research with particular emphasis on the spectroscopy of 1f_7/2 nuclei as well as the international collaborations with Amsterdam, Orsay, Munich groups is underlined. The evolution following the advent of heavy-ion accelerators and of the new more performant gamma-ray detectors, together with the invented in-beam spectroscopy is accounted for in describing the important achievements in this field of that collaboration. A report is presented about the further developments in Italy with the installation at the LNL of the XTU Tandem, the first national heavy-ion accelerator, opening also in Italy a large area of investigation including the advent of other facilities (LNS with a second Tandem accelerator; the coupling of the two Tandems with the superconducting Cyclotron at LNS and LINAC at LNL, respectively The extension to new areas of research and to new collaborations are mentioned. Finally the promotion of and the participation to the enterprises concerning nuclear physics programs at CERN in the frame of large national and international collaborations concerning experiments with anti-nucleons at LEAR (OBELIX) and relativistic heavy ions at the SPS and at the LHC (ALICE) are pointed out shedding some light on the most interesting results. Conclusions about the different steps of a long journey with physics are drawn.