Table of contents

The International Symposium on 'Exotic Nuclear Structure From Nucleons (ENSFN2012)' was held at the Koshiba Hall, the University of Tokyo, Japan, from October 10th to 12th, 2012. This symposium was supported by RIKEN Nishina Center (RNC) and the Center for Nuclear Study (CNS), University of Tokyo.

This symposium was devoted to discussing recent achievement and perspectives in the structure of exotic nuclei from the viewpoint of the nuclear force.

The following subjects were covered in this symposium from both theoretical and experimental sides:

• Evolution of shell structure and collectivity in exotic nuclei

• Ab-initio theory and its application to exotic nuclei

• Advancement in large-scale nuclear-structure calculations

• Effective Hamiltonian and energy density functional

• Spin-isospin responses

• New aspects of two- and three-body forces

• Impact on nuclear astrophysics

Emphasis was placed on the development of large-scale nuclear-structure calculations and the new experimental information on exotic nuclei.

Around 80 participants attended this symposium and we enjoyed 37 excellent invited talks and 9 selected oral presentations. A special talk was presented to celebrate the 60th birthday of professor Takaharu Otsuka, who has made invaluable contribution to the progress in the fields covered in this symposium.

The organizing committee consisted of T Abe (Tokyo), M Honma (Aizu; chair), N Itagaki (YITP, Kyoto), T Mizusaki (Senshu), T Nakatsukasa (RIKEN), H Sakurai (Tokyo/RIKEN), N Shimizu (CNS, Tokyo; scientific secretary), S Shimoura (CNS, Tokyo), Y Utsuno (JAEA/CNS, Tokyo; scientific secretary).

Finally, we would like to thank all the speakers and the participants as well as the other organizers for their contributions which made the symposium very successful.

Michio Honma, Yutaka Utsuno and Noritaka Shimizu

Editors Tokyo, April 2013

The PDF also contains the conference program.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

Recent progress on three nucleon force study with three nucleon scattering at at intermediate energies (E ≳ 100 MeV/nucleon) are presented, especially focusing on the experimental work on deuteron-proton elastic scattering at RIKEN.

Significant progress has been made in our microscopic understanding of the properties of light nuclei, starting from the basic nucleon-nucleon and three-nucleon interactions among the particles inside the nucleus. The main challenge now is to extend these successes for light nuclei (A ≤ 16) to heavier mass nuclei. Here we discuss three recent approaches within the No Core Shell Model for possibly going beyond the 0p-shell.

We present a novel method to calculate a microscopic effective interaction in many-body systems. This method applies not only to degenerate model spaces but also to non-degenerate model spaces, and therefore allows us to construct microscopically the effective interaction in multi-major-shell model spaces. As an application of this novel method, we examine the effective interaction between valence neutrons of ¹⁸O in the sd-shell (model space of single-major-shell), and in the sdf₇p₃-shell (model space of multi-major-shells). We find that the microscopic cross-shell interactions are much more attractive than have been expected by ad hoc methods. Our approach presents an essential step to a microscopic description of nuclei in multi-major-shells, which is crucial, e.g., to describe many of the neutron-rich nuclei.

We report a history of the developments of the Monte Carlo shell model (MCSM). The MCSM was proposed in order to perform large-scale shell-model calculations which direct diagonalization method cannot reach. Since 1999 PC clusters were introduced for parallel computation of the MCSM. Since 2011 we participated the High Performance Computing Infrastructure Strategic Program and developed a new MCSM code for current massively parallel computers such as K computer. We discuss future perspectives concerning a new framework and parallel computation of the MCSM by incorporating conjugate gradient method and energy-variance extrapolation.

The low-lying excited states of ¹⁰Be and ¹²Be are investigated within a no-core Monte Carlo Shell Model (MCSM) framework employing a realistic potential obtained via the Unitary Correlation Operator Method. The excitation energies of the 2⁺₁ and 2⁺₂ states and the B(E2; 2⁺_1,2 → 0⁺_g.s.) for ¹⁰Be in the MCSM with a standard treatment of spurious center-of-mass motion show good agreement with experimental data. Some properties of low-lying states of ¹⁰Be are studied in terms of quadrupole moments and E2 transitions. The E2 transition probability of ¹⁰C, the mirror nucleus of ¹⁰Be, is also presented with a good agreement to experiment. The triaxial deformation of ¹⁰Be and ¹⁰C is discussed in terms of the B(E2) values.

The nuclear potential and resulting shell structure are well established for the valley of stability, however, dramatic modifications to the familiar ordering of single-particle orbitals in rare isotopes with a large imbalance of proton and neutron numbers have been found: new shell gaps emerge and conventional magic numbers are no longer valid. Current efforts in nuclear structure physics are aimed at unraveling the driving forces behind this structural evolution, which was found most dramatic in neutron-rich species. This manuscript will outline some of the recent efforts at NSCL aimed at shedding light on the shell evolution around neutron number N = 28 in neutron-rich Ar, Cl and Si isotopes.

This contribution focusses on recent measurements of nuclear moments and spins using two complementary methods. The ground state magnetic moments and spins of the exotic isotopes ^49,51K have been measured at the ISOLDE facility at CERN using bunched-beam high-resolution collinear laser spectroscopy. The re-inversion of the ground state spin from I = 1/2 in ^47,49K back to the normal I = 3/2 in ⁵¹K has been established. At GANIL (Caen, France) the quadrupole moment of the ³³Al ground state has been measured using the continuous-beam β-nuclear magnetic resonance method applied to a spin-polarized beam produced at the LISE fragment separator. The large value establishes a very mixed wave function with about equal amounts of normal and neutron particle-hole excited configurations contributing to its ground state wave function. This illustrates the transitional nature of isotopes at the border of the island-of-inversion.

Recent studies on exotic nuclei have rapidly advanced the understanding of the evolution of shell structure, to which Takaharu Otsuka has made remarkable contributions particularly in terms of the nuclear force. This paper presents a brief survey of his achievements, focused on the concept of shell evolution due to the tensor force and the three-nucleon force and on related shell-model works.

Neutron-rich nuclei become increasingly sensitive to three-nucleon forces. These components of nuclear forces are at the forefront of theoretical developments based on effective field theories of quantum chromodynamics. We discuss our understanding of three-nucleon forces and their impact on exotic nuclei, and show how new measurements test and constrain them. Three-nucleon forces therefore provide an exciting link between theoretical and experimental nuclear physics frontiers.

The pairing contribution to the odd-even oscillations in the nuclear binding energies is considered in the framework on the nuclear shell model. Schematic and realistic Hamiltonians are used to understand the trends related to pairing and shell gaps. Detailed results are shown and discussed for the calcium isotopes. Results are also shown for carbon, oxygen and neon as well as the overall trends for all nuclei.

Important roles of the NN interaction in the shell evolution, which have been pointed out by Otsuka and his collaborators, can be investigated by the self-consistent mean-field approaches with the semi-realistic interactions. We show that the shell evolution in the Z = 50 and Z = 20 nuclei is appropriately described by the semi-realistic interactions that include the realistic tensor force. The M1 strengths in ²⁰⁸Pb are also reproduced by the semi-realistic interactions in the HF+RPA, which are another manifestation of the tensor force in nuclear structure.

Excited states in the exotic N = 34 isotope ⁵⁴Ca have been measured for the first time via in-beam γ-ray spectroscopy with proton-knockout reactions from ⁵⁵Sc and ⁵⁶Ti radioactive beams on a Be reaction target at the Radioactive Isotope Beam Factory, Japan. A strong candidate for the transition from the first 2⁺ state to the 0⁺ ground state has been identified, in addition to several other weaker transitions. The structure of the N = 33 isotope ⁵³Ca has also been investigated from the same data. Preliminary γ-ray energy spectra for ⁵⁴Ca and ⁵³Ca will be presented and the significance of the N = 34 subshell closure will be examined. Predictions of several shell-model interactions performed in the fp model space will be discussed in light of the new results.

The geometry of the shears mechanism in nuclei is obtained by taking the limit of large angular momentum of shell-model matrix elements.

A brief review is given on the controversy and its solution about the fact that the angular momentum vector of protons and that of neutrons in well-deformed nuclei at low total angular momenta have a strong correlation that they are oriented in opposite directions. In a simple two-rotor model in 2-dimensional space, this fact is explained as originating from the quantum mechanical uncertainty relation between the angle and the angular momentum for the relative rotation of the two rotors. As the second topic, a more realistic model consisting of two triaxial rotors in 3-dimensional space coupled with a QQ interaction is employed to investigate a possible shears-band-like collective rotation predicted by T. Otsuka, in which the angle at which the angular momentum of protons and that of neutrons intersect changes continuously from 180° at spin zero toward 0° at high spins within the same rotational band. The probability distributions of the angle between the two angular momenta and the angle between the longest principal axes of two rotors are calculated to examine the participation of the scissors mode in the evolution of the ground rotational band versus spin.

A brief overview of the recent advancement in the microscopic study of the interacting boson model (IBM) is given. A new nucleon-boson mapping method has been proposed recently, that derives the IBM Hamiltonian based on the self-consistent mean-field model with the microscopic energy density functional (EDF). The mean-field total energy surface computed with a given EDF is mapped onto the analogous energy expectation value in the boson condensate, thereby the energy spectrum and the transition rates are generated. Since the EDF framework allows an accurate global description of nuclear intrinsic properties, the IBM is derived in a unified way, basically for any situation of low-energy quadrupole collective states of nuclei. The basic notion of the new mapping technique is sketched.

The covariant density functional theory with a few number of parameters allows a very successful description of the ground-state and excited-state properties for the nuclei all over the nuclear chart. The recent progresses on the application of the covariant density functional theory for the nuclear mass and β-decay half-life, as well as their influences on the astrophysical rapid neutron-capture process calculation are reviewed.

The underlying scenario of low-energy heavy-ion collisions is presented based on time-dependent density-functional calculations. A classification of several types of reaction dynamics is given with respect to their time-scales.

In light of availabilities of a variety of radioactive isotope (RI) beams and progress in physics of unstable nuclei, new possibilities in experimental studies of spin-isospin responses are foreseen. They include: 1) studies of spin-isospin responses of unstable nuclei, 2) studies of higher multipoles, in particular spin-dipole responses, 3) studies of higher tones, such as isovector monopole resonances, and 4) studies of many phonon states. In this article, we discuss how the study of spin-isospin responses will be proceeded, taking examples from experiments with the SHARAQ spectrometer at RI Beam Factory and with the Grand Raiden spectrometer at Research Center for Nuclear Phyics, Osaka University.

We apply the continuum quasiparticle random phase approximation to calculate the direct neutron capture cross section relevant to the r-process nucleo-synthesis. The electric dipole strength function in an even-even n-rich nucleus is decomposed with respect to the channels of direct neutron decays. Using the detailed balance relation, the partial dipole strengths are converted to obtain the direct neutron-capture cross sections. Numerical examples are given for ¹⁴²Sn.

With the advent of high analysis technology in detecting the Gamow-Teller (GT) excited states beyond one nucleon emission threshold, the quenching of the GT strength to the Ikeda sum rule (ISR) seems to be recovered by the high-lying (HL) GT states. We address that these HL GT excited states result from the smearing of the Fermi surface by the increase of the chemical potential owing to the deformation within a framework of the deformed quasi-particle random phase approximation (DQRPA). Detailed mechanism leading to the smearing is discussed, and comparisons to the available experimental data on ⁷⁶Ge,⁸²Se and N = 20 nuclei are shown to explain the strong peaks on the HL GT excited states.

We carry out a systematic study of electric dipole mode (E1) for neutron-rich isotopes from nickel (Z=28) to tin (Z=50) using a time-dependent mean-field theory. Our time-dependent scheme is the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory which can self-consistently describe nuclear dynamics with pairing correlation. We focus our discussion on the pygmy dipole resonance (PDR) and E1 polarizability (α_D). The correlation between neutron-skin thickness and PDR strongly depends on the neutron number, but the correlation between the skin thickness and α_D is much more stable.

The close connection between neutrino physics and the physics explored at rare isotope facilities is explored. The duality between the Hamiltonian describing the self-interacting neutrino gas near the proto-neutron star in a core-collapse supernova and the BCS theory of pairing is elucidated. This many neutrino system is unique as it is the only many-body system driven by weak interactions. Its symmetries are discussed.

We summarize several new developments in the nuclear equation of state for supernova simulations and neutron stars. We discuss an updated and improved Notre-Dame-Livermore Equation of State (NDL EoS) for use in supernovae simulations. This Eos contains many updates. Among them are the effects of 3- body nuclear forces at high densities and the possible transition to a QCD chiral and/or super-conducting color phase at densities. We also consider the neutron star equation of state and neutrino transport in the presence of strong magnetic fields. We study a new quantum hadrodynamic (QHD) equation of state for neutron stars (with and without hyperons) in the presence of strong magnetic fields. The parameters are constrained by deduced masses and radii. The calculated adiabatic index for these magnetized neutron stars exhibit rapid changes with density. This may provide a mechanism for star-quakes and flares in magnetars. We also investigate the strong magnetic field effects on the moments of inertia and spin down of neutron stars. The change of the moment of inertia associated with emitted magnetic flares is shown to match well with observed glitches in some magnetars. We also discuss a perturbative calculation of neutrino scattering and absorption in hot and dense hyperonic neutron-star matter in the presence of a strong magnetic field. The absorption cross-sections show a remarkable angular dependence in that the neutrino absorption strength is reduced in a direction parallel to the magnetic field and enhanced in the opposite direction. The pulsar kick velocities associated with this asymmetry comparable to observed pulsar velocities and may affect the early spin down rate of proto-neutron star magnetars with a toroidal field configuration.

We study the nuclear weak response in light-to-heavy mass nuclei and calculate neutrino-nucleus cross sections. We apply these cross sections to the explosive nucleosynthesis in core-collapse supernovae and find that several isotopes of rare elements ⁷Li, ¹¹B, ¹³⁸La, ¹⁸⁰Ta and several others are predominantly produced by the neutrino-process nucleosynthesis. We discuss how to determine the suitable neutrino spectra of three different flavors and their anti-particles in order to explain the observed solar system abundances of these isotopes, combined with Galactic chemical evolution of the light nuclei and the heavy r-process elements. Light-mass nuclei like ⁷Li and ¹¹B, which are produced in outer He-layer, are strongly affected by the neutrino flavor oscillation due to the MSW (Mikheyev-Smirnov-Wolfenstein) effect, while heavy-mass nuclei like ¹³⁸La, ¹⁸⁰Ta and r-process elements, which are produced in the inner O-Ne-Mg layer or the atmosphere of proto-neutron star, are likely to be free from the MSW effect. Using such a different nature of the neutrino-process nucleosynthesis, we study the neutrino oscillation effects on their abundances, and propose a new novel method to determine the unknown neutrino oscillation parameters, θ₁₃ and mass hierarchy, simultaneously. There is recent evidence that some SiC X grains from the Murchison meteorite may contain supernova-produced neutrino-process ¹¹B and ⁷Li encapsulated in the grains. Combining the recent experimental constraints on θ₁₃, we show that although the uncertainties are still large, our method hints at a marginal preference for an inverted neutrino mass hierarchy for the first time.

Recent data compilations of abundances of Strontium and Barium in Extremely Metal Poor Stars show that large fluctuations exist in the ratio of the abundances of those elements. Two models exist for explaining those fluctuations, as well as the apparent truncation of data for those elements for stars having metallicity of [Fe/H] < −3.5. We study the factors that place upper limits on the logarithmic ratio [Sr/Ba] in the two models. A model has been developed in which the collapse of type II supernovae may produce a pronounced [Sr/Ba] enhancement in single-site r-process enriched stars. This model is consistent with galactic chemical constraints of light-element enrichment in metal-poor stars.

The A ~ 60-70 mass region of neutron-rich nuclei with Z ≤ 28 presents several interesting properties when approaching N=40. At this subshell closure a new region of deformation develops. From the experimental side, these nuclei can be populated at relatively high spin by means of multi-nucleon and deep-inelastic collisions. Selected results on the gamma-ray spectroscopy of the neutron-rich nuclei in this mass region are discussed. In particular, the shape coexistence in ⁶⁷Co at low excitation energy, populated by bombarding a ²³⁸U target with a 460 MeV ⁷⁰Zn beam at the Legnaro National Laboratory is interpreted by means of shell model calculations in a large valence space. These calculations are extended to the description of excited states in Zn isotopes.

Low-frequency collective modes of excitation in neutron-rich nuclei are investigated in the framework of the nuclear energy-density functional method. It is shown that the collective Hamiltonian approach gives the quantitative description of the low-lying states in transitional nuclei with the Skyrme and pairing energy-density functionals as a microscopic input. The inertial functions for large-amplitude vibration and rotation are evaluated by the local normal modes along the axial quadrupole collective coordinate. The time-odd components of the mean fields are fully included in the derived masses.

We study Cr and Ni isotopes by Monte Carlo shell model (MCSM) calculations in a pfg₉d₅ shell. In the MCSM, the wave function is represented as a linear combination of angular-momentum- and parity-projected deformed Slater determinants (MCSM bases), and we can calculate eigenstates in a large model space such as the pfg₉d₅ shell. We study the intrinsic shape of nuclei by using deformations of the unprojected MCSM bases. We show calculated results of Cr and Ni isotopes and a level scheme of ⁶⁸Ni, and discuss the strength of the magicity of N = 40 in Cr and Ni isotopes and shape coexistence in ⁶⁸Ni.

Using the shell-model Monte Carlo method, we investigate how temperature and rotation affect pairing properties for nuclei in the fp - gds region. The re-entrance of pairing correlations with temperature is predicted at high rotational frequencies. It manifests through an anomalous behavior of the specific heat and level density.

The one-quadrupole phonon excitation of mixed symmetry, the 2⁺_1,ms state, is a fundamental building block of nuclear structure. This article gives a summary of our recent experimental research on this excitation mode in the A = 90 and A = 130 mass regions.

A study of the shape transition from spherical to axially deformed nuclei in the even C_e isotopes using the nucleon-pair approximation of the shell model is reported. As long as the structure of the dominant collective pairs is defined in a framework appropriate to deformed nuclei, the model is able to produce a shape transition. The resulting transition is too rapid, however, with nuclei that should be transitional being fairly well deformed. The possibility of using several pairs with each angular momentum to improve the description of the transitional region is discussed as is the possibility of using a larger single-particle space to better describe the moments of inertia in the deformed regime.

The band structure of the neutron-rich Se and Ge isotopes has been studied in terms of the full-fledged shell model. The monopole and quadrupole pairing plus quadrupole-quadrupole interaction is employed as an effective interaction. The model reproduces well the energy levels of high-spin states as well as the low-lying states. In order to investigate the structure of the high-spin states and low-lying collective states, the energy spectra in the shell model are compared with those in the quantum-number-projected generator coordinate method. It is shown that the triaxial components play essential roles in describing the γ bands.

Breakup reactions play important roles in elucidating the structures near the drip lines, such as nuclear halo. The recent experimental results using the Coulomb and nuclear breakup reactions for the neutron-drip-line nuclei at the new-generation RI beam facility, RIBF at RIKEN, are presented. Focuses are put on the results on the newly found halo nucleus ³¹Ne, which is intriguing also in that this nucleus is in the island-of-inversion and thus could be strongly deformed. The results on other Ne/Mg/Si neutron rich isotopes ranging from N=20 towards N=28 are also briefly reported. The first breakup experiments using SAMURAI facility at RIBF and future perspectives are also presented.

The anomaly in the interaction cross section of ²³O is discussed through a new experiment performed at the FRS, GSI. The matter radius of ²³O is derived through a Glauber model analysis. Results using ab initio coupled cluster theory as well as densities from mean field models are presented.

We present recent results from no-core configuration interaction calculations for ⁸Be, ¹⁰Be, and ¹²Be using the phenomenological two-body interaction JISP16. We calculate the binding energies of the ground state and the excitation energies of the low-lying positive-parity states. We discuss the contributions from the proton and neutron intrinsic spin and orbital motion to the total spin for several states, and use this to identify states which may be dominated by α-cluster configurations. In addition, we also calculate other observables such as dipole and quadrupole moments, as well as transition rates for select E2 transitions.

Investigations of exotic cluster-like phenomena in the framework of the Skyrme-Hartree-Fock approach are reported. The occurrence of highly excited isomeric states is discussed in connection with the question of their stability in static and time-dependent Hartree Fock (TDHF) calculations. We find rotational stabilization of a 4α chain structure in ¹⁶O occurring for a limited range of angular momenta. A toroidal configuration of ⁴⁰Ca was also stabilized by rotation and provides a very interesting example of rotation about a symmetry axis with a strictly quantized total angular momentum. Finally we look at the formation of nuclear pasta phases in a time-dependent approach and their classification.

Structures of ground and excited states of C isotopes are theoretically investigated with the method of antisymmetrized molecular dynamics. For ¹⁴C, it is suggested that a linear-chain 3a structure can be stabilized by the excess neutrons and may construct an rotational band near the ¹⁰Be+α threshold energy. In ¹¹C and its mirror nucleus ¹¹B, a cluster gas state and a linear-like cluster state are suggested in excited states. Possible assignment of the cluster states in ¹¹B with the experimental energy levels are discussed. Deformations of proton and neutron densities of the ground bands in neutron-rich C are also discussed.

The wave functions of the ground states for ^8,10Be which are obtained from the Monte Carlo shell model (MCSM) are investigated. A method to define an intrinsic state in the MCSM is discussed. The appearance of two-α-cluster structure in ⁸Be and the property of the valence neutrons in ¹⁰Be are discussed.