Nuclear Structure Problems

The following sections are included:

• PREFACE

• CONTENTS

GANIL presently offers unique opportunities in nuclear physics and many other fields that arise from not only the provision of low-energy stable beams, fragmentation beams and re-accelerated radioactive species, but also from the availability of a wide range of state-of-the-art spectrometers and instrumentation. An overview of the physics with secondary beams carried out at GANIL is presented. Selected examples of recent experiments using fragmentation of high energy intense stable heavy ions beams and reaccelerated SPIRAL1 “exotic” beams and the associated instruments are used to illustrate the ongoing physics program. With the construction of SPIRAL2 over the next few years, GANIL is in a good position to retain its world-leading capability. As selected by the ESFRI committee, the next generation of ISOL facility in Europe is represented by the SPIRAL2 project to be built at GANIL (Caen, France). The future prospects of the accelerator complex GANIL-SPIRAL1 and the path towards SPIRAL2 is also briefly introduced.

Brief introduction to Nishina Center for Accelerator-Based Science and the present status of Japanese nuclear physic are presented.

I report present status and perspectives of “RI Beam Factory (RIBF)” at RIKEN. RIBF is a top world-class in-flight RIB facility. Emphasis is given to on-going and future programs at the new facility through introducing experimental devices and recent highlights.

The characteristics of the new N = 16 shell gap at the neutron drip-line can be deduced from the neutron excitations of ²⁴O. An experiment was carried out to investigate the unbound excited states of ²⁴O using the proton elastic and inelastic proton scattering. It was performed in the BigRIPS line and combines the unique intensities of the RIBF ²⁴O beam with the state-of-the-art particle detector array MUST2. The method is explained.

The high-resolution SHARAQ spectrometer has been constructed at the RI Beam Factory to facilitate missing mass spectroscopy with RI-beam induced reactions. Cathode read-out drift chambers developed under GANIL-CNS collaboration were installed at the SHARAQ focal plane and were successfully applied to tracking of Z = 1−7 ions. We studied ion-optical properties of the SHARAQ spectrometer and the beam-line and accomplished simultaneous fulfillment of lateral and angular dispersion-matching conditions for a secondary ¹⁰C beam. A series of experiments to investigate IVMRs were performed with the SHARAQ spectrometer in 2009–2010.

The measurement of nuclear moments of a μ-second isomeric state have been successfully performed using the RIKEN Radioactive Ion Beam Facility. The Time Dependent Perturbed Angular Distribution technique was applied on the ⁴³S isomeric state produced by the fragmentation of a ⁴⁸Ca beam and selected with the BigRIPS spectrometer. Following the measurement of the known g-factor of the isomer the quadrupole moment of this state was measured. Its spectroscopic quadrupole moment |Q_S| = 23(3) efm² agreed with both shell model and beyond mean field calculations.

Based on the technique of fragmentation-induced spin polarization combined with the β-NMR method, we have conducted a series of ground-state nuclear-moment measurements in a region of light neutron-rich nuclei at RIKEN. The research has recently been extended also at GANIL. The ground-state studies will be further enhanced by the upgrade of RIPS proposed in the RIBF Phase-II program. Also, utilizing the technique of fragmentation-induced spin-orientation, nuclear-moment measurements of isomeric state were conducted. Remarkably, we have recently developed a method to produce highly spin-aligned RI beams in a new promising scheme. The method was first examined using BigRIPS, where a highly spin-aligned isomeric ^32mAl beam was successfully produced through the two-step projectile fragmentation reaction.

Shell structure evolution in the regions around Z=8 and around N=68 has been inferred from transfer reaction studies using the MUST2 detector. A low-lying state in ¹²O has been observed in the study of the two-neutron transfer reaction ¹⁴O(p,t) evidencing mirror symmetry of the previously observed quenching of N=8 magic number on the neutronrich side. In the higher mass region the ⁶⁸Ni(d,p) reaction has been investigated to selectively study the neutron shell orbitals that are crucial to interpret the strong shell effects observed around ⁶⁸Ni. Preliminary results show a strongly excited state around 2.5 MeV excitation energy in ⁶⁹Ni that could correspond to the 2d5/2 orbital.

We have performed the first direct lifetime measurement of the state in ⁷⁴Zn. The neutron-rich ⁷⁴Zn beam was produced by in-flight fragmentation of ⁷⁶Ge at the Grand Accélérateur National d'Ions Lourds and separated with the LISE spectrometer. The lifetime of the state was measured by the recoil-distance Doppler-shift method with the Cologne plunger device combined with the EXOGAM detectors. The lifetime of the state in ⁷⁴Zn was determined to be 27.0(24) ps, which corresponds to a reduced transition probability .

Recently some approaches to photonuclear reaction, based on the density functional theory, have been developed. We show some results of photoabsorption cross sections for spherical and deformed nuclei. We are now ready for a systematic calculation of excited states for whole nuclear chart, using the next-generation supercomputer.

Effects of Skyrme tensor interactions on the spin-orbit splittings are studied by using Hartree-Fock-Bogoliubov model. The charge-exchange spin-dipole (SD) excitations of ²⁰⁸Pb are also studied by using a fully self-consistent Skyrme Hartree-Fock plus Random Phase Approximation (HF+RPA) formalism including the tensor interaction. It is found that the tensor correlations have a unique, multipole-dependent effect on the SD excitations, that is, they produce softening of 1⁻ states, but hardening of 0⁻ and 2⁻ states. This paves the way to a clear assessment of the strength of the tensor terms.

Deformation and many particle and many hole configurations in the island of inversion are investigated with antisymmetrized molecular dynamics (AMD). The result suggests the coexistence of many particle and many hole configurations with different deformation at small excitation energy. Detailed study of the excitation spectrum is performed for ³³Mg. We suggest the negative-parity assignment for the ground state, and the coexistence of many particle hole states at very small excitation energy is predicted.

Structures in low-lying states of ⁴²Ca have been studied focusing on various deformations and ± cluster correlations using the antisymmetrized molecular dynamics and the generator coordinate method. Three deformed states coexist in low-lying states of ⁴²Ca, and one of them contain much ±–³⁸Ar cluster structure components.

We extend top-on-top model to even-A nuclei, where two particles in different single-particle orbitals (tops) correlate with the triaxial rotor (top). We apply the model to describe the energy levels and transition rates for the triaxial, strongly deformed (TSD) bands in odd-odd nucleus ¹⁶⁴Lu.

In order to solve the nature of ⁹He ground state, additional information on this unbound nucleus with extreme N/Z ratio was needed. The present study was performed via the (d,p) reaction, a standard tool for determination of neutron single-particle distribution.

We propose a new theoretical approach to describe nucleus using bare nuclear interaction, in which the tensor and short-range correlations are described with the tensor optimized shell model (TOSM) and the unitary correlation operator method (UCOM), respectively. We show the obtained results of He isotopes using TOSM+UCOM, such as the importance of the pn-pair correlated by the tensor force, and the structure differences in the LS partner states of ⁵He.

We calculated isoscalar giant monopole and isovector giant dipole resonances (GDRs) in tin isotopes using the quasi-particle random phase approximation (QRPA). Centroid energies for the giant resonances are derived from relevant strength distributions and compared to the available data. Roles of the pairing energies in the giant resonances are also discussed in detail.

We systematically investigate the E1 strength distributions of even-even nuclei (Z = 8 – 20 isotopes) using the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory that can describe the dynamics of superfluid nuclei. Especially, we focus on the low-lying E1 strength that is often called pygmy dipole resonance and investigate the neutron-number dependence of the strength in neutron-rich nuclei. The evolution of the low-lying E1 strength is determined by several factors including the neutron-shell effects, the deformation and the pairing.

The generalized two-center cluster model (GTCM), which can treat various single particle configurations in general two center systems, is applied to the light neutron-excess system, Be isotopes (α+α+N+N+…). We show that the covalent and ionic configurations coexist in a same nucleus.

Resonances observed in the ²⁸Si + ²⁸Si collision are studied by a molecular model. At high spins, a stable dinuclear configuration is found to be equator-equator touching one. Energy spectrum of the normal modes around the equilibrium is shown. These modes are expected to be the origin of the large number of resonances observed, hence theoretical analyses for the physical quantities are done. Disalignments between the orbital angular momentum and the fragment spins in the resonance state are clarified. Moreover the analyses of the angular correlations indicate a characteristic feature for each normal-mode excitation. Thus it is possible to identify the mode.

We briefly review our formula for a proton-nucleus total reaction cross section, σ^R, constructed in the black-sphere approximation of nuclei, in which a nucleus is viewed as a “black” sphere of radius “a”. An extension to reactions involving neutron-rich nuclei is also reported.

Second RPA calculations with a Skyrme force are performed to describe both high- and low-lying excited states in ¹⁶O and ⁴⁸Ca. The coupling between 1 particle-1 hole and 2 particle-2 hole as well as that between 2 particle-2 hole configurations are fully taken into account and the residual interaction is considered with the proper rearrangement terms. A several-MeV shift to lower energies is systematically found with respect to the RPA distributions for the strength distributions of giant resonances. The nature of the low-energy dipole excitations is analyzed in ⁴⁸Ca: it is found that in general these excitations cannot be in interpreted in terms of oscillations of the neutron skin against the core, with the exception of the peak with the largest B(E1) value, which is located at 9.09 MeV. For this peak the neutron transition density dominates and the neutron and proton transition densities oscillate out of phase in the internal part of the nucleus leading to a strong mixing of isoscalar and isovector components. Therefore, this state shows some features usually associated to pygmy resonances.

A Hamiltonian of the interacting boson model (IBM) is determined from the mean- eld theory with nuclear energy density functionals (EDFs). The multinucleon dynamics of the surface deformation is simulated in terms of the boson degrees of freedom. The interaction strengths of the IBM Hamiltonian are determined so that the potential energy surfaces (PESs) of a given EDF with quadrupole degrees of freedom is compared with the corresponding PES of IBM. A fermion-to-boson mapping for a rotational nucleus is discussed. Some examples resulting from the present spectroscopic calculations are shown for neutron-rich Pt, Os and W isotopes.

The miroscopic method of deriving the quadrupole collective Hamiltonian is presented. Shape changes and transitions in neutron-rich magnesium and chromium isotopes are discussed using the quadrupole collective Hamiltonian.

We propose a practical method for determining the collective potential and inertial functions in the five-dimensional quadrupole collective Hamiltonian. We have applied this method to large-amplitude shape mixing dynamics in the low-lying states of proton-rich Kr isotopes.

The decay of the ground-state two-proton emitters ⁴⁵Fe and ⁵⁴Zn was studied with a time-projection chamber and the emission of two protons was unambiguously identified. The total decay energy and the half-life measured agree with the results from previous experiments. The energy sharing between the two protons and their relative emission angle was determined with a time projection chamber and is compared to model predictions. In parallel, we observed directly β-delayed two- and three-proton emission from ⁴³Cr, a known β-delayed two-proton emitter.

Using the proportionality relationship between the forward angle (p, n) cross section and the reduced transition probability B(GT), the |J_στ (q = 0)| values have been deduced for recent (p, n) reaction data on ¹⁴Be at E_p = 69.4 MeV and for existing data on ¹²C at various incident energies. A discussion was made on the energy dependence of |J_στ(q = 0)| and on mutual consistency between the values for ¹⁴Be and ¹²C.

The present work aims at experimentally clarifying the structure change of neutron-rich Mg isotopes as a function of the neutron number by firmly establishing the level schemes of the Mg isotopes in a wide excitation energy range. We use our unique method of β-decay spectroscopy which takes advantage of anisotropic β decay of spin-polarized Na isotopes. The asymmetry parameters of the β decay are the effective tool to unambiguously assign the spin-parity of levels in the daughter nucleus. As the first step of the systematic studies on neutron-rich Mg isotopes from lighter region outside of the N = 20 “island of inversion” to heavier one across through the island, very detailed level scheme of ²⁸Mg and ²⁹Mg have been successfully established at TRIUMF, where the world-highest polarized alkali beams are available.

A new γ-ray spectroscopy method was developed using low-energy (around 5-10 MeV/u) RI beam induced fusion reaction, which enables us to study high-spin states of nuclei in wider mass region where high-spin states could not be produced by the combination of the stable beam and stable target. The low-energy ¹⁷N RI beam was produced by the direct reaction using low-energy primary beam and was transported up to the secondary target using the EN beam line at RCNP, Osaka University. Two experiments were performed to investigate the high-spin states in ¹⁴²Pr (N=83 isotone) and in ¹³⁶Ba (N=80 isotone) by this new γ-ray spectroscopy method using the low-energy ¹⁷N RI beam.

In order to establish the HICE using the super-allowed Fermi type reaction that is selective to isovector the non-spin-flip mode, the ⁹⁰Zr(¹⁰C,¹⁰B(IAS)) experiment at 200 MeV/u was performed. We successfully observed the signature of the isovector non-spin-flip transition by detecting the gamma-ray emitted from ¹⁰B(IAS). We also observed strength at around more than Ex > 20 MeV in ⁹⁰Nb coincident with 1022-keV gamma-ray which indicates the non-spin-flip transition.

The unbound nucleus ¹³Be was investigated by means of invariant-mass method in the one-neutron removal reaction of ¹⁴Be at 69 MeV/nucleon. A p-wave resonance was observed at 0.51 MeV in the decay energy spectrum. The existence of the low-lying p state shows the quenching of the N = 8 shell gap.

Studying the weak nuclear response, especially the Gamow-Teller (GT) transitions, starting from stable as well as unstable pf-shell nuclei, is one of the key issues in nuclear and nuclear-astro physics. We study the GT transitions starting from T_z = ±2 mirror nuclei, respectively, by means of β decays and complementary hadronic (³He, t) charge-exchange reactions. Under the assumption that isospin is a good quantum number, symmetry is expected for the structure of mirror nuclei and the GT transitions starting from them. The β-decay halflife and branching ratios and the strength distribution of GT transitions from the (³He, t) reaction are compared and also combined for the understanding of the nuclear structure of pf-shell far-from-stability nuclei.

We here discuss how to determine the total neutrino mass and oscillation parameters from supernova nucleosynthesis, the Galactic chemical evolution, and the CMB anisotropies. Neutrinos play the critical roles in nucleosynthesis of light-to-heavy mass nuclei in core-collapse supernovae. We study the nucleosynthesis induced by neutrino interactions and find suitable average neutrino temperatures in order to explain the observed solar system abundances of several isotopes ⁷Li, ¹¹B, ¹³⁸La and ¹⁸⁰Ta. These isotopes are predominantly synthesized by the supernova ν-process. We also study the neutrino oscillation effects on their abundances and propose an astrophysical method to determine the unknown neutrino oscillation parameters θ₁₃ and mass hierarchy.

Neutron-rich isotones with neutron shell closure N = 126 on the r-process path are supposed to be progenitors which form a peak around A = 195 in the r-abundance element distribution. Their β decay properties are considered to play critical roles for better understanding where the heavy elements such as gold and platinum were made in the universe. We are now advancing a project to construct KEK Isotope Separation System to study β decay properties and nuclear structures of neutron-rich nuclei around N = 126 experimentally. Those isotopes will be obtained via multi-nucleon transfer reactions induced by low-energy beams. For the study of the rare channel reaction products, it is essential to select both the element and mass number of them. We will adopt a gas catcher system combined with the laser resonance ionization and ISOL, which collect all reaction products and select the atomic number and mass of them efficiently. That system allows us to measure their β decay properties by two-layer plastic scintillators and germanium detectors.

New shell model Hamiltonians, which give successful description of spin responses in nuclei, are applied to astrophysical processes in stars induced by nuclear weak interactions. Neutrino-nucleus reactions in supernova explosions, electron capture reactions in stellar core-collapse process and β-decays in r-process are discussed.

We examine how the uncertainties in nuclear data inputs affect the νp-process in the neutrino-driven winds. We find that a small variation of the rates of triple-α and of the (n, p) reaction on ⁵⁶Ni leads to a substantial change in the p-nuclei production. The uncertainty in the nuclear mass of ⁸²Zr can also lead to a factor of two reduction in the abundance of the p-isotope ⁸⁴Sr.

The momentum dependence of dissipation in heavy-ion reactions is studied. Special attention is paid to the dissipation due to the spin-orbit and spincurrent tensor contributions in the Skyrme energy-density functional formalism. The spin polarization, which brings about large dissipation in the early stage of heavy-ion reactions, mainly arises from those two contributions.

The following sections are included:

• Introduction

• On the polarization potential

• Near- and above-barrier fusion

• Discussion of the ¹¹Be+ ⁶⁴Zn quasi-elastic scattering

• References

Super-Heavy Elements (SHE) are synthesized by fusion reactions between heavy ions. Unfortunately, the fusion of very heavy systems is experimentally known to be strongly hindered, though the mechanism is not clearly understood yet. We have studied mainly the mechanism by numerical calculations, but recently have started the study with analytical method, which is supposed to clarify dynamical aspects of the physical mechanism. From where the hindrance comes, what the mechanism is, and to where the results are developed are briefly presented in the present talk.

We study further a recent model for fission-fragment yield distributions based on Brownian shape motion on 5D potential-energy surfaces. Previously it was shown that this model describes well the transition between symmetric and asymmetric fission in the light Th region; here we study this transition near ²⁵⁸Fm and compare to scission-type yield models. We also study the impact of the relative density of grid points in the different shape coordinates. Although extreme changes in grid spacing affect the calculated yields to some degree, we find that the full 5D model with our origina grid choice is remarkably robust and that it is therefore suitable for applications, for example fission yields relevant for fission recycling in the r-process and its termination by fission.

We present the installation and validation of the TNT2D digital cards on the JUROGAM and JUROGAM2 germanium arrays and their use for the low cross-section experiment on ²⁴⁶Fm.

In-flight gamma spectroscopy of rare isotopes at relativistic energies, from fifty to several hundreds of MeV/nucleon, is one of the most efficient tools to investigate shell effects in exotic nuclei.We propose a new method to increase the sensitivity of prompt-gamma spectroscopy by more than one order of magnitude compared to existing setups, leading to a significant step forward. The intended program is based on proton-induced knockout reactions such as (p, 2p). Experiments should take advantage of the most exotic neutron-rich beams produced at the RIBF¹ in RIKEN and the upcoming european FAIR facility. MINOS has been funded by the European Research Council for the 2010-2015 period.

A new experimental apparatus has been developed to measure proton elastic scattering from radioactive ion beams using inverse kinematics. We have performed experiments for several unstable nuclei such as ^9,10,11C, ²⁰O, and ^66,70Ni. While the experiments, the new apparatus has provided a high performance of a long-term use of 1-mm-thick and 30-mm-ø solid hydrogen target, and a excitation energy resolution of ΔE_x ∼ 500 keV.

The vector analyzing power has been measured for the elastic scattering of neutron-rich ⁶He from polarized protons at 71 MeV/A making use of a newly constructed solid polarized proton target operated in a low magnetic eld of 0.1 T and at a relatively high temperature of 100 K. An optical model analysis revealed that the spin-orbit potential for ⁶He is characterized by shallow and long-ranged shape compared with the global systematics of stable nuclei. Such a characteristics re ect a di used density distribution of the neutron-rich isotopes.

The DESIR collaboration proposes the construction of a low-energy beam facility at GANIL-SPIRAL2 to study the properties of exotic nuclei in unexplored regions of the nuclide chart. Beam preparation devices including gas catchers, radiofrequency quadrupoles, high resolution separators and ion traps are under construction in order to provide high quality beams to the users. The DESIR Physics program addresses by means of complementary experimental techniques most of the current interrogations regarding the structure of exotic nuclei, the fundamental interactions driving their properties, as well as their formation in the universe.

An electron scattering facility dedicated for the structure studies of short-lived nuclei is under construction at RIKEN RI Beam Factory. This facility aims at carrying out neveryet-performed electron scattering experiments for short-lived nuclei to study their electromagnetic properties of the ground state, such as the charge density distributions. The facility is expected to start its operation in the year of 2014.

The new SPIRAL2 LINAG accelerator, developed for production of high intensity deuteron beam, will deliver unprecedented high intensity stable beams. Used for direct reactions at the Super Separator Spectrometer (S³) target they will open new horizons for the physics of nuclei with low production crosssection and rare nuclei at the extreme limits of the nuclear chart. This article presents the research and development program launched in order to design the best setup according to the three main physics cases of this project: Synthesis of new Super Heavy Elements, Spectroscopy of Very and Super Heavy Elements and Spectroscopy of neutron-deficient nuclei around ¹⁰⁰Sn.

SAMURAI is a spectrometer which is now being constructed at RIKEN RIBF. This spectrometer is characterized by a large angular- and momentumacceptance enabling, for example, multi-particle coincidence measurements. The on-site construction started in October 2010, and the rst experiments will be performed in early 2012. Here the current status and future plan of this SAMURAI project is presented.

The recent upgrade and performances of the VAMOS spectrometer installed at Ganil are presented. The ”dual” character of VAMOS combined with its large acceptance makes the device unique worldwide, and of key importance for the efficient use of stable and future radioactive beams at Ganil.

Final remarks of this symposium are given. Physics of exotic nuclei with RIbeam is rapidly developing, and many exciting results and ideas were presented in this symposium. I also noted that the observation of the second 0⁺ state of ³⁴Si isotope is of particular interest.

The following sections are included:

• PARTICIPANTS

• PROGRAM