Modern Physics Letters A

The R-matrix method is applied to the Continuum Discretized Coupled Channel (CDCC) approximation. The variational basis is chosen as Lagrange functions, which are shown to be efficient and accurate. We apply the general formalism to the d + ⁵⁸Ni elastic scattering at E_d = 80 MeV. Future developments are briefly discussed.

³He + p scattering phase shifts for the S- and P-waves are studied in a microscopic cluster model in order to investigate the role of the d + 2p channel in the low-energy phase shifts. In the present cluster model, the description of the ³He wave function is extended from a simple (0s)³ model to a three-body model and two different nucleon-nucleon interactions, the Minnesota and AV8' potentials, are employed. The present extended cluster model shows that the d + 2p channel is indispensable to reproduce the resonant phase shifts in the AV8' potential while it plays a minor role in the MN potential. On the contrary, the role of this channel in the S-wave non-resonant phase shifts is negligible in both potentials.

This article is composed of three subjects. First, the relation between the method of continuum-discretized coupled channels (CDCC) and the Faddeev theory is clarified to show the validity of CDCC. Second, CDCC is applied to four-body reactions such as (⁶He, nn⁴He) as an example of recent progress in CDCC. Third, we propose a microscopic version of CDCC in which a localized form of the microscopic nucleon-nucleus optical potential is used as an input of CDCC calculation instead of the phenomenological optical potential commonly used. The validity of the Brieva-Rook localization is shown for the proton scattering in a wide incident-energy range.

We solve the nd scattering in the Faddeev formalism, employing the NN sector of the quark-model baryon-baryon interaction fss2. The energy-dependence of the NN interaction, inherent to the (3q)-(3q) resonating-group formulation, is eliminated by the standard off-shell transformation utilizing the factor, where N is the normalization kernel for the (3q)-(3q) system. This procedure yields an extra nonlocality to the quark-model exchange kernel, which is very important to reproduce all the observables for the bound state and elastic scattering below E_n ≤ 65 MeV.

The Coulomb dissociation of the proton-rich nuclei ³¹Cl was studied experimentally using ³¹Cl beams at 58 MeV/nucleon with a lead target. The relative energy between the reaction products, ³⁰S and proton, was obtained. The first excited state in ³¹Cl was observed which is relevant to the resonant capture of stellar ³⁰S(p,γ)³¹Cl reaction.

Self-consistent theory frameworks have been introduced for description of excitations in nuclei at finite temperature, based on energy density functionals formulated using i) relativistic mean field Lagrangian with density dependent meson-nucleon vertex functions, and ii) Skyrme-type functionals. Finite temperature random phase approximation (FTRPA) has been employed in description of multipole excitations and charge-exchange modes. It is shown that in the temperature range T = 1–2 MeV additional transition strength appears at low energies due to thermal unblocking of single-particle orbitals close to the Fermi level. Within the finite temperature Hartree-Fock+RPA based on Skyrme functionals, the electron capture cross sections have been studied for target nuclei at temperatures relevant in modeling the supernova evolution.

Most of the Skyrme interactions are known to predict spin or isospin instabilities beyond the saturation density of nuclear matter which contradict predictions based on realistic interactions. A modification of the standard Skyrme interaction is proposed so that the ferromagnetic instability is removed. The new terms are density dependent and modify only the spin p-h interaction in the case of spin-saturated system. We have shown that these new terms change the total binding energy of odd-nuclei by only few tenths of keV. From the analysis of the spin instabilities of nuclear matter, restrictions on the parameters governing the spin-density dependent terms are evaluated. We conclude that with the extended Skyrme interaction, the Landau parameters G₀ and could be tuned with a large flexibility without changing the ground-state properties in nuclei and in nuclear matter.

Fully consistent axially-symmetric-deformed Quasi-particle Random Phase Approximation (QRPA) calculations have been performed with the D1S Gogny force. Impact of the deformation in giant multipole resonances is discussed. QRPA and 5 Dimensional Collective Hamiltonian results are compared for low lying 2⁺ states in N = 16 isotones and Ni isotopes. Multipole resonances are also obtained for the heavy nucleus ²³⁸U.

Systematic studies of dipole and other multipole excitations in stable and exotic nuclei are discussed theoretically. Exploring the relation of the strengths of low-energy dipole and quadrupole pygmy resonances to the thickness of the neutron (proton) skin a close connection between static and dynamic properties of the nucleus is observed. The fine structure of low-energy dipole strength in ¹³⁸Ba nucleus is revealed from E1 and spin-flip M1 strengths distributions.

Giant resonances and the pygmy mode in neutron-rich Mg isotopes close to the drip line are investigated by means of the deformed Hartree-Fock-Bogoliubov and quasiparticle random-phase approximations using a Skyrme energy-density functional. It is found that the giant monopole resonance has a two-peak structure due to the deformation. The lower-energy resonance is generated associated with the mixing with the K^π = 0⁺ component of the giant quadrupole resonance. We find for the negative-parity excitations that the pygmy dipole resonance appeared just above the threshold has a significant mixing effect among the isovector dipole, isoscalar octupole and compression dipole excitations.

This contribution sketches recent efforts to explicitly include fluctuations in collective degrees of freedom into a universal energy density functional method for nuclear structure, their successes, and some remaining open questions.

A rotational band with five cascade γ-ray transitions was newly found in ⁴⁰Ar. The deduced transition quadrupole moment of has demonstrated this band as having a superdeformed shape of β₂ ~ 0.5. The structure of the band was discussed in the framework of cranked Hartree-Fock-Bogoliubov calculations and the assignment of multiparticle–multihole configuration has been made.

We develop an efficient microscopic method of deriving the five-dimensional quadrupole collective Hamiltonian on the basis of the adiabatic self-consistent collective coordinate method. We illustrate its usefulness by applying it to the oblate-prolate shape coexistence/mixing phenomena and anharmonic vibrations in Se isotopes.

The nuclei ¹³¹I and ¹³³I have been populated in multi-nucleon transfer reactions between ¹³⁶Xe ions and various targets, and their structure investigated by time-correlated γ-ray coincidence spectroscopy and the measurement of γ-ray angular correlations. A 19/2^- isomer at 1918 keV, with a half-life of 24(1) µs, has been identified in ¹³¹I, as well as nanosecond isomers with J^π = 23/2⁺ in both isotopes. A T_1/2 = 25(3) ns isomer at 4308 keV in ¹³¹I is suggested to have J^π = (31/2^-, 33/2^-) and is primarily attributed to the coupling of an odd proton in the d_5/2 or g_7/2 orbit with the configuration in ¹³⁰Te, responsible for the 15^- isomer in that nucleus. The observed level properties are compared with predictions of a shell-model calculation.

At RIKEN Nishina Center, a series of experiments for studying the heaviest elements has been done by using a gas-filled recoil ion separator (GARIS). Isotopes of the 112th and the 113th elements, ²⁷⁷Cn and ²⁷⁸113 by the ⁷⁰Zn induced one neutron emission reactions on the targets ²⁰⁸Pb and ²⁰⁹Bi, respectively. The former provided an independent confirmation of the production of an isotope, ²⁷⁷Cn, of the 112th element reported firstly by the GSI (Helmholtzzentrum für Schwerionenforschung GmbH, Germany) research group. The latter was the first observation of the 113th element produced by the 'cold fusion' reaction. A gas-jet transport system coupled to GARIS was successfully operated for the chemistry study of the heaviest elements.

The effect of tensor interaction is discussed on the deformation and the shell structure of heavy and superheavy nuclei within the deformed Skyrme Hartree-Fock+BCS model. The importance of the tensor correlations is shown for the single particle spectra of protons in ²⁴⁹Bk. The large shell gaps of superheavy nuclei are found at Z = 114 and Z = 120 for protons and N = 184 for neutrons with the spherical shape irrespective of the tensor correlations. It is also shown that Z = 114 and N = 164 shell gaps are more pronounced by the tensor correlations in the case of SLy5+T interaction.

A general recipe is given how to use the method of complex scaling in calculation of scattering observables. The physical quantity has to be expressed in an explicit form in terms of the total Green operator and this operator have to be replaced with the continuum discretized complex scaled Green-operator. Contrary to earlier expectations the two-body scattering problem in the presence of the Coulomb interaction can be solved using the standard uniform complex scaling. It is sketched how to apply the procedure in the case of three-body scattering. The great advantage of the use of the complex scaling is that the explicit construction of the scattering boundary condition can be avoided.

The α-condensed state in nuclear systems has been proposed by Tohsaki et al. and given rise to interesting discussions. The Hoyle state of ¹²C has been studied as the most typical example of such an α-condensed state. A new resonant state (E_r = 1.66 MeV, Γ = 1.48 MeV) is predicted as an excited α-condensed state in addition to the second 0⁺ state of the Hoyle state by calculations of the complex scaled 3α model. Based on this result, the breakup strengths of the inversion reaction for sequential (⁸Be + α → ¹²C + γ) and direct (α + α + α → ¹²C + γ) processes are calculated.

The structure of the unbound nuclei ⁹He, ¹⁰Li and ¹³Be has been explored using breakup and proton-knockout from intermediate energy ¹¹Be and ^14,15B beams. In the case of both N = 7 isotones, virtual s-wave strength is observed near threshold together with a higher-lying resonance. A very narrow structure at threshold in the ¹²Be + n relative energy spectrum is demonstrated to arise from the decay of the ¹⁴Be*(2⁺), discounting earlier reports of a strong virtual s-wave state in ¹³Be.

We study the di-neutron correlations in the super neutron-rich nucleus ⁷H with the AMD triple-S (AMD superposition of selected snapshots). ⁷H is the most neutron-rich nucleus in the neutron ratio to the proton (N/Z = 6). And the strong di-neutron correlations are expected due to the weak binding properties. In this paper, the mixing of di-neutron cluster components is estimated by calculating the squared overlap with the di-neutron condensate type wave function. The calculated results show significant mixing of di-neutron (t + ²n + ²n) components (70 ~ 80%).

The cluster structure of ¹²C is explored and recent measurements of proton inelastic scattering, suggesting a 2⁺ state close to 9.6 MeV are presented. Resonant scattering studies of ¹⁰Be + ⁴He used to populate resonances in ¹⁴C are briefly discussed.

The α-clustering and molecular-orbitals of ²²Ne and ²²Mg are investigated based on antisymmetrized molecular dynamics. The observed candidates for the α cluster states are understood as the molecular-orbital states and α + ¹⁸O di-nuclei states. The molecular-orbitals in neutron-rich F isotopes are predicted and the drastic reduction of their excitation energy toward the neutron-drip line is discussed.

Using a three-body model with density-dependent contact interaction, we discuss the role of dineutron correlation in the ground state properties as well as in the dipole excitation of typical weakly-bound Borromean nuclei, ¹¹Li and ⁶He. We show that, while both the nuclei manifest themselves similar strong dineutron correlations to each other in the ground state, the energy distributions for the two emitted neutrons from the dipole excitation are considerably different. We also discuss briefly the diproton correlation in a proton-rich Borromean nucleus, ¹⁷Ne.

Nuclear break-up as a tool to study neutron correlations is investigated both theoretically and experimentally. First a time dependent theory going beyond mean field has been developed and shows that correlations between nucleons can be probed through nuclear break-up. Secondly, nuclear break-up of ⁶He on ²⁰⁸Pb target was studied at 20 A.MeV using a secondary beam of ⁶He produced by the SPIRAL facility at GANIL. From the correlation function, a strong contribution of the di-neutron configuration of ⁶He is found.

Spatial correlations of spin-zero neutron pairs in ⁶He and ⁸He are investigated by analyzing two-neutron density of microscopic wave functions obtained by antisymmetrized molecular dynamics (AMD). Results suggest dineutron correlations at the surface of these neutron-rich He isotopes. The dineutron correlations are weaker in the ground state of ⁸He than in ⁶He but again pronounced in the excited of ⁸He.

In this work, a new functional is introduced to treat pairing correlations in finite many-body systems. Guided by the projected BCS framework, the energy is written as a functional of occupation numbers. It is shown to generalize the BCS approach and to provide an alternative to Variation After Projection framework. Illustrations of the new approach are given for the pairing Hamiltonian for various particle numbers and coupling strengths. In all case, a very good agreement with the exact solution is found.

Cluster structures in the neutron-rich nucleus ¹²Be were experimentally investigated via α-inelastic scattering. Excited states in the ¹²Be nucleus were populated by a ¹²Be(αα') reaction at 60 A MeV in the inverse kinematics, and identified by measuring a ⁶He+⁶He and α+⁸He breakup channels in coincidence. The differential cross section and the angular correlations between the decay particles were obtained for each excitation energy at 10–20 MeV for ⁶He+⁶He and at 9–19 MeV for α+⁸He, respectively, reconstructed by the measured momentum vectors of the two helium isotopes. A multipole decomposition analysis based on the distorted-wave Born approximation was applied for the angular distribution of the inelastic scattering together with the angular correlation between the decay particles with respect to the directions of the incident beam and to the momentum transfer simultaneously. From the decomposed excitation energy spectra for J=0-4, several new excited states were identified. The 0⁺ excited states were candidates of the band-head of a largely deformed rotational band. The 11.3-MeV 0⁺ state was found to decay only into the ⁶He+⁶He channel. This result support the recent theoretical result by the generalized two-center cluster model. Several negative-parity excited states were observed in the α+⁸He channel. These excited states possibly forming a negative-parity rotational band, which is very closed to the positive-parity band, can be connected to the existence of the extremely developed cluster structure in ¹²Be.

The generalized two-center cluster model (GTCM), which can treat various single particle configurations in general two center systems, is applied to light neutron-rich systems, Be isotopes (α+α+XN). We discuss the change of the neutrons' configuration around two α-cores as a variation of an excitation energy. We show that the asymmetric clusters, which correspond to the atomic or ionic configurations, appear in the unbound region above the α particle-decay threshold systematically.

We present Skyrme-force Hartree–Fock calculations of metastable three-α chain-state configurations in ¹²C, ¹⁶C, and ²⁰C. A microscopic dynamical study of reactions involving three ⁴He clusters shows that the triple-α linear chain configuration of ¹²C is formed with a certain lifetime and subsequently decays into a triangular configuration of ¹²C and then to a configuration near the ground state.

Excited states in ²¹²Po have been populated by α transfer using the ²⁰⁸Pb(¹⁸O,¹⁴C) reaction and studied with the Euroball γ multidetector array. Very enhanced E1 transitions have been revealed by very short lifetimes measured by the DSAM method, found in the [0.1-1.4] ps range. The emitting states, which have non-natural parity values, are the fingerprints of the "α-²⁰⁸Pb" structure present in ²¹²Po.

Correlation functions measured in heavy-ion collisions are used to extract information about the space-time extent of the emitting sources. Similar techniques can be applied to study some spectroscopic properties of unbound states produced during the dynamical evolution of the colliding system.

Interaction cross sections (σ_I) for Ne isotopes from the stability line to the vicinity of neutron-drip line have been measured using the RIBF facility at RIKEN. Measurements have been performed for ^20–32Ne on C target at energies around 240 MeV/nucleon. A large enhancement of σ_I beyond the systematics of stable nuclei have been observed for neutron-rich Ne isotopes. The possible halo structures with lower orbital angular momentum for ^29,31Ne are discussed by the preliminary analysis.

A candidate of a neutron-halo nucleus, ³¹Ne, contains a single neutron in the pf shell. Within Glauber and eikonal models, we analyze reactions used to study ³¹Ne. We show in a ³⁰Ne+n model that the magnitudes of the total reaction and above all of the one-neutron removal cross sections of ³¹Ne on ¹²C and ²⁰⁸Pb targets strongly depend on the orbital angular momentum of the valence neutron, thereby providing efficient ways to determine the structure of ³¹Ne ground state. We also show that elastic-breakup observables exhibit a strong dependence upon the orbital of the valence neutron.

Effects of tensor interactions in nucleus are discussed from the experimental view points. Two recent studies, one is the mixing of s- and p- waves in ¹¹Li halo and the other is the high momentum component in the nucleon wave function from a transfer reaction. Preliminary results of ¹⁶O(p,d)¹⁵O reaction show an abnormal relative enhancement of the transition to the positive parity state of ¹⁵O, which is not a hole state, consistent with contents of high momentum nucleon expected from the tensor interactions. The importance of the inclusion of tensor force, that can not be described in the mean field model, is discussed.

A Gamma-ray spectroscopic study of excited states of isobaric multiplets has been performed in recent years, with a view to gaining a quantitative understanding of energy differences between excited states in terms of a range of Coulomb and other isospin breaking phenomena. Recently, the experimental programme has been augmented by a study of isobaric analogue states of mirror nuclei populated in mirrored fragmentation reactions. In this presentation, recent results on the analogue states in the mirror pair ⁵³Ni/⁵³Mn will be summarised. In this work, further strong evidence is found for the need to include an anomalous isospin-breaking two-body matrix element for angular-momentum couplings of J = 2, in addition the expected Coulomb contribution, in order to account for the experimental data.

The β-decay spectroscopy on ²⁴Si was carried out in order to investigate characteristic properties of proton-rich nuclei from a perspective of mirror asymmetry. We observed two β transitions to low-lying bound states in ²⁴Al for the first time. The B(GT) of ²⁴Si were deduced to be 0.13(2) and 0.14(2), which were smaller than those of the mirror transition by 22(11)% and 10(8)%, respectively. Through the comparison with theoretical calculations taking into account the Coulomb force and the Thomas-Ehrman shift, the mirror asymmetry of B(GT) is attributed to the lowering of the proton 1s_1/2 orbital.

We attempt at describing the particle-hole and cluster excitations for A ~ 16 nuclei in a single scheme of a ¹²C core plus few-nucleon model. A nucleon-¹²C potential is derived based on a collective model taking into account the core excitation and its parameters are determined to reproduce the low-lying spectrum of ¹³C. The model is tested in three- and four-body systems, ¹⁴C, ¹⁴N and ¹⁵C. Preliminary results of the five-body systems for ¹⁶C and ¹⁶O are reported.

We present a new method of smoothing discrete breakup cross sections calculated by the method of continuum-discretized coupled-channels. In the four-body breakup reaction of ¹²C(⁶He, nn⁴He) at E_in = 229.8 MeV, the continuous breakup cross section is evaluated as a function of the excitation energy of ⁶He. Convergence of the cross section with respect to extending the modelspace is also confirmed.

We investigate the three-body Coulomb breakup of a two-neutron halo nucleus, ⁶He. The three-body scattering states of ⁶He are described by using the Complex-scaled solutions of the Lippmann-Schwinger equation. We calculate the breakup cross section and the invariant mass spectra, and discuss the relations between the structures in these observables and the n-n and α-n correlations of ⁶He.

We have developed an m-scheme cluster-orbital shell model approach to study neutron- and proton-rich nuclei toward the drip-lines. We discuss the property of the neutron-rich oxygen isotopes with analyzing the relation between the energy and r.m.s. radius.

Superdeformed (SD) states in ⁴⁰Ar have been studied using the deformed-basis antisymmetrized molecular dynamics and the generator coordinate method (GCM). GCM basis wave functions were obtained by the energy variation with a constraint on the quadrupole deformation parameter β, while other quantities such as triaxiality γ were optimized by the energy variation. An SD band is obtained just above the ground state band. The SD band involves a K^π = 2⁺ side band due to the triaxiality. The calculated quadrupole electric transition strengths of the SD band reproduce well the experimental values. Triaxiality is significantly important to understand low-lying states.

Second RPA calculations with a Skyrme force are performed to describe both high- and low-lying excited states in ¹⁶O. 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 never neglected. For the rearrangement terms in the matrix elements beyond standard RPA two approximations are employed: they are either neglected or evaluated with the RPA procedure. A several-MeV shift of the strength distribution to lower energies is systematically found with respect to RPA distributions. A better description of the excitation energies of the low-lying 0⁺ and 2⁺ states is obtained with second RPA with respect to RPA.

We propose a local energy density functional for global description of pairing correlations by focusing on the neutron excess dependence. We show the clear correlation between pairing gaps and effective mass parameters as a function of neutron excess. This effect can be taken into account to the density functional by the isovector density dependence in the particle-particle channel.

We review some applications of self-consistent Green's function theory to studies of one- and two-nucleon structure in finite nuclei. Large-scale microscopic calculations that employ realistic nuclear forces are now possible. Effects of long-range correlations are seen to play a dominant role in determining the quenching of absolute spectroscopic factors. They also enhance considerably (e,e'pn) cross sections in superparallel kinematics, in agreement with observations.

We show some results of systematic calculation on electric dipole responses of even-even nuclei, employing a Hartree-Fock plus RPA approach. For an easy implementation of the fully self-consistent calculation, a finite amplitude method which we proposed recently is employed. We show a systematic comparison of calculated peak energies of giant dipole resonances and an importance of low-angular momentum orbit for emergence of pygmy dipole resonances.

In order to search for the α condensed state in ¹⁶O, we have performed the decay particle measurement via the reaction. Although the decay branching ratio of the α + ¹²C channel was predicted to be small, the branching ratio between the α + ¹²C and channels was obtained to be 7:3 by using the result of a simple simulation.

The α-particle condensed state in ¹⁶O is investigated by the use of 4α OCM (Orthogonality Condition Model). Low-lying spectrum in experiment is well reproduced up to around the 4α break-up threshold. The excited state obtained around the 4α threshold as the state is shown to have a dilute density structure and give strong enhancement of the occupation of the S-state c.o.m. orbital of the α-particles. This is strong evidence that the state is regarded as the 4α condensed state.

Cluster structures of 3/2^- and 1/2⁺ states in ¹¹B are investigated with a semi-microscopic α + α + t cluster model based on the Gaussian expansion method. The state, characterized by the monopole transition strength as large as the Hoyle state ( at E_x = 7.65 MeV in ¹²C), was found to have a loosely bound α+α+t cluster structure, although its features is not similar to those of the Hoyle state with the dilute 3α-condensate-like character (0S_α)³, in which the α particle is occupied in a single 0S-orbit with about 70% probability. We indicate that the 12.56-MeV state (J^π = 1/2⁺) around the α + α +t threshold observed in the ⁷Li(⁷Li,¹¹B*)t reaction etc. is a strong candidate for the Hoyle-analogue state with the main configuration of (0S_α)²(0S_t) from the analyses of the single-cluster motions in ¹¹B.

We have studied three α states around ⁴⁰Ca based on a microscopic α-cluster model, which has been succeeded experimentally quite recently. This was performed by introducing a Monte Carlo technique for the description of the THSR (Tohsaki Horiuchi Schuck Röpke) wave function, which is called the "virtual THSR" wave function. The three α cluster state around ⁴⁰Ca has an energy below the Coulomb barrier top energy with a spatial extension comparable to the second 0⁺ state of ¹²C.

Experiments based on the isomer-spectroscopy method were performed using the secondary beam line at RCNP, Osaka University. Recently, a new γ-ray spectroscopy method was established using fusion reaction induced by low-energy RI beam. This method enables us to study high-spin states of nuclei in wider mass region where it is difficult to populate them by using the combination of stable beams and stable targets. This method works well although low production of nuclei, because (1) the combination of beams and targets can be selected with large-reaction cross section and (2) high-S/N measurement can be performed by the event-by-event detection to select the events correlated with RI beam, which reduces background γ rays, competing with γ rays emitted from fusion products.

As the first step, high-spin states of ¹⁴²Pr were studied using fusion reaction induced by low-energy ¹⁷N RI beam. Large cross section was obtained by the ¹³⁰Te(¹⁷N,5n) reaction with 4.9 MeV/u ¹⁷N beam. Event selection, which was carried out by the event-by-event detection with low-beam intensity of 2×10⁴ pps, enables high-S/N measurement.

The upcoming FAIR facility in Darmstadt, Germany, will produce intense high energy beams of exotic nuclei, which will be used to explore the properties of new regions of the chart of nuclides of key importance for both nuclear structure and nuclear astrophysics. In the EXL project, heavy ion beams are first cooled in the New Experimental Storage Ring (NESR) and then used to induce reactions on windowless thin Hydrogen, Deuterium and Helium gas targets in the ring. High luminosities can be achieved because of the recirculation of the beam with a frequency of about 1 MHz. The EXL system will be ideal for high resolution reaction studies at low momentum transfer. The design of the detector system considered is universal in the sense that it should allow the use of a large variety of nuclear reactions, addressing numerous physics questions. The detector system provides the capability of fully exclusive kinematical measurements, with target recoil detectors, fast ejectile forward detectors and an in-ring heavy-ion spectrometer. The physics case and detector design considerations for EXL along with tests experiments performed at KVI and GSI, paving the way to the full EXL detection system, are presented in this contribution.

The shell structure of the neutron-rich Ca and Ni nuclei is investigated by the spherical Hartree-Fock calculations with the semi-realistic NN interactions. The tensor force plays a significant role in the Z dependence of the shell structure, as is exemplified by N = 32 and N = 40. Loose binding may lead to a submagic number N = 58 in ⁸⁶Ni, assisted by the weak pair coupling.

We report our recent numerical results of total reaction cross sections of light neutron-rich nuclei, such as carbons and oxygens, in the Glauber approximation to study the exotic structure of neutron-rich unstable nuclei.

Low-lying excitation properties of exotic nuclei in the vicinity of the canonical magic number 8 have been investigated through the level lifetime measurement on the neutron-rich isotope ¹³B with N = 8 and the missing-mass spectroscopy on the proton unbound nucleus ¹²O with Z = 8. The observed trends of the transition probabilities and level schemes have been discussed in comparison with the advanced shell model calculations, which points to the universality as well as the charge independence of the shell quenching phenomena far from stability.

The level structures of ²⁸Mg and ²⁹Mg have been investigated by the β-decay of spin-polarized²⁸Na and ²⁹Na at ISAC, TRIUMF. The detailed β-γ and γ-γ coincidence measurements were performed. New γ rays and β transitions were observed both in ²⁸Mg and ²⁹Mg. We have succeeded in assigning spins and parities of many levels in ²⁸Mg and ²⁹Mg. Comparison with shell model calculations using USD Hamiltonian suggest that the structure of ²⁸Mg and ²⁹Mg are well explained in the sd-shell configurations, except for two levels at 1.095 and 1.430 MeV in ²⁹Mg. This suggests negative parity assignments for these levels. The evolution of sd-pf shell is discussed.

Under the assumption of good isospin symmetry, T_z = ±3/2 → ±1/2 Gamow-Teller (GT) transitions in a mass A isobar are analogous, where T_z is the z component of isospin T defined by 1/2(N - Z). We studied the T_z = +3/2 → +1/2 GT transitions by using the ³⁷Cl(³He,t)³⁷Ar and ⁴¹K(³He,t)⁴¹Ca reactions at E_beam = 140 MeV/nucleon. The GT transition strengths in ³⁷Ar and ⁴¹Ca were obtained up to the excitation energy (E_x) of 14.2 MeV and 10.4 MeV with energy resolutions of 30 and 35 keV, respectively. The obtained GT strengths were compared with those of the T_z = -2/3 → -1/2 mirror transitions, measured by the β-decay of ³⁷Ca and ⁴¹Ti, respectively. It was found that the overall distributions of the mirror transitions were similar in both A = 37 and A = 41 systems. In A = 37 the differences seen at lower excitation energies are suggested to be the effect of the tensor interaction in the charge-exchange reaction. The differences seen at higher excitation energies are suggested to be the effect of the Coulomb interaction that can break the mirror symmetry of the strength distributions.

A symmetry-adapted open-core shell model with SU(3) the underpinning symmetry is described. The model reduces to the well established Elliott SU(3) model in its 0ħΩ limit and to the no-core shell model (NCSM) – successful in describing low-energy dynamics of light nuclei – if stripped of its special symmetry considerations. We show that this approach is effective in providing an efficient description of low-lying eigenstates of ¹²C and ¹⁶O. A symmetry-guided framework is suggested based on our recent findings of low-spin and high-deformation dominance in realistic NCSM results. This holds promise to significantly enhance the reach of ab initio shell models toward heavier nuclear systems as well as descriptions of collective and cluster phenomena.

We propose a new method to describe nuclear structure using bare nuclear interaction, in which the tensor and short-range correlations are described by using the tensor optimized shell model (TOSM) and the unitary correlation operator method (UCOM), respectively.

We perform a systematic study of the odd-even mass staggering generated using a pairing interaction computed at first order in low-momentum interactions. Building on previous work including the (nuclear plus Coulomb) two-nucleon interaction only, we focus here on the first-order contribution from chiral three-nucleon forces. We observe a significant repulsive effect from the three-nucleon interaction. The combined contribution from two- and three-nucleon interactions accounts for approximately 70% of the experimental pairing gaps. This leaves room for higher-order contributions to the pairing kernel and the normal self-energy that need to be computed consistently.

In this closing address I attempt to summarize the Symposium by systematizing the topics covered, and I express our appreciation to all whom it is due to.

We discuss pairing vibrations in the context of Time-Dependent Energy-Density-Functional formalism. The focus is put on the pairing part of the energy functional. We found that the density-dependence of the pairing functional impacts 2-nucleons transfer strengths.

We present the finite amplitude method (FAM) for the Quasi Particle Random Phase Approximation (QRPA). This method allows to extract a QRPA code starting from a Hartree-Fock-Bogoliubov (HFB) code. The code obtained is fully self consistent, moreover since the FAM is not restricted to spherical symmetry it can be used to obtain deformed QRPA codes.

We derive the Canonical-basis Time-Dependent Hartree-Fock-Bogoliubov (CbTDHFB) equations using time-dependent variational principle with a special pairing energy functional. We obtain the isoscalar quadrupole strength functions for Magnesium isotopes with small-amplitude CbTDHFB calculation in the three-dimensional coordinate-space representation.

Studying the Gamow-Teller (GT) transitions of stable as well as unstable pf-shell nuclei is one of the key issues in nuclear and astro-nuclear physics. Under the assumption that isospin T is a good quantum number, symmetry is expected for mirror nuclei and the GT transitions starting from the mirror nuclei. We study the GT transitions starting from T_z = ±1 mirror nuclei, respectively, by means of hadronic (³He, t) charge-exchange reactions and complementary β decays.

We apply our quark-model NN interaction fss2 to the nd scattering in the Faddeev formalism. A consistent description of the triton binding energy, the nd scattering length, the differential cross sections, and spin observables of the elastic scattering up to 65 MeV is achieved without introducing three-body forces.

We introduce the form factor and short range correlation in the relativistic Hartree-Fock approximation (RHFU) to study the properties of nuclear matter. We treat the short range correlation with the unitary correlation operator method (UCOM). In this framework, we can perfectly reproduce the equation of state of pure neutron matter obtained by the relativistic Brueckner-Hartree-Fock theory with the Bonn potential. We apply the RHFU model to symmetric nuclear matter. The contribution of ρ meson is cut down largely by the form factor of the size in the realistic nucleon-nucleon interaction. The short range correlation has a significant effect on the Fock energies of pion and ρ meson exchange interaction.

Low-energy dipole excitations in Neon isotopes and N = 16 isotones are calculated with a fully consistent axially-symmetric-deformed Quasi-particle Random Phase Approximation (QRPA) approach based on Hartree-Fock-Bogolyubov (HFB) states. The same Gogny D1S effective force has been used both in HFB and QRPA calculations. The behavior of proton and neutron transition densities is presented in order to determine the isoscalar or isovector nature of the excitations.

β-decay half-lives around ⁷⁸Ni and ¹³²Sn are studied with proton-neutron Quasiparticle Random Phase Approximation on the basis of Skyrme-Hartree-Fock (SHF) method. We take into account tensor force correlation in calculating the ground and excited states and find it improves the half-life of ¹³²Sn. However, the Q value is still underestimated. We also discuss that half-lives do not strongly depend on type of particle-particle interaction in isospin T = 0 channel.

Reaction cross sections for ¹¹Be and ⁸B on proton targets at 40A - 120A MeV have been measured by the transmission method. With these data, we can discuss the proton- and neutron- density distributions at the nuclear surface independently in principle using the Glauber theory. Our experimental results support that the constituent of halo in ¹¹Be is neutron dominantly and that of ⁸B is proton dominantly.

We review the notion of symmetry breaking and restoration within the frame of nuclear energy density functional methods. We focus on key differences between wave-function- and energy-functional-based methods. In particular, we point to difficulties to formulate the restoration of symmetries within the energy functional framework.

From a viewpoint of oblate-prolate symmetry and its breaking, we propose a simple model based on the quadrupole collective Hamiltonian to study dynamics of triaxial deformation in shape coexistence phenomena. The numerical results suggest that the oblate-prolate symmetry breaking in the rotational moments of inertia can play an important role for the oblate-prolate shape coexistence as well as that in the collective potential.

We develop a method of determining microscopically the collective potential and inertial masses in the five-dimensional quadrupole collective Hamiltonian on the basis of the adiabatic self-consistent collective coordinate method. We apply this method to shape coexistence/mixing phenomena in low-lying states of the proton-rich Kr isotopes.

The fusion-fission excitation functions for the decay of compound nucleus ²¹⁵Fr*, formed in ¹¹B+²⁰⁴Pb and ¹⁸O+¹⁹⁷Au reaction channels, are studied on the Dynamical Cluster-decay Model (DCM), showing entrance channel independence, in agreement with experiments, not invoking any quasi-fission (qf) process in either of the two channels.

We discuss the pair transfer mode populating pair vibration state in neutron-rich Sn isotopes by means of the continuum quasi particle random phase approximation (continuum QRPA). It is seen that the strength of the two-neutron addition transfer from the ground state to the state is significantly enhanced beyond the N=82 shell gap.

We propose a new method of the β-γ constraint for quadrupole deformation in antisymmetrized molecular dynamics (AMD) to describe various cluster and shell-model structures in the ground and excited states of light nuclei. To check its applicability, we apply this method to N = 6 isotones, ¹⁰Be, 12C, ⁹Li, and ¹¹B, and find various shell-model and cluster structures as functions of the deformation parameters, β and γ. We also investigate ¹⁴C with the β-γ constraint AMD. For positive-parity states, above the ground band, three excited bands with the developed 3α-cluster core structures are suggested. Characteristic structures such as a triaxial structure and a linear-chain structure having ¹⁰Be+α correlation appear in the excited bands.

Excited states in the T_z = -1 nucleus ⁴⁴V have been observed for the first time. The states have been identified through recoil-γ-γ coincidences and comparison with analogue states in the mirror nucleus ⁴⁴Sc. Mirror energy differences have been extracted and compared to state-of-the-art fp shell-model calculations which include charge symmetry breaking forces.

In order to investigate the particle capture reactions at the astrophysical energy, we consider that the structure of the negative-parity states near the threshold energy becomes important. To study the structure, it is necessary to extend the model space take into account the effect of the core excitation. In this paper, we discuss the effect of the core excitation for the reaction cross sections at the astrophysical energy.