Table of contents

The International Symposium on `Structure of Exotic Nuclei and Nuclear Forces' was held at The Koshiba Hall, University of Tokyo, on 9–12 March 2006. This symposium was organized as an activity of the Grant-in-Aid for the specially promoted area `Monte Carlo Shell Model' from the Ministry of Education, Science, Sports and Culture (MEXT) of Japan. The symposium was sponsored by the Center for Nuclear Study (CNS) and by RIKEN.

The purpose of the symposium was to discuss theoretical and experimental developments in the study of the structure of exotic nuclei and its relationship with nuclear forces. There has been much progress recently in our understanding of what the structure of exotic nuclei is and how it can be linked to nuclear forces, with emerging intriguing perspectives.

The following subjects were covered in this symposium

• Present status and future of the shell model

• Effective interaction theories

• Experimental results and perspectives

• Few-body methods including ab initio calculations

• Advancements of mean-fieeld models

• Transition between shell and cluster structure

• Nuclear astrophysics and nuclear structure

• Particle physics and the shell model

Emphasis was placed on the interplay between many-body structures and nuclear forces, and on the experimental clarification of these topics.

Around 80 participants attended the symposium and we enjoyed 34 excellent and lively invited talks and 26 oral presentations.

The organizing committee consisted of B A Brown (MSU), S Fujii (CNS), M Honma (Aizu), T Kajino (NAO), T Mizusaki (Senshu), T Motobayashi (RIKEN), K Muto (TIT), T Otsuka (Chair, Tokyo/CNS/RIKEN), P Ring (TMU), N Shimizu (Scientific Secretary, Tokyo), S Shimoura (CNS), Y Utsuno (Scientific Secretary, JAEA).

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 so successful.

We review recent developments in the ab initio no-core shell model, such as the influence of 3NFs on the binding energies and excitation spectra of light nuclei. Our calculations permit us to compare the effect of different choices for the theoretical 3NF on the properties of light nuclei. This is of particular interest in determining the best choice of the values for the contact terms in 3NFs derived from Chiral Perturbation Theory. Other recent developments in the NCSM include an investigation of the renormalization properties of physical operators, besides the nuclear Hamiltonian, as well as the Lorentz integral transform approach to the description of select reaction observables in light nuclei.

The structure of the neutron-rich carbon nucleus ¹⁶C is described within a new microscopic shell-model framework. The model space is composed of the 0s, 0p, 1s0d and 1p0f shells, and thus a sort of no-core type. The effective interaction is microscopically derived from the Idaho N3LO NN potential and the Coulomb force through a unitary transformation theory. Calculated low-lying energy levels of ¹⁶C agree well with the experimental values. Furthermore, the anomalously hindered B(E2; 2⁺₁ → 0⁺₁) value for ¹⁶C, measured recently, is well described by the calculation with the bare charges.

The 2⁺₁ state in neutron rich ¹⁶C was studied via inelastic proton scattering in inverse kinematics, using a 33 MeV/nucleon beam. The deformation parameter β_pp' = 0.47(5) obtained is greater than the deformation parameter deduced from the lifetime measurement. Combining these two results, the ratio of the neutron and proton quadrupole matrix elements is deduced to be approximately 7, indicating a neutron-dominant quadrupole collectivity in ¹⁶C.

There has been a significant progress in ab initio approaches to the structure of light nuclei. Starting from realistic two- and three-nucleon interactions the ab initio no-core shell model (NCSM) can predict low-lying levels in p-shell nuclei. It is a challenging task to extend ab initio methods to describe nuclear reactions. In this contribution, we present a brief overview of the the first steps taken toward nuclear reaction applications. In particular, we discuss our calculation of the ⁷Be(p,γ)⁸B S-factor. In addition, we present our preliminary results of the ³He(α,γ)⁷Be S-factor. These two reactions correspond to the most important uncertainties in solar model predictions of neutrino fluxes.

We assess the sensitivity of the intermediate energy, direct two-nucleon knockout reaction mechanism to details of the correlated motions of the two removed nucleons - as might be revealed by measurements of partial cross sections to different final states of the mass A-2 reaction residues. Comparisons of new reaction calculations with recent data for exotic nuclei in the sd-shell suggest that this sensitivity is significant and that the coherence of the twonucleon configurations to the reaction allows small wave function components to be probed. The relative yields for the different J^πtransitions are well described by the USD shell model calculations, however the measured cross sections require an overall suppression of the shell model two-nucleon spectroscopic strengths.

We have measured the ¹H(¹⁹C,¹⁸C+n)¹H and ¹H(¹⁴Be,¹³B+n)n reactions at 70 MeV/nucleon using the invariant mass method in inverse kinematics. A new state was identified at 1.49 MeV in ¹⁹C. In the latter (p, n) reaction, a resonance peak corresponding to the 1.28 MeV state in ¹⁴B recently reported in a beta-decay study was clearly observed. Forward peaked character in the differential cross section supports the 1⁺assignment for this state.

Gamow-Teller (GT) transition is the most popular nuclear weak process with the nature of spin-isospin excitation. GT transitions in pf-shell nuclei, including those starting from unstable nuclei, are of interest, due to their importance in astrophysical processes. Weak processes, however, gives us rather limited information on the GT response of nuclei. We introduce high-resolution (³He, t) reaction at 0° and at an intermediate beam energy as a new spectroscopic tool for studying GT excitations. Owing to the high energy-resolution of the reaction (≈ 30 keV), individual transitions can be observed up to the region of GT giant resonance. Assuming isospin symmetry for the T_z = ±1 → 0 isobaric analogous transitions in isobars with mass number A, we present a new method to deduce GT transition strengths starting from proton rich exotic nuclei.

Gamow-Teller transitions in p-shell and fp-shell nuclei are invesigated based on new shell model interactions. Neutrino-nucleus reactions induced by accelerator and supernova neutrinos are studied for ¹²C as well as Fe and Ni isotopes by using the Gamow-Teller strengths obtained by the shell models. The charge exchange reaction cross section on ¹²C is found to be enhanced compared with previous calculations both for decay-at-rest (DAR) neutrinos and supernova neutrinos. In the charge exchange reaction on ⁵⁶Fe, the cross section is also found to be enhanced for a new shell model interaction in comparison with a previous shell model calculation. Neutrino-³⁷Cl reaction is studied for solar neutrinos with the use of a recent experimental Gamow-Teller strength, and compared with shell model calculations. The USD shell model interaction with the universal quenching of the axial-vector coupling constant (g_A) is found to well reproduce the cross section obtained from the observed Gamow-Teller strength.

We studied tensor-force effects on nuclear shell structures by mean-field calculations. We have found that the tensor force affects single-particle energies of nuclei, for example, F and Sb isotopes, in interesting ways different from what the spin-orbit force produces.

We performed an experiment of the inelastic scattering of the two neutron halo nucleus ¹⁴Be at 68 A MeV on a carbon target. Since ¹⁴Be has no bound excited state, ¹⁴Be breaks up into ¹²Be and two neutrons. Using the invariant-mass method, the first excited state of ¹⁴Be is clearly observed at E_ex = 1.56(13) MeV. A distorted-wave Born approximation analysis is performed and the spin-parity corresponding to the peak is assigned to be J_π = 2⁺. Deformation length of ¹⁴Be is extracted to be ∂^C = 1.53(10) fm. These experimental results are compared with shell-model calculations.

We have developed an effective interaction for shell model calculations in the model space consisting of four orbits 1p_3/2, 0f_5/2, 1p_1/2 and 0g_9/2. Starting from a renormalized Gmatrix interaction, we have modified 45 linear combinations of Hamiltonian parameters by fitting to 400 experimental binding and excitation energy data out of 87 nuclei with masses A = 63–96. The resultant effective interaction is shown to be successful for describing irregular behavior of the 0⁺₂states in Ge isotopes. We have evaluated the two-neutrino double-beta-decay matrix elements for ⁷⁶Ge and ⁸²Se which are in reasonable agreement with the experimental data.

The Gamow-Teller transition of ⁴⁶Cr to the N = Z odd-odd nucleus ⁴⁶V has been observed for the first time. By means of β-γ coincidence measurements, a γ-ray peak at 993 keV corresponding to the decay of the 1⁺₁ state in ⁴⁶V was observed. The branching ratio of the decay to this state was found to be b_GT = 0.25 ± 0.050. The half-life of ⁴⁶Cr was measured to be T_1/2 = 240 ± 140 ms. The transition strength was determined to be B(GT) = 0.64 ± 0.20. This result was compared with theoretical calculations.

β-delayed γ-ray measurements have been part of an experimental program at the NSCL to understand the role of the πf_7/2 - νf_5/2 proton-neutron monopole interaction in neutron-rich pf-shell nuclei above ⁴⁸Ca. Central to this study has been an attempt to observe the development of new shell structure at N = 32, 34 through the systematic observation of E(2⁺₁ ) as a function of neutron number. Additionally, the ground state spin and parity of odd-odd and odd-A nuclei were interpreted in an extreme single-particle model to follow the monopole migration of the νf_5/2 as protons are removed from the πf_7/2state.

A broad range of physics phenomena can be addressed by high-resolution in-beam γ-ray spectroscopy experiments with radioactive beams offered within the Rare ISotopes INvestigation at GSI (RISING) project. It combines the EUROBALL Ge-Cluster detectors, the MINIBALL Ge detectors, the HECTOR-BaF detectors, and the fragment separator FRS. The secondary beams produced at relativistic energies are used for Coulomb excitation or secondary fragmentation experiments to study projectile like nuclei far off the stability line by measuring de-excitation photons. The physics studied comprises the evolution of shell structure towards the drip lines and its signatures as inferred from excitation energies, mirror symmetry and electromagnetic transition strengths. The first results of the "fast beam campaign" are discussed in comparison to various shell model calculations including the structure of light Sn isotopes based on Coulomb excitation of ¹⁰⁸Sn, the discussion of the N = 32,34 sub-shell closure based on neutron-rich ^56,58Cr isotopes, and the shell structure in light proton-rich Ca isotopes from the fragmentation of a ³⁷Ca radioactive beam.

We have investigated structure of the neutron-rich Ge isotopes at and around N = 50 via intermediate-energy Coulomb excitation. A new method of intermediate-energy twostep Coulomb excitation has been tested to study the second excited states, such as the 2⁺₂ and 4⁺₁states, in neutron-rich even-even nuclei. The first application of the method and its results are presented.

Within a unified formalism the chain of helium isotopes linked by neutron decay reactions is explored from bound states to resonances and cross sections in continuum. Using this realistic example the Continuum Shell Model formalism is presented and discussed.

Resonances and continuum states in the complex scaling method construct an extended completeness relation, which is one of useful instruments to investigate drip-line nuclei. Because an appropriate L² basis set is used in the complex scaling method to describe resonant and continuum states, we can discretize the continuum states naturally. We apply this method to calculation of continuum level density and the scattering phase shifts.

The structure of neutron-rich nuclei around the N = 20 magic number is studied through the measurements of static electromagnetic moments. Recent data on the magnetic dipole moments and electric quadrupole moments for neutron-rich Al isotopes are discussed to clarify whether the emergence of a strong deformation reported for Z = 10−12 nuclei in this region might happen also in these Z = 13 nuclei. Possibility to study the nuclear structure via the β transition matrix elements is also discussed.

By comparing the excitation energies of analogue states in mirror nuclei, several nuclear structure properties can be studied as a function of the angular momentum up to high spin states. They can be described in the shell model framework by including electromagnetic and nuclear isospin-non-conserving interactions. Calculations for the mirror energy differences in nuclei of the f_7/2shell are described and compared with recent experimental data. These studies are extended to mirror nuclei in the upper sd and fp shells.

Excited states in the neutron-rich ^55,57V nuclei have been populated in multi nucleon transfer reactions and observed by using the large acceptance magnetic spectrometer PRISMAand the highly efficient γ-detector array CLARA. These results confirm the sub-shell closure for N = 32 but there is not clear evidence of the existence of the N = 34 sub-shell closure.

Relativistic mean field theory with density dependent coupling constants is used to investigate ground state properties and properties of excited configurations in nuclei far from stability. It turns out that it is very important to consider also a density dependence the isovector channel. This provides not only an improved description of the equation of state for neutron matter and asymmetric nuclear matter but also for isovector properties of finite nuclei far from stability such as the neutron skin thickness, and the isoscalar and isovector giant resonances.

Two of the key issues in understanding the neutron-to-proton ratio in a corecollapse supernova are discussed. One of these is the behavior of the neutrino-nucleon cross sections as supernova energies. The other issue is the many-body properties of the neutrino gas near the core when both one- and two-body interaction terms are included.

Neutrino-less double beta decays(0νββ) are of great interest for studying the Majorana nature of ν's and the absolute ν-mass scale. The present report is a brief review of the 0νββ studies with emphasis on future experiments with the mass sensitivity of an order of 25∼100 meV and on experimental probes for investigating 0νββ nuclear matrix elements.

Nuclear double beta decay is reviewed from a nuclear structure point of view, with an emphasis on spin-isospin modes of transitions. The double beta decay is expected to reveal fundamental properties of neutrinos by using nuclei as a microscopic laboratory. The goal of nuclear structure studies is to predict reliable nuclear matrix elements relevant to the determination of neutrino mass.

The competition between the cluster and shell structure of light nuclei is discussed. First, we demonstrate in ¹²C by superimposing many Slater determinants that the cluster structure dissolute when the shell-model-like model space is introduced. The decrease of the energy from the 3α configuration by about 6 MeV is a clue to resolve a long-standing problem of the binding energies of ¹²C and ¹⁶O. As a next step, we propose a simple model to include the spin-orbit interaction (SMSO). By introducing only one parameter (Γ) to the wave function, describing an asymptotic transition of ¹²C from a 3α configuration to a 2α+4N configuration is represented, and we show a strong contribution of the spin-orbit interaction in the ground state. Furthermore, we propose a simplified model to directly take into account the contribution of the tensor interaction (SMT) for light nuclei by extending α-cluster model. The coupling effect of SMSO and SMT is shown to be important in ¹²C, contrary to ⁸Be.

The cluster structures of ¹⁶O,¹⁸O and ²⁰O are investigated by the antisymmettrized molecular dynamics (AMD) plus generator coordinate method (GCM), using MV1+G3RS force. We have found ¹⁴C+α cluster structure which makes K^π = 0^± parity doublet band for ¹⁸O, and ¹⁴C+⁶He cluster structure which makes K^π = 0^±band is found for ²⁰O.

Structure of Ne isotopes are investigated by a microscopic model, where thousands of Slater determinants are stochastically generated, and important ones are selected out of them. The importance of the α-cluster correlation is systematically shown, and also, the singleparticle parity of each nucleon is studied, and deviation from the pure shell-model-like picture is discussed.

We investigate the shell evolution in unstable nuclei with large-scale shell-model calculations. Since the tensor force has been pointed out to be promising in accounting for the shell evolution, we construct a new interaction in the sd-pf shell region whose tensor force in the cross-shell part is determined with attention. The resulting strength is much stronger than the Millener-Kurath (MK) interaction which has been often used as the cross-shell interaction, giving rise to a significant difference from that by MK in the proton shells in the N = 28 region and the nuclear structure of ⁴²Si.

We derive new Hamiltonians for the sd-shell, USDA and USDB, based on a renormalized G matrix with linear combinations of two-body matrix elements adjusted to fit a complete set of data for experimental binding energies and excitation energies for the sd-shell nuclei. These hamiltonians provide a new level of precision for realistic sd-shell wavefunctions for applications to nuclear structure and nuclear astrophysics.

The magnetic moment and electric quadrupole moment of ³²Al (Z = 13,N = 19) have been measured. We performed β-NMR spectroscopy with spin-polarized ³²Al nuclei produced via the projectile fragmentation reaction. Both the moments are well reproduced by full sd-shell model calculations using the USD effective interaction. The result has provided clear evidence that ³²Al is located out of the island of inversion.

Stucture of N = 17,18 nuclei has been investigated via proton inelastic scattering and neutron removal reactions up to the neutron dripline in inverse kinematics by use of radioctive ion beams provided by the RIKEN isotope separator, RIPS. Low energy excited states have been found in all the ^26,27F and ²⁷Ne nuclei, which are out of the neutron sd shell configuration space and are considered as intruder states arisng from cross shell excitations. Monte-Carlo shell model calculations with the sdpf-m interaction predict low energy negative parity excited states from neutron cross shell excitation at N = 17,18, which is in agreement with our experimental results. Observation of intruder states even at N = 17, especially the p_3/2 state in ²⁷Ne at 765 keV is a clear indication of a vanishing N = 20 shell gap at Z = 8 as predicted by the sdpf-m shell model calculations.

Shell structure evolution in nuclei situated at the extremes of neutron and proton excess are investigated using in-beam gamma spectroscopy techniques with radioactive beams at GANIL. A selection of results obtained very recently is presented: i) The reduced transition probabilities B(E2;0⁺₁ → 2⁺) of the neutron-rich ⁷⁴Zn and ⁷⁰Ni nuclei have been measured using Coulomb excitation at intermediate energy. An unexpected large proton core polarization has been found in ⁷⁰Ni and interpreted as being due to the monopole interaction between the neutron g_9/2 and protons f_7/2 and f_5/2 spin-orbit partner orbitals. ii) Two proton knock-out reactions has been performed in order to study the most neutron-rich nuclei at the N = 28 shell closure. Gamma rays spectra and momentum distribution have been obtained for 42Si and neighboring nuclei. Evidence has been found for a deformed structure at N = 28 for Silicon, despite a relatively large Z = 14 gap. iii) The in-beam gamma spectroscopy of ³⁶Ca performed using neutron knock-out reactions revealed that N = 16 is as large sub-shell closure as Z = 16 in ³⁶S. The uniquely large excitation energy difference of the first 2⁺ state in these mirror nuclei turns out to be a consequence of their relatively pure neutron or proton 1p(d_3/2)-1h(s_1/2) nature.

Proton inelastic scattering was applied to ³²Mg located at the island of inversion to study higher excited states. Angle-integrated and differential cross sections for E_x = 885 keV and 2321 keV states were obtained by measuring de-excitation γ rays and scattering angles of ³²Mg. From the present analysis, the transferred angular momentum from the ground state to 2321 keV state was close to ΔL = 4 rather than ΔL = 3.

The α inelastic scatterings and the (α,t) reaction on exotic nuclei at 50–60 A MeV are discussed. A new multipole decomposition analysis taking into account the angular correlation of decaying process originated from the alignments of the residual nucleus is applied for a study of cluster states in ¹²Be. The proton transfer reaction on the ¹²Be nucleus populates a possible proton single-particle state bound by a deformed core in the ¹³B nucleus of which ground state is spherical.

The direct reactions of the ⁸He beam on proton, (p,p') and (p,d), were measured at 15.7 A.MeV. The excitation spectra for the weakly-bound ⁸He and the unbound ⁷He were extracted. The spectroscopy of these drip-line nuclei is compared to the predictions of microscopic models.

A new kinematically complete measurement of the Coulomb breakup of twoneutron halo nucleus ¹¹Li on a Pb target has revealed a strong soft-E1 transition strength peaking at E_x∼0.6 MeV. This soft E1 strength amounts to 1.42±0.18 e²fm², corresponding to 4.5±0.6 Weisskopf units(W.u.). The observed B(E1) distribution has been found in excellent agreement with a three-body calculation with strong two-neutron correlation and final state interactions.

An experiment was conducted at the National Superconducting Cyclotron Laboratory (MSU) to study N∼20 Ne and Na nuclei. A 140 MeV/A ⁴⁸Ca primary beam produced secondary-beam "cocktails" (²⁹Na/³⁰Mg/³²Al, ³²Mg/³³Al/³⁵Si) which underwent secondary reactions to produce Ne and Na; γ-ray decays were detected by the segmented Ge array, SeGA. The data provide information on the transition to the island of inversion and a test of recent shell-model calculations.

New levels were attributed to ⁸¹₃₁Ga₅₀ and ⁸³₃₂Ge₅₁ which were fed by the β-decay of their respective mother nuclei ⁸¹₃₀Zn₅₁ and ⁸³₃₁Ga₅₂ produced by fission at the "PARRNe" ISOL set-up installed at the Tandem accelerator of the Institut de Physique NucléLeaire, Orsay. We show that the low energy structure of ⁸¹₃₁Ga₅₀ and ⁸³₃₂Ge₅₁ can easily be explained within the natural hypothesis of a strong energy gap at N = 50 and a doubly-magic character for ⁷⁸Ni.

A new polarized proton solid target has been constructed at Center for Nuclear Study, University of Tokyo. The target is designed specifically for use in radioactive nuclear beam experiments. We have measured the analyzing power for the p-⁶He elastic scattering by using the polarized proton target. The results are incompatible with any microscopic calculations presented before the measurement. Planned experiments at RIBF with the polarized target are also described.

We investigate the roles of the tensor correlation on the structures of ^4,5He. For ⁴He, we take the high angular momentum states as much as possible with the 2p2h excitations of the shell model type method to describe the tensor correlation. Three specific configurations are found to be favored for the tensor correlation. This correlation is also important to describe the scattering phenomena of the ⁴He+nsystem including the higher partial waves consistently.

We solve a five-body problem of pentaquark (q⁴) state of Λ(1405). The hamiltonian, which reproduces reasonably well the energies of ground state baryons (N, Λ, Σ, Ξ and Δ) and mesons (π, K, ρ, K*), includes kinetic energy of semi-relativistic form, linear confinement potential, and a color-magnetic interaction with Gaussian form factor. Flavor symmetry breaking (m_s> m_u,d) is taken into account. The energy calculated for the pentaquark state of Λ(1405) is lower than the energy for the three-quark state. The present result suggests that the Λ(1405) is a pentaquark-dominated state if the color-magnetic potential plays a leading role of the quark-quark and quark-antiquark interactions.

The nuclear structure of the quadrupole collective states of even-even Te, Xe, and Ba isotopes is discussed using the nuclear shell model. It shows various phenomena, including the transition of spherical, axially symmetric deformed and triaxially deformed shapes. We show these phenomena are reproduced by our microscopic calculation, and the analysis of the anomalously small B(E2) value of ¹³⁶Te. We also discuss the g-factors of Xe isotopes, which exhibit the transition between the spherical and the triaxially deformed shapes.

Nuclear structure of the doublet bands in the doubly-odd nuclei with mass A ∼ 130 is studied in terms of a pair-truncated shell model. The model reproduces quite well the energy levels of the doublet bands and the electromagnetic transitions. The doublet bands turn out to be realized by the chopsticks-like motion of two angular momenta of the unpaired neutron and the unpaired proton, weakly coupled with the quadrupole collective excitations of the even-even part of the nucleus.

This paper considers the implementation of the simulated annealing method to fit the values of the Skyrme interaction parameters. By searching for the global minimum in the hypersurface of the χ² function the values of the Skyrme parameters have been fitted to an extensive set of experimental data.

We found a set of quantum numbers for the particle-rotor model with one nucleon coupled to a triaxially deformed core. These quantum numbers classify the rotational bands, and lead the selection rules for the electromagnetic intraband and interband transitions.

A variety γ-spectroscopy experiments are successfully performed at RIPS, RIKEN. Among them, we report on the proton inelastic scattering on ^60,62Cr. Large quadrupole deformation parameters were obtained showing the enhancement of the collectivity in these nuclei. The perspective in the γ-spectroscopy experiment at RIBF are discussed.

The proton single-particle states have been investigated using the in-beam γ-ray spectroscopy technique via the following reactions: ⁴He(²²O,²³F); ⁴He(²³F,²³F); ⁴He(²⁴F,²³F); and ⁴He(²⁵Ne,²³F). The characters of excited states in ²³F were deduced by comparison of the population strengths in these reactions. We found that the 2268- and 4059-keV levels have strong proton single-particle nature of the s1/2 and d3/2 orbitals, respectively. These singleparticle states are located at higher excitation energies than the shell model predictions for the USD and SDPF-M interactions, which indicates that the centroid energy gaps for πd_5/2−πs_1/2 and πd_5/2−πd_3/2 are wider than predicted.

Experiments of ¹⁴Be and ¹⁶C have shown an interesting result for a nuclear deformation. By using the shell model calculation with 2ℏω excitations, we investigate E2 transitions for Be and C isotopes with N = 6 − 12. The numerical calculations show that neutrons are active for a quadrupole transition in the case of N > 8 isotopes.

The new clustering aspects of sd-shell nuclei found by the recent application of the antisymmetrized molecular dynamics are reported. In this paper we present two topics, "superdeformed band of ³²S and ¹⁶O + ¹⁶O clustering" and "molecular-orbital and di-nuclei states in ²²Ne". In the first topic, it will be shown that the superdeformed band of 32S has a considerable amount of ¹⁶O + ¹⁶O cluster component, and can be regarded as to belong to a family of the ¹⁶O + ¹⁶O molecular bands. In the second topic, the presence of the molecularorbital band which has an α + ¹⁶O cluster core surrounded by two covalently neutrons is suggested together with an α + ¹⁸O di-nuclei band.

The molecular structure and the reaction dynamics in ¹⁰Be are investigated by employing the microscopic α + α + n + n model. The coexistence of the atomic and molecular structures are found in the excited states of this system. The calculation of the low-energy scattering and the breakup reaction predict the strong enhancements in the decay channels going to the ⁶He(2⁺₁) state.

For a better understanding of the dynamics of complex exotic nuclei it is of crucial importance to develop a practical microscopic theory easy to be applied to a wide range of masses. In this paper we propose to calculate the structure of neutron-rich nuclei within a dynamic model based on the EoM theory.

The cluster structures of the excited states in ¹¹B are studied by analyzing the isoscalar monopole and quadrupole strengths in the ¹¹B(d, d') reaction at E_d = 200 MeV. The excitation strengths are compared with the theoretical predictions by the antisymmetrized molecular-dynamics (AMD) calculations. It is found that the large monopole strength for the 3/2⁻₃ state at E_x = 8.56 MeV is well described by the AMD wave function with a dilute 2α + tcluster structure.