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We systematically investigate the relationship between the nuclear structure and reaction in the 10Be nucleus using a theoretical framework. The structure of the 10Be nucleus is constructed with a cluster model based on a microscopic viewpoint. In this paper, the 10Be nucleus with different structures is prepared by manipulating the parameters of an effective nucleon-nucleon interaction. The nuclear structure and expectation values of physical quantities are drastically changed by the modification. We summarize such changes and show the effects on the elastic and inelastic scatterings for the proton and 12C targets in the microscopic coupled-channel calculation. Especially, we recently reported the visualization of dineutron correlation in 10Be on proton inelastic scattering in [Phys. Rev. C104, 034613 (2021)]. In this preceding work, we found that the changing degree of dineutron correlation in 10Be leads to drastic changes of the inelastic cross section for the 2$_2^+$ state. The development (or breaking) of the dineutron correlation is governed by the strength of the spin-orbit interaction of the structure calculation. However, in the previous work, some of the realistic physical points were missing, for example, the binding energy. Therefore, we reconstruct the 10Be nucleus by adjusting the effective nucleon-nucleon interaction to obtain the reasonable binding energy of the ground state. With this improvement, we again discuss the dineutron correlation in the 10Be nucleus. We reconfirm the way to measure the degree of the development (or breaking) of dineutron cluster structure; the sensitivity to the inelastic cross section of the ground state to the 2$_2^+$ state of 10Be.

We investigated the development and breaking of the dineutron correlation in $^{10}\mathrm{Be}$ by analyzing the elastic and inelastic scatterings with a framework combining the microscopic structure and reaction models. For studying the structure, the $^{10}\mathrm{Be}$ nucleus was constructed under the assumption of a four-body ($\ensuremath{\alpha}+\ensuremath{\alpha}+n+n$) cluster model. In this paper, we focused on the change in the inner structure for the ${0}_{1}^{+}$, ${2}_{1}^{+}$, and ${2}_{2}^{+}$ states when the strength of the spin-orbit interaction is varied. The inner structure, including various physical quantities such as energy, radius, and transition strength, is drastically influenced by the strength of the spin-orbit interaction. In particular, the development and breaking of the dineutron correlation are governed by the spin-orbit strength. The differences in the inner structure can be manifested by applying the obtained wave functions to elastic and inelastic scatterings with a proton target at $E/A=$ 59.4 and 200 MeV. Although the ${0}_{1}^{+}$ and ${2}_{1}^{+}$ states are significantly influenced by the spin-orbit strength of the nuclear structure calculation, the elastic and inelastic cross sections are not much affected. On the other hand, the inelastic cross section of the ${2}_{2}^{+}$ state depends greatly on the spin-orbit strength of the structure calculation. Thus, we discovered a way to measure the degree of the development of the dineutron cluster structure based on its sensitivity to the inelastic cross section of the ${2}_{2}^{+}$ state of $^{10}\mathrm{Be}$.

It is a well-known fact that a cluster of nucleons can be formed in the interior of an atomic nucleus, and such clusters may occupy molecular-like orbitals, showing characteristics similar to normal molecules consisting of atoms. Chemical molecules having a linear alignment are commonly seen in nature, such as carbon dioxide. A similar linear alignment of the nuclear clusters, referred to as linear-chain cluster state (LCCS), has been studied since the 1950s, however, up to now there is no clear experimental evidence demonstrating the existence of such a state. Recently, it was proposed that an excess of neutrons may offer just such a stabilizing mechanism, revitalizing interest in the nuclear LCCS, specifically with predictions for their emergence in neutron-rich carbon isotopes. Here we present the experimental observation of {\alpha}-cluster states in the radioactive 14C nucleus. Using the 10Be+{\alpha} resonant scattering method with a radioactive beam, we observed a series of levels which completely agree with theoretically predicted levels having an explicit linear-chain cluster configuration. We regard this as the first strong indication of the linear-chain clustered nucleus., Comment: 15 pages, 3 figures

Studies on nuclear astrophysics, nuclear structure, and other interests have been performed using the radioactive-isotope (RI) beams at the low-energy RI beam separator CRIB, operated by Center for Nuclear Study (CNS), the University of Tokyo. The elastic resonant scattering is a striking tool to study astrophysical reactions and nuclear clusters. In particular, when it is coupled with a thick target and inverse kinematics, the measurement can be very efficient and even feasible with RI beams. By measuring resonant scattering, we can study the properties of resonant states which could play an important role in the astrophysical reaction, or have an exotic nuclear structure. The 10Be+α elastic scattering has been measured at CRIB, and three resonances which are in agreement with the prediction of a linear-chain structure by Suhara-En’yo were observed, giving a strong indication of the existence of such an exotic structure. Measurements based on the indirect technique of the reaction measurement, such as the Trojan horse method, have also been performed at CRIB.

We formulate the ``tensor-optimized high-momentum antisymmetrized molecular dynamics'' (TO-HMAMD) framework for ab initio calculations of nuclei by hybridizing the tensor-optimized (TO) and high-momentum (HM) AMD approaches. This hybrid approach has advantages in both analytical simplicity and numerical efficiency compared with other AMD-based methods which treat the bare interaction, especially for heavier nuclear systems. In this work, the $s$-shell nucleus $^{4}\mathrm{He}$ is calculated with TO-HMAMD by including up to double product of nucleon-nucleon ($NN$) correlations, described by using high-momentum pairs and spatial correlation functions of nucleons. The total energy and radius of the $^{4}\mathrm{He}$ nucleus are well reproduced using the $\mathrm{AV}{8}^{\ensuremath{'}}$ interaction. The spin-isospin channel dependence is also discussed for $NN$ correlations, which are found to be mostly contributed in the even-state channels, especially the triplet-even channel. Analyses of the analytical formation and numerical results suggest that TO-HMAMD could be a promising framework for $p$-shell nuclear systems.

The glue-like behavior of valence neutrons has been investigated in the Li isotopes. The 7Li nucleus is well known to be weakly bound system with the α + t cluster structure. By adding the valence neutrons, the reduction of the root-mean-square (RMS) radius of the proton density for the 7Li, 8Li and, 9Li nuclei is also well known from the viewpoint of the experimental data and theoretical approach. Elastic scattering cross sections of the Li isotopes on the 12C and 28Si targets at E/A ∼ 50 MeV are calculated. We find the change of the channel coupling (CC) effect on elastic scatterings of such Li isotopes by the glue-like role of the valence neutrons. Finally, we realize that the valence neutrons stabilize the binding of core parts, and the CC effect related the core excitation is indeed reduced., PROCEEDINGS OF THE 4TH INTERNATIONAL WORKSHOP ON “STATE OF THE ART IN NUCLEAR CLUSTER PHYSICS” (SOTANCP4), 13–18 May 2018, Texas, USA.

International audience; Studies on nuclear astrophysics, nuclear structure, and other interests have been performed using the radioactive-isotope (RI) beams at the low-energy RI beam separator CRIB, operated by Center for Nuclear Study (CNS), the University of Tokyo. A type of measurement to study astophysical reactions at CRIB is by the elastic resonant scattering with the thick-target method in inverse kinematics. An example is the α resonant scattering with 7Be beam, related to the astrophysical 7Be(α,γ) reactions, which is relevant in the hot p-p chain and νp-process in supernovae. Other α resonant scattering measurements with 30S, 10Be, 15O, and 18Ne beams have been performed at CRIB, using the thick-target method. There have also been measurements based on other experimental methods. The first Trojan horse method (THM) measurement using an RI beam has been performed at CRIB, to study the 18F(p, α)15O reaction at astrophysical energies via the three body reaction 2H(18F, α15O)n. The 18F(p, α)15O reaction rate is crucial to understand the 511-keV γ-ray production in nova explosion phenomena, and we successfully evaluated the reaction cross section at novae temperature and below experimentally for the first time.

Linear-chain and gas-like structures have been investigated in nuclei near 12C by using antisymmetrized molecular dynamics combined with generator coordinate method. We found that linear-chain structures and gas-like structures of three clusters exist quite universally. 10Be, 11B, and 12C have gas-like states of 2α+dineutron, 2α+t, and 3α structures, respectively. There are linear-chain states, in which 2α clusters are formed and valence nucleons occupy the σ-orbit. In neutron-rich C isotopes, linear-chain structures of three α clusters surrounded by excess neutrons appear. Excess neutrons stabilize the linear chain structures, and therefore, linear-chain states appear below the 3α+Xn threshold energy. In 14C, candidates of the linear-chain states are observed in recent 10Be+α resonant scattering experiments.Linear-chain and gas-like structures have been investigated in nuclei near 12C by using antisymmetrized molecular dynamics combined with generator coordinate method. We found that linear-chain structures and gas-like structures of three clusters exist quite universally. 10Be, 11B, and 12C have gas-like states of 2α+dineutron, 2α+t, and 3α structures, respectively. There are linear-chain states, in which 2α clusters are formed and valence nucleons occupy the σ-orbit. In neutron-rich C isotopes, linear-chain structures of three α clusters surrounded by excess neutrons appear. Excess neutrons stabilize the linear chain structures, and therefore, linear-chain states appear below the 3α+Xn threshold energy. In 14C, candidates of the linear-chain states are observed in recent 10Be+α resonant scattering experiments.

We developed a new variational method of tensor-optimized antisymmetrized molecular dynamics (TOAMD) to treat the bare interactions for finite nuclei. In TOAMD, two kinds of the correlation functions for tensor force and short-range repulsion are multiplied to the AMD wave function successively in the power series form. Each correlation function in every correlation term is independently optimized in the total energy variation. We show the results of TOAMD for s-shell nuclei using bare AV8’ NN potential. The binding energy and the Hamiltonian components nicely reproduce the values of the few-body calculations. The energies obtained in TOAMD are shown to be lower than those of the variational Monte Carlo method based on the Jastrow’s product-type correlation functions. This means that the power series expansion using the independent correlation functions in TOAMD describes the nuclei better than the Jastrow correlation method. We further extended TOAMD by adopting the multi-configuration of the AMD wave functions, which include the high-momentum (HM) components of nucleon motions. This framework is called high-momentum TOAMD (HM-TOAMD) and we show the results of HM-TOAMD for s-shell nuclei.We developed a new variational method of tensor-optimized antisymmetrized molecular dynamics (TOAMD) to treat the bare interactions for finite nuclei. In TOAMD, two kinds of the correlation functions for tensor force and short-range repulsion are multiplied to the AMD wave function successively in the power series form. Each correlation function in every correlation term is independently optimized in the total energy variation. We show the results of TOAMD for s-shell nuclei using bare AV8’ NN potential. The binding energy and the Hamiltonian components nicely reproduce the values of the few-body calculations. The energies obtained in TOAMD are shown to be lower than those of the variational Monte Carlo method based on the Jastrow’s product-type correlation functions. This means that the power series expansion using the independent correlation functions in TOAMD describes the nuclei better than the Jastrow correlation method. We further extended TOAMD by adopting the multi-configuration of the AMD wave fu...

Herein, we investigated the channel coupling (CC) effect on the elastic scatterings of lithium (Li) isotopes ($A =$ 6--9) for the $^{12}$C and $^{28}$Si targets at $E/A =$ 50--60 MeV. The wave functions of the Li isotopes were obtained using the stochastic multi-configuration mixing (SMCM) method based on the microscopic-cluster model. The proton radii of the $^{7}$Li, $^{8}$Li, and $^{9}$Li nuclei became smaller as the number of valence neutrons increased. The valence neutrons in the $^{8}$Li and $^{9}$Li nuclei exhibited a glue-like behavior, thereby attracting the $\alpha$ and $t$ clusters. Based on the transition densities derived from these microscopic wave functions, the elastic-scattering cross section was calculated using a microscopic coupled-channel (MCC) method with a complex $G$-matrix interaction. The existing experimental data for the elastic scatterings of the Li isotopes and $^{10}$Be nuclei were well reproduced. The Li isotope elastic cross sections were demonstrated for the $^{12}$C and $^{28}$Si targets at $E/A$ =53 MeV. The glue-like effect of the valence neutrons on the Li isotope was clearly demonstrated by the CC effect on elastic scattering. Finally, we realize that the valence neutrons stabilized the bindings of the core parts and the CC effect related to core excitation was indeed reduced., Comment: 21 pages, 9 figures, 2 tables, accepted in Physical Review C

We treat the tensor correlation in antisymmetrized molecular dynamics (AMD) including large-relative-momentum components among nucleon pairs for finite nuclei. The tensor correlation is described by using large imaginary centroid vectors of Gaussian wave packets for nucleon pairs with opposite directions, which makes a large relative momentum. We superpose the AMD basis states, in which one nucleon pair has various relative momenta for all directions; this new method is called "high-momentum AMD" (HM-AMD). We show the results for $^4$He using the effective interaction having a strong tensor force. It is found that HM-AMD provides a large tensor matrix element comparable to the case of the tensor-optimized shell model (TOSM), in which the two-particle-two-hole (2p-2h) excitations are fully included to describe the tensor correlation. The results of two methods agree with each other at the level of the Hamiltonian components of $^4$He. This indicates that in HM-AMD the high-momentum components described by the imaginary centroid vectors of the nucleon pair provide the equivalent effect of the 2p-2h excitations for the tensor correlation., 11 pages, 4 figures, added references

We recently proposed a new variational theory of "tensor-optimized antisymmetrized molecular dynamics" (TOAMD), which treats the strong interaction explicitly for finite nuclei [T. Myo et al., Prog. Theor. Exp. Phys. 2015, 073D02 (2015)]. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiple products are successively operated to the AMD state. The correlated Hamiltonian is expanded into many-body operators by using the cluster expansion and all the resulting operators are taken into account in the calculation without any truncation. We show detailed results for TOAMD with the nucleon-nucleon interaction AV8$^\prime$ for $s$-shell nuclei. The binding energy and the Hamiltonian components are successively converged to exact values of the few-body calculations. We also apply TOAMD to the Malfliet-Tjon central potential having a strong short-range repulsion. TOAMD can treat the short-range correlation and provided accurate energies of $s$-shell nuclei, reproducing the results of few-body calculations. It turns out that the numerical accuracy of TOAMD with double products of the correlation functions is beyond the variational Monte Carlo method with Jastrow's product-type correlation functions., 25 pages, 24 figures, corrected typos

Recently, we proposed the microscopic structure and reaction models. The model firstly constructs the nuclear structure by the stochastic multi-configuration mixing (SMCM) method based on the cluster model. Next, the cross section is obtained by the microscopic coupled-channel (MCC) calculation based on the folding model with the complex G-matrix interaction. In this work, we compare the $^{9}$Li nucleus with the $^{10}$Be nucleus from the viewpoint of the nuclear structure and reaction. The $^{9}$Li ($^{10}$Be) nucleus is described as an $\alpha$ + $t$ ($\alpha$) + $n$ + $n$ four-body system based on the cluster model. The elastic and inelastic scattering cross sections for the $^{9}$Li + $^{12}$C and $^{10}$Be + $^{12}$C systems are obtained by the MCC calculation with the MPa interaction which is the latest version of the complex G-matrix interaction derived from the ESC nucleon-nucleon interaction model. The excitation energies of the low-lying states for the $^{9}$Li and $^{10}$Be nuclei well reproduce the data. The MCC model including the excitation effect of the projectile and target shows the visible channel coupling effect on the elastic cross section. The contribution of the $^{10}$Be excitation effect is clearly larger than that of the $^{9}$Li excitation effect.

Tensor-optimized antisymmetrized molecular dynamics (TOAMD) is the basis of the successive variational method for nuclear many-body problem. We apply TOAMD to finite nuclei to be described by the central interaction with strong short-range repulsion, and compare the results with the unitary correlation operator method (UCOM). In TOAMD, the pair-type correlation functions and their multiple products are operated to the AMD wave function. We show the results of TOAMD using the Malfliet-Tjon central potential containing the strong short-range repulsion. Adding the double products of the correlation functions in TOAMD, the binding energies are converged quickly to the exact values of the few-body calculations for s-shell nuclei. This indicates the high efficiency of TOAMD for treating the short-range repulsion in nuclei. We also employ the s-wave configurations of nuclei with the central part of UCOM, which reduces the short-range relative amplitudes of nucleon pair in nuclei to avoid the short-range repulsion. In UCOM, we further perform the superposition of the s-wave configurations with various size parameters, which provides a satisfactory solution of energies close to the exact and TOAMD values., Comment: 8 pages, 9 figures

Many-body correlations play an essential role in the ab initio description of nuclei with nuclear bare interactions. We propose a new framework to describe light nuclei by the hybridization of the tensor-optimized antisymmetrized molecular dynamics (TOAMD) and the high-momentum AMD (HM-AMD), which we call "HM-TOAMD". In this framework, we describe the many-body correlations in terms of not only the correlation functions in TOAMD, but also the high-momentum pairs in the AMD wave function. With the bare nucleon-nucleon interaction AV8', we sufficiently reproduce the energy and radius of the 3H nucleus in HM-TOAMD. The effects of tensor force and short-range repulsion in the bare interaction are nicely described in this new framework. We also discuss the convergence in calculation and flexibility of the model space for this new method., Comment: 9 pages, 5 figures, 1 table, Accepted by PTEP

We study the tensor-optimized antisymmetrized molecular dynamics (TOAMD) as a successive variational method in many-body systems with strong interaction for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiples are operated to the AMD state as the variational wave function. The total wave function is expressed as the sum of all the components and the variational space can be increased successively with the multiple correlation functions to achieve convergence. All the necessary matrix elements of many-body operators, consisting of the multiple correlation functions and the Hamiltonian, are expressed analytically using the Gaussian integral formula. In this paper we show the results of TOAMD with up to the double products of the correlation functions for the s-shell nuclei, 3H and 4He, using the nucleon-nucleon interaction AV8'. It is found that the energies and Hamiltonian components of two nuclei converge rapidly with respect to the multiple of correlation functions. This result indicates the efficiency of TOAMD for the power series expansion in terms of the tensor and short-range correlation functions., Comment: 7 pages, 5 figures, added references, corrected typos

We developed a new variational method for tensor-optimized antisymmetrized molecular dynamics (TOAMD) for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion are introduced and used in the power series form of the wave function, which is different from the Jastrow method. Here, nucleon pairs are correlated in multi-steps with different forms, while they are correlated only once including all pairs in the Jastrow correlation method. Each correlation function in every term is independently optimized in the variation of total energy in TOAMD. For $s$-shell nuclei using the nucleon-nucleon interaction, the energies in TOAMD are better than those in the variational Monte Carlo method with the Jastrow correlation function. This means that the power series expansion using the correlation functions in TOAMD describes the nuclei better than the Jastrow correlation method., Comment: 7 pages, 4 figures. arXiv admin note: text overlap with arXiv:1706.09560, update references

Structures of excited states in 11B are investigated with a method of β – γ constraint antisymmetrized molecular dynamics in combination with the generator coordinate method. Various cluster structures are suggested in excited states. For negative-parity states, we suggest a band with a 2α + t cluster structure. This band starts from the \({3/2^{-}_{3}}\) state and can correspond to the experimental band observed recently. We find that the feature of the \({3/2^{-}_{3}}\) is quite similar to the \({0^{+}_{2}}\) state in 12C.

The antisymmetrized quasi-cluster model (AQCM) is a method to describe transitions from the α cluster wave functions to jj-coupling shell model wave functions. In this model, the cluster-shell transition is characterized by only two parameters: R representing the distance between α clusters and describing the breaking of α clusters. The contribution of the spin-orbit interaction, very important in the jj-coupling shell model, can be taken into account starting with the α cluster modelwave function. In this article we showthe generality ofAQCMby extending the application to heavier regions: various 4N nuclei from [4]He to [100]Sn. The characteristic magic numbers of the jj-coupling shell model, 28 and 50, are described starting with the α cluster model. The competition of two different configurations is discussed in [20]Ne ([16]O + one quasi-cluster and [12]C + two quasi-clusters) and [28]Si (pentagon shape of five quasi-clusters and [12]C+[16]O). Also, we compare the energy curves for the α+[40]Ca cluster configuration calculated with and without the α breaking effect in [44]Ti.

Background: Direct evidence of the $\ensuremath{\alpha}\text{-cluster}$ manifestation in bound states has not been obtained yet, although a number of experimental studies were carried out to extract the information of the clustering. In particular in conventional analyses of $\ensuremath{\alpha}\text{-transfer}$ reactions, there exist a few significant problems on reaction models, which are insufficient to qualitatively discuss the cluster structure.Purpose: We aim to verify the manifestation of the $\ensuremath{\alpha}\text{-cluster}$ structure from observables. As the first application, we plan to extract the spatial information of the cluster structure of the $^{20}\mathrm{Ne}$ nucleus in its ground state through the cross section of the $\ensuremath{\alpha}\text{-transfer}$ reaction $^{16}\mathrm{O}(^{6}\mathrm{Li},\phantom{\rule{0.16em}{0ex}}d)^{20}\mathrm{Ne}$.Methods: For the analysis of the transfer reaction, we work with the coupled-channel Born approximation (CCBA) approach, in which the breakup effect of $^{6}\mathrm{Li}$ is explicitly taken into account by means of the continuum-discretized coupled-channel method based on the three-body $\ensuremath{\alpha}+d+^{16}\mathrm{O}$ model. The two methods are adopted to calculate the overlap function between $^{20}\mathrm{Ne}$ and $\ensuremath{\alpha}+^{16}\mathrm{O}$; one is the microscopic cluster model (MCM) with the generator coordinate method, and the other is the phenomenological two-body potential model (PM).Results: We show that the CCBA calculation with the MCM wave function gives a significant improvement of the theoretical result on the angular distribution of the transfer cross section, which is consistent with the experimental data. Employing the PM, it is discussed which region of the cluster wave function is probed on the transfer cross section.Conclusions: It is found that the surface region of the cluster wave function is sensitive to the cross section. The present work is situated as the first step in obtaining important information to systematically investigate the cluster structure.

We present a review of recent works on clustering phenomena in unstable nuclei studied by antisymmetrized molecular dynamics (AMD). The AMD studies in these decades have uncovered novel types of clustering phenomena brought about by the excess neutrons. Among them, this review focuses on the molecule-like structure of unstable nuclei. One of the earliest discussions on the clustering in unstable nuclei was made for neutron-rich Be and B isotopes. AMD calculations predicted that the ground state clustering is enhanced or reduced depending on the number of excess neutrons. Today, the experiments are confirming this prediction as the change of the proton radii. Behind this enhancement and reduction of the clustering, there are underlying shell effects called molecular- and atomic-orbits. These orbits form covalent and ionic bonding of the clusters analogous to the atomic molecules. It was found that this "molecular-orbit picture" reasonably explains the low-lying spectra of Be isotopes. The molecular-orbit picture is extended to other systems having parity asymmetric cluster cores and to the three cluster systems. O and Ne isotopes are the candidates of the former, while the $3\alpha$ linear chains in C isotopes are the latter. For both subjects, many intensive studies are now in progress. We also pay a special attention to the observables which are the fingerprint of the clustering. In particular, we focus on the monopole and dipole transitions which are recently regarded as good probe for the clustering. We discuss how they have and will reveal the exotic clustering., Comment: 96 pages, 44 figures

Spatial correlations of spin-zero neutron pairs in 6 He and 8 He 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 8 He than in 6 He but again pronounced in the excited [Formula: see text] of 8 He .

We propose a new method of the $��$-$��$ 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. We apply this method to N=6 isotones, $^{10}$Be, $^{12}$C, $^{9}$Li, and $^{11}$B, and find various structures as functions of the deformation parameters, $��$ and $��$. In these nuclei, shell-model-like structures appear in the small $��$ region, while cluster structures develop well in the large $��$ region where various geometric configurations of clusters are obtained depending on the $��$ parameter. For $^{10}$Be and $^{12}$C, we superpose the basis AMD wave functions obtained by the $��$-$��$ constraint method to calculate energy spectra, and prove the advantages of the present method of the two-dimensional $��$-$��$ constraint in the framework of AMD., 23pages, 14 figures

Structure of excited states in 14 C were investigated with a method of the antisymmetrized molecular dynamics model. Variation with constraints on the quadrupole deformations (β, γ) was performed, and the configurations were superposed within the AMD framework. Above the ground band, three excited bands with the developed 3α-cluster core structures were suggested. Characteristic structures such as a triaxial structure and a linear-chain structure appear in the excited bands. It was found that the 10 Be correlation exists in the linear-chain structure.

We report three-center cluster structures in the excited states of 11 B (11 C ), 8 He and 14 C based on theoretical calculations with the antisymmetrized molecular dynamics (AMD). In particular we discuss the cluster gas-like states 2α + t(2α+3 He ) in 11 B (11 C ) and α + 2n + 2n in 8 He . In 14 C , the 3α linear-chain structure is discussed.

To clarify the effects of $\ensuremath{\alpha}$-cluster breaking on $3\ensuremath{\alpha}$-cluster structures in $^{12}\mathrm{C}$, we investigate $^{12}\mathrm{C}$ using a hybrid model that combines the Brink-Bloch cluster model with the ${p}_{3/2}$ subshell closure wave function. We have found that $\ensuremath{\alpha}$-cluster breaking caused by spin-orbit force significantly changes cluster structures of excited ${0}^{+}$ states through orthogonality to lower states. Spatially developed cluster components of the ${0}_{2}{}^{+}$ state are reduced. The ${0}_{3}{}^{+}$ state changes from a vibration mode in the bending motion of three $\ensuremath{\alpha}$ clusters to a chainlike $3\ensuremath{\alpha}$ structure having an open triangle configuration. As a result of these structure changes of ${0}^{+}$ states, the band assignment for the ${2}_{2}{}^{+}$ state is changed by the $\ensuremath{\alpha}$-cluster breaking effect. Namely, in model calculations without the $\ensuremath{\alpha}$-cluster breaking effect, the ${0}_{2}{}^{+}$ state is assigned to be the band-head of the ${2}_{2}{}^{+}$ state. However, when we incorporate $\ensuremath{\alpha}$-cluster breaking caused by the spin-orbit force, the ${0}_{3}{}^{+}$ state is regarded as the bandhead of the ${2}_{2}{}^{+}$ state.

Alpha resonant scattering is a simple and promising method to study α-cluster structure in nuclei. It has several good features which enable us to perform measurements with short-lived and relatively low-intense RI beams. Several measurements on alpha resonant scattering have been carried out at CRIB (CNS Radioactive Ion Beam separator), which is a low-energy RI beam separator at Center for Nuclear Study (CNS) of the University of Tokyo. Recent α resonant scattering studies at CRIB, using7Li,7Be and10Be beams with a helium gas target, are discussed.

Studies on nuclear reactions relevant for astrophysics have been performed using the radioactive-isotope (RI) beams at the low-energy RI beam separator CRIB, operated by Center for Nuclear Study (CNS), the University of Tokyo. A type of measurement to study astrophysical reactions at CRIB is by the elastic resonant scattering with the thick-target method in inverse kinematics. We introduce the α resonant scattering with 7 Be beam, related to the astrophysical 7 Be(α, γ) reactions, which is relevant in the hot p-p chain and νp-process in supernovae. Other α resonant scattering measurements with 30 S, 10 Be, 15 O, and 18 Ne beams have been performed at CRIB, using the thick-target method.

The low-lying states of the $^{9}$Li nucleus are investigated with a unified framework of microscopic structure and reaction models. In the structure model, the wave function is fully antisymmetrized and the $^{9}$Li nucleus is described as an $\alpha$ + $t$ + $n$ + $n$ four-body system, and low-lying 1/2$^{-}$, 3/2$^{-}$, 5/2$^{-}$, and 7/2$^{-}$ states are obtained by the stochastic multi-configuration mixing method. Using these wave functions, the quasi-elastic cross section at $E/A$ = 60 MeV and the elastic and inelastic cross sections at $E/A$ = 50 MeV on the $^{12}$C target are calculated in the framework of the microscopic coupled channel (MCC) method. The characteristic inelastic angular distribution is seen in the 3/2$_{2}^{-}$ state, whose $\alpha+t$ cluster structure and valence neutron configurations are discussed in detail. We find the possibility of triaxial deformation and mixing of di-neutron components in the $^{9}$Li nucleus.

We propose a simple method to approximately evaluate reduced width amplitude (RWA) of a two-body spinless cluster channel using the norm overlap with the Brink-Bloch cluster wave function at the channel radius. The applicability of the present approximation is tested for the $^{16}$O+$\alpha$ channel in $^{20}$Ne as well as the $\alpha$+$\alpha$ channel in $^8$Be. The approximation is found to be reasonable to evaluate the RWA for states near the threshold energy and it is useful to estimate the $\alpha$-decay width of resonance states. The approximation is also applied to $^9$Li, and the partial decay width of the $^6$He($0^+_1$)+$t$ channel is discussed., Comment: 20 pages, 10 figures

Gamow-Teller transitions from the ${}^{14}\mathrm{N}$ ground state to the ${}^{14}\mathrm{C}$ ground and excited states were investigated, based on the model of antisymmetrized molecular dynamics. The calculated strengths for the allowed transitions to the ${0}^{+}$, ${1}^{+}$, and ${2}^{+}$ states of ${}^{14}\mathrm{C}$ were compared with the experimental data measured by high-resolution charge-exchange reactions. The calculated GT transition to the ${2}_{1}^{+}$ state is strong while those to the ${0}_{2,3}^{+}$ and ${2}_{2,3}^{+}$ states having dominant $2\ensuremath{\hbar}\ensuremath{\omega}$ excited configurations are relatively weak. The present calculation cannot describe the anonymously long lifetime of ${}^{14}\mathrm{C}$, though the strength of the ${}^{14}\mathrm{C}$ ground state is somewhat suppressed because of the cluster (many-body) correlation in the ground states of ${}^{14}\mathrm{C}$ and ${}^{14}\mathrm{N}$.

We present a new picture that the $\ensuremath{\alpha}$-linear-chain structure for $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ has one-dimensional $\ensuremath{\alpha}$ condensate character. The wave functions of linear-chain states that are described by superposing a large number of Brink wave functions have extremely large overlaps of nearly 100% with single Tohsaki-Horiuchi-Schuck-R\"opke wave functions, which were proposed to describe the $\ensuremath{\alpha}$ condensed ``gaslike'' states. Although this new picture is different from the conventional idea of the spatial localization of $\ensuremath{\alpha}$ clusters, the density distributions are shown to have localized $\ensuremath{\alpha}$ clusters due to the inter-$\ensuremath{\alpha}$ Pauli repulsion.

We propose an improved version of Antisymmetrized Quasi-Cluster Model (AQCM) to describe a smooth transition from the $\alpha$-cluster wave function to the $jj$-coupling shell model wave function and apply it to the ground state of $^{12}$C. The cluster-shell transition in $^{12}$C is characterized in AQCM by only two parameters: $R$ representing the distance between $\alpha$ clusters and the center of mass, and $\Lambda$ describing the break of $\alpha$ clusters. The optimal AQCM wave function for the ground state of $^{12}$C is an intermediate state between the three-$\alpha$ cluster state and the shell model state with the $p_{3/2}$ subshell closure configuration. The result is consistent with that of the Antisymmetrized Molecular Dynamics (AMD), and the optimal AQCM wave function quantitatively agrees with the AMD one, although the number of degrees of freedom in AQCM is significantly fewer.

Structures of excited states in $^{11}$B are investigated with a method of $\beta$-$\gamma$ constraint antisymmetrized molecular dynamics in combination with the generator coordinate method. Various excited states with developed cluster core structures are suggested in positive- and negative-parity states. For negative-parity states, we suggest a band with a $2\alpha+t$ cluster structure. This band starts from the $3/2^{-}_{3}$ state and can correspond to the experimental band observed recently. In positive-parity states, two $\alpha$ core cluster structures with surrounding nucleons are found. A $K^\pi=1/2^+$ band is suggested to be constructed from a remarkably developed cluster structure with a large prolate deformation. We discuss features of the cluster structure in association with molecular orbital structures of $^{10}$Be., Comment: 13 pages, 9 figures. arXiv admin note: text overlap with arXiv:1004.4954

Cluster states in ${}^{9}$Li are investigated with calculations of a ${}^{6}$He-$t$ cluster model. Results suggest ${}^{6}$He-$t$ cluster states near the ${}^{6}$He-$t$ threshold energy. These states construct a ${K}^{\ensuremath{\pi}}=1/{2}^{\ensuremath{-}}$ band and their neutron configuration is similar to that of the ${K}^{\ensuremath{\pi}}={0}_{2}^{+}$ band in ${}^{10}$Be.

We propose a method to obtain adiabatic internuclear potentials via energy variation with the intercluster-distance constraint. The adiabatic $^{16}$O + $^{16,18}$O potentials obtained by the proposed method are applied to investigate the effects of valence neutrons in $^{16}$O + $^{18}$O sub-barrier fusions. Sub-barrier fusion cross sections of $^{16}$O + $^{18}$O are enhanced more compared to those of $^{16}$O + $^{16}$O because of distortion of valence neutrons in $^{18}$O., 11 pages, 5 figures