Table of contents

The 3rd International Workshop on "State of the Art in Nuclear Cluster Physics"(SOTANCP3) was held at KGU Kannai Media Center, Kanto Gakuin University, Yokohama, Japan, from May 26 to 30, 2014. Yokohama is the second largest city in Japan, about 25 km southeast of Tokyo. The first workshop of the series was held in Strasbourg, France, in 2008 and the second one was in Brussels, Belgium, in 2010. The purpose of SOTANCP3 was to discuss the present status and future perspectives of the nuclear cluster physics. The following nine topics were selected in order to cover most of the scientific programme and highlight an area where new ideas have emerged over recent years:

(1) Cluster structures and many-body correlations in stable and unstable nuclei

(2) Clustering aspects of nuclear reactions and resonances

(3) Alpha condensates and analogy with condensed matter approaches

(4) Role of tensor force in cluster physics and ab initio approaches

(5) Clustering in hypernuclei

(6) Nuclear fission, superheavy nuclei, and cluster decay

(7) Cluster physics and nuclear astrophysics

(8) Clustering in nuclear matter and neutron stars

(9) Clustering in hadron and atomic physics

There were 122 participants, including 53 from 17 foreign countries. In addition to invited talks, we had many talks selected from contributed papers. There were plenary, parallel, and poster sessions. Poster contributions were also presented as four-minute talks in parallel sessions. This proceedings contains the papers presented in invited and selected talks together with those presented in poster sessions.

We would like to express our gratitude to the members of the International Advisory Committee and those of the Organizing Committee for their efforts which made this workshop successful. In particular we would like to present our great thanks to Drs. Y. Funaki, W. Horiuchi, N. Itagaki, M. Kimura, T. Myo, and T. Yoshida. We would like also to thank the following organizations for their sponsors: RCNP (Research Center for Nuclear Physics, Osaka University), CNS (Center for Nuclear Study, University of Tokyo), JICFuS (Joint Institute for Computational Fundamental Science), and RIKEN (Nishina Center for Accelerator-Based Science, Institute of Physical and Chemical Research). This workshop was supported by Yokohama Convention & Visitors Bureau and Kanto Gakuin University. It remains to be announced that the next, the fourth in this series of SOTANCP workshops, SOTANCP4, will be held in Galveston, Texas, USA, in 2018.

The committee members for the 3rd International Workshop on "State of the Art in Nuclear Cluster Physics" SOTANCP3

- International advisory committee

- Organizing committee

- Editorial board

The programme for the 3rd International Workshop on "State of the Art in Nuclear Cluster Physics" which was held at the KGU (Kanto Gakuin University) Kannai Media Center (8th floor of Yokohoma Media Business Center (YMBC))

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

Ladies and Gentlemen,

it is my great honor and pleasure to present an opening address of the 3rd International Workshop on "State of the Art in Nuclear Cluster Physics"(SOTANCP3). On the behalf of the organizing committee, I certainly welcome all your visits to KGU Kannai Media Center belonging to Kanto Gakuin University, and stay in Yokohama. In particular, to whom come from abroad more than 17 countries, I would appreciate your participations after long long trips from your homeland to Yokohama.

The first international workshop on "State of the Art in Nuclear Cluster Physics", called SOTANCP, was held in Strasbourg, France, in 2008, and the second one was held in Brussels, Belgium, in 2010. Then the third workshop is now held in Yokohama. In this period, we had the traditional 10th cluster conference in Debrecen, Hungary, in 2012. Thus we have the traditional cluster conference and SOTANCP, one after another, every two years. This obviously shows our field of nuclear cluster physics is very active and flourishing.

It is for the first time in about 10 years to hold the international workshop on nuclear cluster physics in Japan, because the last cluster conference held in Japan was in Nara in 2003, about 10 years ago. The president in Nara conference was Prof. K. Ikeda, and the chairpersons were Prof. H. Horiuchi and Prof. I. Tanihata. I think, quite a lot of persons in this room had participated at the Nara conference. Since then, about ten years passed. So, this workshop has profound significance for our Japanese colleagues.

The subjects of this workshop are to discuss "the state of the art in nuclear cluster physics" and also discuss the prospect of this field. In a couple of years, we saw significant progresses of this field both in theory and in experiment, which have brought better and new understandings on the clustering aspects in stable and unstable nuclei. I think, the concept of clustering has been more important than ever. This is true also in the related fields such as nuclear astrophysics, hypernuclear physics, hadron physics, and condensate matter physics so on. In fact, in this workshop, we also discuss the clustering aspects in the related fields. Thus, I expect in this workshop we can grasp the present status of the nuclear cluster physics and demonstrate its perspective in near future.

This workshop is sponsored by several institutes and organizations. In particular, I would express our thanks for financial supports to Research Center for Nuclear Physics (RCNP), Osaka University, Center for Nuclear Study (CNS), University of Tokyo, Joint Institute for Computational Fundamental Science (JICFuS), and RIKEN Nishina Center for Accelerator- Based Science. They are cohosting this workshop.

I would like also to appreciate my University, Kanto Gakuin University, who offers this nice place for one week and helps us to hold this workshop smoothly and conveniently. Today, the president of my University, Prof. Kuku, is here to present a welcome address. Thank you very much.

Finally, with many of the participants leading this field both in theory and in experiment, we wish this workshop offers an opportunity to simulate communications not only during the workshop but also in the future. In addition, we hope you enjoy exploring city of Yokohama and the area around, as well as scientific discussions. Thank you very much for your attention.

Ladies and Gentlemen,

It is an honor for me to present my welcome address in the 3rd International Workshop on "State of the Art in Nuclear Cluster Physics"(SOTANCP3), as the president of Kanto Gakuin University. Particularly to those from abroad more than 17 countries, I am very grateful for your participation after long long trips from your home to Yokohama. On the behalf of the Kanto Gakuin University, we certainly welcome your visit to our university and stay in Yokohama.

First I would like to introduce Kanto Gakuin University briefly. Kanto Gakuin University, which is called KGU, traces its roots back to the Yokohama Baptist Seminary founded in 1884 in Yamate, Yokohama. The seminary's founder was Albert Arnold Bennett, alumnus of Brown University, who came to Japan from the United States to establish a theological seminary for cultivating and training Japanese missionaries.

Now KGU is a major member of the Kanto Gakuin School Corporation, which is composed of two kindergartens, two primary schools, two junior high schools, two senior high schools as well as KGU. In this university, we have eight faculties with graduate school including Humanities, Economics, Law, Sciences and Engineering, Architecture and Environmental Design, Human and Environmental Studies, Nursing, and Law School. Over eleven thousands students are currently learning in our university.

By the way, my major is the geotechnical engineering, and I belong to the faculty of Sciences and Engineering in my university. Prof. T. Yamada, here, is my colleague in the same faculty. I know that the nuclear physics is one of the most active academic fields in the world. In fact, about half of the participants, namely, more than 50 scientists, come from abroad in this conference. Moreover, I know that the nuclear physics is related to not only the other fundamental physics such as the elementary particle physics and astrophysics but also chemistry, medical sciences, medical cares, and radiation metrology etc. Therefore, I am very happy that the excellent scientists of nuclear physics over 120 visit to our university for discussing the latest results and scope in nuclear physics, and enjoy our facilities and City of Yokohama. I believe that this conference will transmit the forefront of the nuclear physics from Yokohama to the world.

Finally, I hope this international workshop will be successful and fruitful, and all you have nice days in Yokohama. Thank you very much for your attention.

A list of the participants of the 3rd International Workshop on "State of the Art in Nuclear Cluster Physics"

Present status is discussed, from the theoretical viewpoint, for some selected topics of nuclear cluster physics. What is stressed here is that many of basic concepts of nuclear cluster physics since the days of K. Wildermuth are now examined and revived in new lights. An important example is the duality character of the ground-state wave function which was well known already in 1950's and has been recently revived in order to explain observed large magnitudes of E0 transitions between cluster states and the ground state in many nuclei. The other topics we discuss are (1) spatial localization of clusters v.s. THSR wave function, (2) coexistence of cluster states with mean-field-type states, and (3) spatial localization of clusters and ab initio calculations of cluster states.

Knowledge on nuclear cluster physics has increased considerably as nuclear clustering remains one of the most fruitful domains of nuclear physics, facing some of the greatest challenges and opportunities in the years ahead. The occurrence of "exotic" shapes in light N = Z α-like nuclei and the evolution of clustering from stability to the drip-lines are being investigated more and more accurately both theoretically and experimentally. Experimental progresses in understanding these questions were recently examined and will be further revisited in this introductory talk: clustering aspects are, in particular, discussed for light exotic nuclei with a large neutron excess such as neutron-rich Oxygen isotopes with their complete spectrocopy.

We discuss a container structure for non-gaslike cluster states, in which single Tohsaki-Horiuchi-Schuck-ROpke (THSR) wave functions are shown to be almost 100% equivalent to the full solutions of the corresponding RGM/GCM equations, for the inversion doublet band states in ²⁰Ne, α-linear-chain states, and α + α + A cluster states in ⁹_ΛBe. The recognition of the fact that the THSR wave function describes well not only gaslike cluster states but also non-gaslike cluster states is a recent remarkable development of nuclear cluster physics. This fact tells us that the cluster structure is composed of cluster-mean-field motion under the constraint of inter-cluster Pauli repulsion, in which we call the cluster-mean-field potential the container. We demonstrate that the evolution of the cluster structure of a nucleus is governed by the size parameter of the cluster-mean-field potential (container), for ¹⁶O nucleus.

Clustering phenomena in ¹⁰Be and ¹⁸O were studied by means of resonance elastic scattering of α-particles on ⁶He and ¹⁴C. Excitation functions for α+⁶He and α+¹⁴C were measured and detailed R-matrix analyses of the excitation functions was performed. We compare the experimental results with the predictions of modern theoretical approaches and discuss properties of cluster rotational bands.

Cluster structure of highly excited states of ²⁴Mg has been investigated by the antisymmetrized molecular dynamics. Imposing the constraints on the expectation values of harmonic oscillator quanta, α+²⁰Ne, ¹²C+¹²C and 6α cluster wave functions were generated without any a priori assumption. The isoscalar monopole excitation function is also calculated and reasonably agrees with the observation. It is found that α+²⁰Ne, ¹²C+¹²C and 6α clusters appear as the prominent peaks in the strength function.

Nuclear states are often described as quantum liquid states. Using the localisation parameter, it is possible to understand cluster states in nuclei as hybrid states between quantum liquid and crystal states. Recent calculations discussing the effect of the depth of the confining potential, as well as various lengthscales ratios, are presented in order to provide a complementary view on the cluster phenomenon in nuclei.

A container picture is proposed for understanding cluster dynamics where the clusters make nonlocalized motion occupying the lowest orbit of the cluster mean-field potential characterized by the size parameter "B" in the THSR (Tohsaki-Horiuchi-Schuck-Röpke) wave function. The nonlocalized cluster aspects of the inversion-doublet bands in ²⁰Ne which have been considered as a typical manifestation of localized clustering are discussed. In the α+¹⁶O system, localization is entirely of kinematical origin, that is, due to the inter-cluster Pauli repulsion. It is concluded that this feature is general for nuclear cluster states.

We present a new picture that the α-linear-chain structure for ¹²C and ¹⁶O has one-dimensional α condensate character. The wave functions of linear-chain states which are described by superposing a large number of Brink wave functions have extremely large overlaps of nearly 100% with single Tohsaki-Horiuchi-Schuck-Ropke (THSR) wave functions, which were proposed to describe the α condensed "gas-like" states. Although this new picture is different from the conventional idea of the spatial localization of α clusters, the density distributions are shown to have localized a-clusters which is due to the inter-α Pauli repulsion.

We investigated decay properties of the broad resonance around 10 MeV in ¹²C and measured inelastic scattering of 386 MeV α particles on ¹⁶O at extremely forward angles including 0°. We have found that the lower component of the broad 0⁺ resonance at 10 MeV in ¹²C decayed to the ⁸Be + α channel, and that the higher component decayed both to the ⁸Be + α channel and to the ⁸Be(2+) + α channel. On the ¹⁶O nucleus, we have found two 0⁺ resonances at 16.7 MeV and 18.8 MeV, which are near the 4α breakup threshold. On the analogy to the broad resonances near the 3α threshold in ¹²C, they are considered to have the ¹²C(0⁺₂) + α cluster and the ⁸Be + ⁸Be cluster structures, respectively. It is consistent with the result of the experiment for the ¹²C(⁴He,⁸Be)⁸Be and ¹²C(⁴He,¹²C* → ⁸Be + α)α reactions.

Recent key experimental results on the spectroscopy of ¹²C have been made, which, when taken together, provide much needed clarity on the structure of the ground- and Hoyle- state excitations and provided new avenues for future research. High excitation energies in light nuclei are being explored with evermore precision and recent examples of this in ¹²C, ¹⁶O and ²⁰Ne are presented. These steps forward are examined and the outstanding issue of clustering versus condensation explored.

The newly measured high spin J^π = 5⁻ state at 22.4(2) MeV in ¹²C reported in this conference, fits very well to the predicted (ground state) rotational band of an oblate equilateral triangular spinning top with a D_3h symmetry characterized by the sequence of states: 0⁺, 2⁺, 3⁻ 4^±, 5⁻ with almost degenerate 4⁺ and 4⁻ (parity doublet) states. Such a D_3h symmetry was observed in triatomic molecules, and it is observed here for the first time in nuclear physics. We discuss a classification of other rotation-vibration bands in ¹²C such as the (0⁺) Hoyle band and the (1⁻) bending mode band and suggest measurements in search of the predicted ("missing") states that may shed new light on clustering in ¹²C and light nuclei. In particular, the observation (or non observation) of the predicted ("missing") states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.654 MeV in ¹² C.

α clustering and α condensation in lighter nuclei is presently strongly and increasingly discussed in the literature both from the experimental side as from the theoretical one. In proto-neutron stars a macroscopic condensate of α particles may occur. A discussion of the present status of the theory' for quartet condensation in general and for α particle condensation in nuclear matter in particular will be presented.

We report preliminary results from an experimental study of the p + ¹¹B reaction at beam energies of 2.00 MeV, 2.63 MeV and 3.12 MeV, corresponding to three known 0⁺, 2⁺ and 3⁻ resonances in ¹²C at excitation energies of 17.79 MeV, 18.38 MeV and 18.81 MeV. The resonances have small γ-decay branches to lower-lying resonances of the order of 10⁻⁶- 10⁻⁵. By detecting the three outgoing a particles in coincidence and measuring their momenta, we obtain complete kinematics information. From the combined energy of the α particles we determine the energy of the γ transition. In this way, we identify two previously observed transitions, (0⁺, 17.79) → (1+, 12.71) and (3⁻, 18.38) → (3⁻ 9.64), and one new transition, (2⁺, 18.81) → (1+, 12.71). The results demonstrate the usefulness of γ decay as a probe of the low-lying resonance spectrum of ¹²C in the search for new broad (cluster) resonances.

Cross sections for the alpha inelastic scattering exciting the low-lying monopole states in ¹²C, ¹⁶O, ²⁴Mg, ²⁸Si, and ⁴⁰Ca were measured and compared with the distorted- wave Born-approximation (DWBA) calculation to examine the puzzle of the missing monopole strength of the Hoyle state. It was found the DWBA calculation using the density-dependent aN interaction systematically overestimates the cross sections for the 0⁺ transitions, and the puzzle is a universal problem in light nuclei but not special in the Hoyle state. Since the DWBA calculation using the density-independent interaction reasonably well reproduces the experiment, this puzzle might be related to the density dependence of the effective interaction. The coupled-channel effect for the alpha inelastic scattering is also examined. The coupled- channel effect reduces the calculated cross section, and solve the puzzle of the missing monopole strengths in part, but the improvement of the density dependence of the effective interaction is still necessary to solve the puzzle.

An elaborate folding model + coupled channel analysis of the inelastic α+¹²C scattering has been done using the inelastic form factors based on the nuclear transition densities predicted by the antisymmetrized molecular dynamics. The form factors for the observed isoscalar states of ¹²C were fine-tuned against the measured (α, α') cross sections to estimate the corresponding Eλ transition strengths. A significant E2 transition strength has been allocated for the second 2⁺ state of ¹²C from our consistent coupled channel analysis of the (α, α') data measured at E_α = 240 and 386 MeV. The Eλ transition strengths of the 0⁺₂, 3^-₁, 0⁺₃, and 1^-₁ states were also carefully deduced from the same folding model + coupled channel analysis.

Properties of some ¹²C resonant states at low energies are studied in three-α- particle model. Calculations for breakup reactions of ¹² C bound state leading to three-body continuum states are performed at energies up to a few MeV above the breakup threshold by applying the Faddeev three-body formalism in coordinate space. Calculated cross sections reveal some resonant peaks. Decay modes and the structure at interior region of these resonant states as well as their effects on the triple-alpha reaction rate will be reported.

A formalism based on the complex-scaling method is used to solve a few-particle scattering problem in configuration space. This method allows to use trivial boundary conditions and is compatible with most of the bound state techniques. In this contribution calculations of neutron scattering on triton is presented using realistic nuclear Hamiltonians for neutron energies above four-nucleon breakup threshold.

The bare nucleus astrophysical S(E) factor is the Nuclear Physics parameter to determine the reaction rates in stellar plasmas. Whilst not being accessed in direct measurements, it can be easily determined using the Trojan Horse Method, successful indirect technique for nuclear astrophysics. The basic features of the method will be discussed and some recent results will be presented.

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, using ⁷Li, ⁷Be and ¹⁰Be beams with a helium gas target, are discussed.

A unified microscopic approach based on the algebraic version of the resonating group model has been realized for description of the radiative capture reactions ³H(α, γ)⁷Li and ³He(α, γ)⁷Be, which play an important role for modern nuclear astrophysics. The astrophysical S-factors of the reactions and branching ratios between capture to the ground and first excited states of the ⁷Li and ⁷Be nuclei have been calculated. The comparison with the most recent experimental data demonstrates a good agreement.

A clustering aspect is explained for the ⁹Be nucleus in charged-lepton deep inelastic scattering. Nuclear modifications of the structure function F₂ are studied by the ratio R_EMC = F^A₂/F^D₂, where A and D are a nucleus and the deuteron, respectively. In a JLab experiment, an unexpectedly large nuclear modification slope |dR_EMC/dx| was found for ⁹ Be, which could be related to its clustering structure. We investigated a mean conventional part of a nuclear structure function F^A₂ by a convolution description with nucleon momentum distributions calculated by antisymmetrized (or fermionic) molecular dynamics (AMD) and also by a simple shell model. We found that clustering effects are small in the conventional part, so that the JLab result could be associated with an internal nucleon modification or a short-range nuclear correlation which is caused by high densities due to cluster formation.

We introduce a scattering radius, which characterizes a spatial size of the scattering area, from partial wave decompositions of a cross section for a nucleon-nucleus scattering. The coupled-channel calculations of the p + ¹²C scattering are performed in the range of E_lab = 29.95 MeV to 65 MeV, and the scattering radii for the elastic scattering and the various inelastic channels, which involve the rotational or vibrational excitations and the 3α excitations in ¹²C, are derived from the partial wave decomposition. We found that the scattering radii for the inelastic channels with a well developed 3 a structure are strongly enhanced in comparison to the scattering radius for the elastic and collective channels. This enhancement of the scattering radius for the 3α channel strongly suggests that the scattering radius is sensitive to a size of the intrinsic structure of the finally excited state in the scattering process.

The α-transfer reaction ¹⁶O(⁶Li, d)²⁰Ne is investigated in order to extract the α- clustering probability of ²⁰Ne. The relative wave function for the α-¹⁶O system is calculated by a microscopic cluster model. We show the angular distribution of the transfer cross section is a good probe to see the radial dependence of the α-clustering probability in the surface region.

The ⁸Li+⁴He elastic scattering excitation function was measured by using the inverse kinematic thick target method. The ⁸Li beam was provided by the LNS radioactive facility EXCYT at an energy of 30 MeV and it was delivered into a large scattering chamber filled with ⁴He gas. The detection system was made by three silicon telescopes and one MCP. This last detector was used to measure the number of incident particles as well as the time of flight allowing for the discrimination between elastic and inelastic scattering. The setup and the experimental technique will be described in details and the results, as well as the comparison of the data with an R-matrix calculation, will be shown and discussed.

We study the resonance spectroscopy of the He isotopes and their mirror, proton- rich nuclei with an α + N + N + N + N cluster model. Many-body resonances are treated with the correct boundary condition as the Gamow states using the complex scaling method. We obtain the resonances up to the five-body decaying states in ⁸He and ⁸ C. The spectrum agrees with the recent experiment systematically for energies and decay widths and we predict several resonances. We also discuss the mirror symmetry breaking of He isotopes and their mirror nuclei for the configurations and the spatial distributions of the valence nucleons.

One of the aims of this work is to investigate a two-dineutron condensate state in ⁸He and to discuss the properties of two dineutrons in that state. We suggest that the excited ⁸He(0⁺) state that is the candidate for the two-dineutron condensation would exist above the α + 4n threshold energy by a few MeV and this state contains two compact dineutrons in the lowest S-wave around an α core. Different from a clusters, dineutron clusters in that state is soft in size changing, because two neutrons are not bound in free space and dineutron correlation becomes weak in the low-density structure of the dineutron condensation.

The structures of superdeformed (SD) states in ³⁴S are investigated using the antisymmetrized molecular dynamics and generator coordinate method (GCM). The GCM basis wave functions are calculated via energy variation with a constraint on the quadrupole deformation parameter β. By applying the GCM after parity and angular momentum projections, the coexistence of two positive- and one negative-parity SD bands are predicted, and low-lying states and other deformed bands are obtained. The SD bands have structures of ¹⁶O + ¹⁶O + two valence neutrons in molecular orbitals around the two ¹⁶O cores in a cluster picture. The configurations of the two valence neutrons are δ² and π² for the positive-parity SD bands and π¹δ¹ for the negative-parity SD band.

Nuclear Energy Density Functionals (EDFs) are a microscopic tool of choice extensively used over the whole chart to successfully describe the properties of atomic nuclei ensuing from their quantum liquid nature. In the last decade, they also have proved their ability to deal with the cluster phenomenon, shedding a new light on its fundamental understanding by treating on an equal footing both quantum liquid and cluster aspects of nuclei. Such a unified microscopic description based on nucleonic degrees of freedom enables to tackle the question pertaining to the origin of the cluster phenomenon and emphasizes intrinsic mechanisms leading to the emergence of clusters in nuclei.

Co-existence of different states is a profound concept, which possibly underlies the phase transition and the symmetry breaking. Because of a property inherent to quantum mechanics (cf. uncertainty), the co-existence is expected to appear more naturally in quantum- microscopic systems than in macroscopic systems. In this paper a mathematical theory describing co-existence of states in quantum systems is presented, and the co-existence is classified into 9 types.

The study of the decay of ³²S* and ³¹P* compound systems formed in ²⁰Ne+¹²C and ¹⁹F+¹²C reactions, respectively, is further extended on the basis of collective clusterization process within the dynamical cluster model (DCM) of Gupta and collaborators, with the effects of deformations and orientations included, at an excitation energy E*_CN=60 MeV. In the present study, we have investigated the effects of deformations and orientations on the target, i.e., ¹²C like yield, denoted C-yield (σ_C), which contains fusion-fission (FF) decay cross-section, σ_FF, from compound nucleus process and deep inelastic orbiting (DIO) cross-section, σ_D1O, from non-compound nucleus process. As observed in one of our earlier study for ³²S* system there is a competition between FF and DIO, while, for ³¹P* there is a contribution of FF cross-section only, in the total C-yield. The comparative analysis of C-Yield for the considerations of spherical and oriented nuclei, shows similar results with the only difference of the values of neck length parameter (ΔR), which are more for the later case. The calculated cross-sections ac show good agreement with experimental data for both the considerations.

The properties of few-body clusters (mass number A ≤ 4) are modified if they are immersed in a nuclear medium. In particular, Pauli blocking that reflects the antisymmetrization of the many-body wave function is responsible for the medium modification of light clusters and the dissolution with increasing density. A more consistent description is given with takes also the contribution of correlations in the continuum into account. The relation between cluster formation in warm dense matter and in nuclear structure is discussed.

We show how ultra-relativistic collisions of light nuclei with heavy targets may be used to record snap-shots of the ground-state configurations and reveal information on cluster correlations. The development of collective flow in the formed fireball, which reflects the geometric correlations in the initial state, is essential for the method. As an illustration we analyze the ¹²C-²⁰⁸Pb collisions.

The two-neutron unbound systems of ¹⁶Be, ¹³Li, ¹⁰He, and ²⁶O have been measured using the Modular Neutron Array (MoNA) and 4 Tm Sweeper magnet setup. The correlations of the 3-body decay for the ⁶Be and ³Li were extracted and demonstrated a strong correlated enhancement between the two neutrons. The measurement of the ¹⁰He ground state resonance from a ¹⁴Be(-2p2n) reaction provided insight into previous predictions that wavefunction of the entrance channel, projectile, can influence the observed decay energy spectrum for the unbound system. Lastly, the decay-in-target (DiT) technique was utilized to extract the lifetime of the ²⁶O ground state. The measured lifetime of 4.5^+1.1_−1.5(stat.)±3(sys.) ps provides the first indication of two-neutron radioactivity.

We investigate the three-body Coulomb breakup reactions of two-neutron halo nuclei and discuss the correlations of every binary subsystem such as of core-n and n-n by showing the invariant mass spectra. It is found that the final-state interactions of core-n and n-n binary subsystems dominantly determine the observed energy distributions of the breakup cross sections, such as the low-lying enhancements. Furthermore, we investigate the effects of the ⁹Li core excitations on the Coulomb breakup cross section of ¹¹Li. It is shown that the integrated E1 strength at low energy region is reduced by ~ 15 % by the inclusion of the ⁹Li core excitations.

Models for the description of breakup reactions used to study the structure of exotic cluster structures like halos are reviewed. The sensitivity of these models to the projectile description is presented. Calculations are sensitive to the projectile ground state mostly through its asymptotic normalisation coefficient (ANC). They also probe the continuum of the projectile. This enables studying not only resonant states of the projectile but also its non-resonant continuum both resonant and non-resonant. This opens the possibility to study correlations between both halo neutrons in two-neutron halo nuclei.

The continuum-discretized coupled-channels method (CDCC) has successfully been applied to studies on various reactions involving unstable nuclei. The four-body CDCC method is a new method to calculate three-body breakup continuum in a projectile, which gives an accurate analysis for four-body breakup systems. The eikonal reaction theory is a new approach to calculate inclusive breakup cross sections such as neutron removal cross sections. Moreover, CDCC is a useful tool for evaluation of nuclear data, which are important for nuclear engineering.

The explicit forms of the true asymptotics of the three-body (312) bound state radial wave functions of halo nuclei a both with two loosely bound external neutrons and with two charged particles, valid in different parts of the asymptotic region of the configuration space, are presented. The results for three-body asymptotic normalization factors for α + n + n → ⁶He and n + α + α → ⁹Be obtained from the comparative analysis of these asymptotic forms with the specific approximate model wave functions for asymptotic regions are also given.

In this paper the physics of clustering in atomic nucleus as seen from a mean field perspective will be discussed. Special attention is paid to phenomena involving octupole deformation like the α structure of ²⁰Ne or the emission of heavy clusters. The stabilizing role of spin for cluster-like highly deformed states is also discussed in the case of ³⁶ Ar.

We present a detailed analysis of the a-decay fine structure in 32 deformed odd-mass nuclei from Z = 93 to Z = 102. The α-decay half-lives are systematically calculated within the multichannel cluster model (MCCM), which turns out to well reproduce the experimental data and show the neutron deformed shell structure. The branching ratios for various daughter states are investigated in the MCCM and in the WKB barrier penetration approach, respectively. It is found that the MCCM results agree well with the experimental data, while the WKB results have relatively large deviations from the experimental data for the α transitions to the high-lying members of the rotational band.

The ternary decay in ²⁵²Cf(sf, fff), with three cluster fragments of different masses (e.g.¹³²Sn,^52-48Ca,^68-72Ni), has been observed by the FOBOS group in JINR. This work has established a new decay mode of heavy nuclei, the collinear cluster tripartition, (CCT). This "true ternary fission" of heavy nuclei has been predicted many times in theoretical works during the last decades. In the present report we discuss true ternary fission (FFF) into three nuclei of almost equal size (e.g. Z=98 → Z_i = 32, 34, 32) and other fission modes in the same system. The possible fission channels for ²⁵² Cf(sf) are predicted from potential-energy (PES) calculations. These PES's show pronounced minima for several ternary fragmentation decays, suggesting a variety of collinear ternary fission modes. The FFF-decays have very similar dynamical features as the previously observed collinear CCT-decays, the central fragment has very small kinetic energy. The data of the cited experiment allow the extraction of the yield for some FFF-decays, by using specific gates on the measured parameters.

We extend the THSR wave function into N≠Z nucleon ⁹Be and perform calculations for its ground state. The negative parity of the ground state is correctly described by the introduction of an extra phase factor. The calculation result of the ground state agrees well with other model. We also calculate the density distribution of the extra neutron. The molecular orbit structure of the extra neutron is found to be reproduced correctly with the THSR wave function without prior assumptions.

An active target system MAIKo (μ-PIC based active target for inverse kinematics.) is under development at RCNP. MAIKo is designed to investigate inelastic scattering at forward angles with a radio isotope (RI) beam. The active target is a promising device to study excited states above particle decay thresholds in unstable nuclei. In the present paper, the detailed design of the detector system is described. The first experiment using an accelerated beam was performed to study the detector performance under high counting rate. Preliminary results of the experiment are also discussed.

We study the energy and radius of neutron rich nuclei toward to the drip-line region. We employ the cluster-orbital shell model approach to calculate the radius of the oxygen isotopes. The result shows that the calculated radius underestimates the observed one at ²³O, though the binding energy and the drip-line of the oxygen isotopes are reproduced. Therefore, we propose a coupled-channel approach to explain the sudden increase of the radius of the oxygen isotopes at ²³O. As a result, the sudden change of the radius can be descried in terms of the competition between the available valence neutron orbits and occupied orbits in the core nucleus. For the ²³O case, we show that the excitation to the 1s_1/2-orbit in the core nucleus is a key configuration to reproduce the radius.

The β decays of neutron-rich Zn isotopes are investigated within the extended quasiparticle random-phase approximation, where neutron-neutron, proton-proton, and neutron-proton pairing correlations are considered in the similar manner. The Brückner G-matrix obtained with the charge-dependent Bonn nucleon-nucleon force is used for the residual particle-particle and particle-hole interactions in addition to the pairing interactions. Contributions from both allowed Gamow-Teller and first-forbidden transitions are considered, and β-decay half-lives together with β-delayed neutron emission probabilities are calculated. The calculated results are found to agree well with the available experimental data.

The rotational bands of α + ¹⁵O(1/2⁻) in ¹⁹Ne are calculated by employing a simple potential model. The α−¹⁵ O interaction potential is constructed from the scattering calculation of its mirror system, α + ¹⁵N. The resonance states are identified by imposing the absorbing boundary condition. The present calculations predict the sequence of the spin-orbit splitting states in the unbound region of ¹⁹Ne, which are generated from the higher spin states in the ²⁰Ne nucleus. The excitation function of the α + ¹⁵O elastic scattering is also predicted, and the appropriate condition to observe the resonances is also discussed.

The ²⁸Si+α cluster structure was studied. We construct the ²⁸Si+α cluster model, where structure change of the ²⁸ Si core and the α-cluster breaking are taken into account. It was found that, in the ²⁸Si+α cluster system having a-cluster at the surface of the ²⁸Si core, the structure change of the ²⁸Si core is energetically rather important while the α-cluster breaking is not significant.

The 3α + n cluster states of ¹³C are discussed on the basis of antisymmetrized molecular dynamics with the constraint on the harmonic oscillator quanta. We predict two different kinds of the cluster states, the hoyle analogue state and the linear-chain state. The former is understood as the 0⁺₂ state (Hoyle state) of ¹²C accompanied by a valence neutron occupying the s-wave. The latter constitute the parity doublet bands of K^π = 1/2^± owing to its parity asymmetric intrinsic structure.

We have investigated projectile breakup effects on ⁶Li + ²⁰⁹Bi elastic scattering near the Coulomb barrier with the four-body and three-body continuum-discretized coupled- channels methods. In the analysis, the elastic scattering is well described by the p + n + ⁴He + ²⁰⁹Bi four-body model. Four-body dynamics of the elastic scattering is precisely investigated and we then found that d (p + n) in ⁶Li may hardly break up during the scattering.

The strength function of the linear response by the external field is calculated in the formalism of the absorbing boundary condition (ABC). The dipole excitation of a schematic two-body system is treated in the present study. The extended completeness relation, which is assumed on the analogy of the formulation in the complex scaling method (CSM), is applied to the calculation of the strength function. The calculation of the strength function is successful in the present formalism and hence, the extended completeness relation seems to work well in the ABC formalism. The contributions from the resonance and the non-resonant continuum is also analyzed according to the decomposition of the energy levels in the extended completeness relation.

We study the total reaction and elastic differential cross sections for proton-nucleus and ⁴He-nucleus reactions in the framework of the Glauber theory which describes multiplescattering processes. The input wave functions are obtained using the Skyrme-Hartree-Fock method and prepared for a wide range of mass numbers, O, Ca, Ni, Sn, and Pb isotopes. The theory reproduces experimental data very well. An effect of the multiple scattering is discussed by comparing with a standard optical-limit approximation. We see that the multiple-scattering effects play a crucial role, especially in enhancing the elastic differential cross sections at large scattering angles.

Excited states in ¹²C nuclei play a very important role in the nucleosynthesis in the universe. ¹²C nuclei are synthesized by the triple α reaction. Normally this process proceeds via the 0⁺₂ state (Hoyle state) at E_x = 7.65 MeV in ¹²C, however, at high temperature T > 10⁹ the highly excited 3α resonant states such as the 3⁻₁ state at E_x = 9.64 MeV and the 2⁺₂ state at E_x = 9.84 MeV play a part of the triple α reaction. Unfortunately, the γ-decay probability of the 3p state has not been determined, therefore we planned to determine the 7- decay probability using the inverse kinematic reaction ¹H(¹²C, ¹²Cp) without measuring γ-rays. The test experiment was carried out at the cyclotron facility in RCNP. The results of the test experiment are reported in the present paper.

An experimental technique for studying elastic scattering using a thick gas target is described, with a measurement of the α(²⁴Ne,α) reaction used as an example. Advantages such as ease, detector efficiency, and the possibility of measuring the cross section at 180° in the centre-of-mass are discussed. It is shown that a resolution of tens of keV is practical at zero degrees, and that the dominant contribution to the resolution for large angles is angular straggling of the beam in the entrance window. The use of helium gas as the target allows direct measurement of a-cluster states.

We review some of the key experimental and theoretical studies of α-clustering in ¹⁸F. Particular attention is given to the 4p-2h nature of such α-clustered states, and the interaction between the holes and clusters is examined in terms of both weak and strongcoupling regimes. The experimental work focuses on α-transfer spectroscopy and α resonant scattering as tools for investigating α-clustering.

In this presentation we summarize our progress in the study of α-clustering in the shell model configuration interaction approach. We put forward Cluster-Nucleon Configuration Interaction Model where the study of clustering is facilitated by the SU(3) symmetry of the cluster channels and by Orthogonality Condition Model. Pioneering methods and results concerning α spectroscopic factors in sd-shell nuclei and in ¹⁶ O treated in p-sd shell are presented. Comparison with experimental data is in favor of the approach.

The isovector proton-neutron pairing in self-conjugate nuclei is treated in a formalism of quartets. Quartets are four-body correlated structures built from two neutrons and two protons coupled to total isospin T = 0. The ground state of the isovector pairing Hamiltonian is described as a product of quartets. We review both the case in which the quartets are constrained to be all identical and the case in which they are allowed to be distinct from one another. The quality of the two approaches is tested by making comparisons with exact shell model calculations for N = Z nuclei with valence nucleons outside the ¹⁶O, ⁴⁰Ca, and ¹⁰⁰ Sn cores. We consider both spherical and axially deformed mean fields. Both approaches are found to be very accurate. In the applications to a deformed mean field, in particular, the formalism with distinct quartets gives rise to results which are basically exact.

We developed a cluster model which allows to take into account both shape deformation parameters and cluster degrees of freedom. The important ingredient of the model is the dinuclear system concept in which the wave function of the nucleus is treated as a superposition of a mononucleus and two-cluster configurations. The model is applied to describe the multiple negative-parity bands in the deformed actinides.

Recently it was pointed out that there are abundant light clusters, such as deuteron, triton and helium, in supernova environment. An interesting question is how much neutrino emissions from these light clusters affect supernova explosion mechanism. To address this question through a supernova simulation, neutrino emissivities from these light clusters are necessary input. The deuteron is the simplest cluster, and occupy a substantial portion of the light cluster abundance. Thus in this work, we study neutrino emissions from electron/positron capture on the deuteron and the nucleon-nucleon fusion processes in the surface region of a supernova core. We evaluate these weak processes using one-nucleon impulse current supplemented by two-nucleon exchange-currents, and nuclear wave functions generated by a high precision nucleon-nucleon potential. We present the neutrino emissivities from the deuteron calculated for typical profiles of core-collapsed supernovae. These novel neutrino emissivities are compared with the standard neutrino emission mechanisms.

We construct a new nuclear equation of state (EOS) for core-collapse supernova (SN) simulations using the variational many-body theory. For uniform nuclear matter, the EOS is constructed with the cluster variational method starting from the realistic nuclear Hamiltonian composed of the Argonne v18 two-body potential and the Urbana IX three-body potential. The masses and radii of neutron stars calculated with the obtained EOS at zero temperature are consistent with recent observational data. For non-uniform nuclear matter, we construct the EOS in the Thomas-Fermi approximation. In this approximation, we assume a functional form of the density distributions of protons, neutrons, and alpha-particles, and minimize the free energy density in a Wigner-Seitz cell with respect to the parameters included in the assumed density distribution functions. The phase diagram of hot nuclear matter at a typical temperature is reasonable as compared with that of the Shen EOS.

We perform numerical experiments to investigate the influence of inelastic neutrino reactions with light clusters in hot nuclear matter on core-collapse supernova simulations. These interactions have been neglected in most hydrodynamical supernova simulations. The neutrino absorptions and inelastic interactions with deuterons, tritons, helions and alpha particles are taken into account in the hydrodynamical simulations in addition to the ordinary charged- current interactions with nucleons. Axial symmetry is assumed but no equatorial symmetry is imposed. The time evolutions of shock waves are calculated with a simple light-bulb approximation for the neutrino transport and a multi-nuclei equation of state. We show that the heating rates of deuterons reach as high as ~ 10% of those of nucleons around the bottom of the gain region. On the other hand, alpha particles heat the matter near the shock wave, which is important when the shock wave expands and density and temperature of matter become low. It is also found that the models with heating by light clusters have different evolutions from those without it in non-linear evolution phase. The matter in the gain region has various densities and temperatures and there appear regions that are locally rich in deuterons and alpha particles. These results indicate that the inelastic reactions of light clusters, especially deuterons, should be incorporated in the simulations of core-collapse supernovae.

We report our recent applications of the correlated Gaussian (CG) method to nuclear four- and five-body systems: (I) Spin-dipole response functions of ⁴He and (II) ¹⁶ O as a ¹²C+n + n + p + p five-body model. The CG is flexible to describe complex few-nucleon dynamics. The above examples actually demonstrate the power of the CG, giving a simultaneous description of both four-nucleon bound and unbound states using a realistic nuclear force, and both shell- and cluster-configurations in the ground and first excited 0⁺ states of ¹⁶O.

An innovative symmetry-guided concept, which capitalizes on partial as well as exact symmetries that underpin the structure of nuclei, is discussed. Within this framework, ab initio applications of the theory to light nuclei reveal the origin of collective modes and the emergence a simple orderly pattern from first principles. This provides a strategy for determining the nature of bound states of nuclei in terms of a relatively small fraction of the complete shell-model space, which, in turn, can be used to explore ultra-large model spaces for a description of alpha-cluster and highly deformed structures together with the associated rotations. We find that by using only a fraction of the model space extended far beyond current no-core shell-model limits and a long-range interaction that respects the symmetries in play, the outcome reproduces characteristic features of the low-lying 0⁺ states in ¹² C (including the elusive Hoyle state and its 2⁺ excitation) and agrees with ab initio results in smaller spaces. This is achieved by selecting those particle configurations and components of the interaction found to be foremost responsible for the primary physics governing clustering phenomena and large spatial deformation in the ground-state and Hoyle-state rotational bands of ¹² C. For these states, we offer a novel perspective emerging out of no-core shell-model considerations, including a discussion of associated nuclear deformation, matter radii, and density distribution. The framework we find is also extensible to negative-parity states (e.g., the 3⁻₁ state in ¹²C) and beyond, namely, to the low-lying 0⁺ states of ⁸Be as well as the ground-state rotational band of Ne, Mg, and Si isotopes. The findings inform key features of the nuclear interaction and point to a new insight into the formation of highly-organized simple patterns in nuclear dynamics.

The Hoyle state and other resonances in the continuum above the 3 α threshold in ¹² C are studied in a microscopic cluster model. Whereas the Hoyle state is a very sharp resonance and can be treated reasonably well in bound state approximation, the other higher lying states require a proper treatment of the continuum. The model space consists of an internal region with 3 α particles on a triangular grid and an external region consisting of the ⁸Be ground state and excited (pseudo)-states of ⁸Be with an additional a. The microscopic R-matrix method is used to match the many-body wave function to the asymptotic Coulomb behavior of bound states, Gamow states and scattering states. ⁸Be-α phase shifts are analyzed and resonance properties like radii and transition strengths are investigated.

Properties of Be isotopes are investigated by using Monte Carlo shell model (MCSM). The structure of ¹⁰Be is studied through the intrinsic density. With this density, the appearance of the α-cluster structure and molecular orbits of low-lying states is discussed. Excitation energies for the 2⁺ states are compared with experiments and other theoretical calculations.

The electric quadrupole transitions between 0⁺, 2⁺, and 4⁺ states in ⁸Be and ¹² C are investigated by discretization of the continuum with a box boundary condition. The γ-emission cross sections and the corresponding transition strengths are computed. The consistency of these transition strengths with the expected behavior for transitions between states in a rotational band is investigated.

We investigate the structures of light nuclei focusing on the role of the tensor force. We describe the tensor and short-range correlations with the tensor optimized shell model (TOSM) and the unitary correlation operator method (UCOM), respectively. In the TOSM, the 2p2h states are fully optimized to describe the large tensor contribution that brings high momentum components explicitly in the wave function. We use a bare nucleon-nucleon interaction AV8' and discuss the structures of the He and Li isotopes, such as the excitation energy spectra and the radii. We also investigate the structures of ⁸Be from the ground-band states to the highly excited states. These states of ⁸Be are indicated to have different structures of the 2α clustering states and the shell-model like states.

The differential cross sections of the ¹⁶O(p,d) reaction populating the ground state and several low-lying excited states in ¹⁵O were measured using 198-, 295- and 392-MeV proton beams at the Research Center for Nuclear Physics (RCNP), Osaka University, to study the effect of the tensor interactions in ¹⁶O. Dividing the cross sections for each excited state by the one for the ground state and comparing the ratios over a wide range of momentum transfer, we found a marked enhancement of the ratio for the positive-parity state(s). The observation is consistent with large components of high-momentum neutrons in the ground-state configurations of ¹⁶O due possibly to the tensor interactions.

The ⁹Be(⁶Li,d)¹³C and ^12,13C(⁶Li,d)^16,17O reactions were measured at the São Paulo Pelletron-Enge-Spectrograph facility at 25.5 MeV incident energy. The nuclear emulsion detection technique was applied. Several narrow resonances were populated up to approximately 17 MeV of excitation energy. An excellent energy resolution was obtained: 40 keV for ¹³C and 15-30 keV for ¹⁶O. The upper limit for the resonance widths were determined. Recently, d-a angular correlations were measured at θ_d = 0° with incident energy of 25 MeV using the LNS Tandem-MAGNEX Spectrometer facility.

We report some recent experimental results on the spectroscopy of ¹³C and ²⁰Ne nuclei by means of low energy nuclear reactions carried out with high resolution electrostatic accelerators. In the case of ¹³C we investigated the possible existence of a-cluster states above the a emission threshold by means of low energy elastic resonant scattering α+⁹Be in direct kinematics. Excitation functions show the presence of various resonances that have been reproduced by R-matrix fit. We studied also the structure of ²⁰Ne by means of the ¹⁹F(p,α₀) reaction at sub-barrier energies. The spectroscopy of ²⁰Ne excited states in the region E_x ≈ 13.5-14.0 MeV can be probed by analyzing experimental angular distributions and excitation functions. This reaction plays an important role also in the CNOF cycle and is an important ingredient to describe hydrogen-induced destruction of fluorine in massive stars. For this reason we investigated the trend of S-factor, that has been compared with results previously reported in the literature.

The generalized two-center cluster model (GTCM), which can treat covalent, ionic and atomic configurations in general systems with two inert cores plus valence nucleons, is formulated on the basis of the microscopic cluster model. In this model, the covalent configurations constructed by the molecular orbital (MO) method and the atomic (or ionic) configuration obtained by the valence bonding (VB) method can be handled in a consistent manner. GTCM is applied to the light neutron-rich system, ¹²Be = α + α + 4N. The energy spectra are characterized in terms of the excitation degrees of freedom, such as the the excitation of two a relative motion and the neutrons' single particle excitation. A large enhancement in a monopole transition from a ground MO state to the excited states is found, which seems to be consistent to a recent observation. The systematics of the 0⁺ states in even Be isotopes over a wide range of the excitation energy is also discussed.

We have developed the complex-scaling method (CSM) by using the complex-range (or oscillating) Gaussian basis functions that are suited for describing highly oscillating few-body wave functions. The eigenvalue distribution of the complex scaled Hamiltonian becomes much more precise and the maximum scaling angle becomes drastically larger than those given by the use of real-range Gaussians. Owing to this advantage, we were able to isolate the S-matrix pole of the new broad 0⁺₃ resonance from the 3α continuum. This confirms the Kurokawa-Kato's prediction (2005) of the new 0⁺₃ resonance, which is considered to correspond to the newly observed 0⁺₃ resonance (E_x = 9.04 MeV, Γ = 1.45 MeV) by Itoh et al. (2013). As a result the long-standing puzzle for the 0⁺ and 2⁺ resonances above the 0⁺ Hoyle state in ¹²C was solved. In this paper, the negative parity resonances with J = 1⁻, 2⁻, 3⁻, 4⁻ and 5⁻ are newly calculated.

Measurements of the ¹²C(⁴He,⁴He)¹²C* reaction at 40 MeV were performed using a charged-particle detector array composed of four double-sided silicon strip detectors. Resonances in ¹² C were reconstructed with the requirement that the a-decay proceeded first via the ⁸ Be ground state. Of primary significance was the population of the 13.3 and 22.4 MeV resonances, the latter, observed for the first time in this measurement. By using the angular correlation technique the spins of the resonances, have been established as J^π 4⁺ and J^π=5⁻ respectively.

The photo-disintegration cross section of ⁹Be is investigated in a framework of the α + α + n three-body cluster model. Much interest is concentrated on the nature of the 1/2⁺ state of ⁹Be located just above the three-body threshold. The existence of this 1/2⁺ resonance is a long-standing problem and has been a topic of quite interest in relation to the breakup mechanism of ⁹Be into the ⁸Be(0+)+n and (α + α + n) channels. The newly measured breakup cross sections of the 1/2+ state of Ref. [1] is inconsistent with the old experimental values [2, 3]. The purpose of this study is to clarify the properties of the 1/2+ state of ⁹Be with the possibility of a genuine three-body (α + α + n) resonance or the two-body (⁸Be(0⁺)+n) virtual state.

New data and preliminary results from an experimental study of the p + ¹¹B reaction are presented. Using proton energies in the range of 167 – 170 keV the 2+ resonance in ¹²C at an excitation energy of 16.11 MeV was populated. Detecting the emitted a-particles in full kinematics allows us to study ¹² C resonances and their properties. In addition to the 3-α break-up of the 16.11 MeV resonance we observe γ-transitions to lower lying resonances. Transitions to the 3⁻ state at 9.64MeV, the 1⁻ state at 10.84 MeV and the 1⁺ state at 12.71 MeV are clearly seen. The transitions to the 1⁻ state has not been observed previously. In addition we see decays to structures of natural parity at excitation energies around 11-13 MeV. The results illustrate that the indirect detection of γ-decays is an effective technique for studying the low lying resonance spectrum of ¹²C.

We have recently developed a microscopic cluster model of nucleus-nucleus bremsstrahlung, which takes implicitly account of a part of the meson-exchange current effects, by applying an extension of the Siegert theorem valid for arbitrary photon energy. This model is applied to the α + α bremsstrahlung. The differences between the bremsstrahlung cross sections obtained in the non-Siegert and Siegert approaches are displayed and discussed. The theoretical bremsstrahlung cross sections are compared with experimental measurements. Whereas the agreement with quite old experimental data is fair, a rather important discrepancy between the theoretical results and the more recent experimental data is noticed. Some paths to investigate this disagreement are proposed.

In this work we report the proton- and deuteron-induced fission of ²⁰⁸Pb at 500A MeV in inverse kinematics. We obtained two observables that allow us to investigate dynamical effects in the fission process: partial fission cross sections and the width of the fission fragment charge distribution as a function of the atomic number of the fissioning system. Results are compared to nuclear reaction model calculations in order to describe the evolution of the system from ground to saddle.

We treat explicitly Δ(1232) isobar degrees of freedom using a bare nucleon-nucleon interaction for few-body systems, where Δ excitations can be the origin of the three-body force via the pion exchange. We adopt the Argonne two-body potential including Δ, named as AV28 potential, and study the role of Δ explicitly in two-body and three-body systems. It was found that the additional Δ states generate strong tensor correlations caused by the transitions between N and Δ states, and change tensor matrix elements largely from the results with only nucleons. We studied the effects of three-body force in the triton and obtained 0.8 MeV attraction due to the intermediate Δ excitation. Due to the lack of the total binding energy for the triton in the delta model, we further studied carefully the effects of the delta excitation in various two body channels and compared with the nucleon only model in the AV14 potential. We modified slightly the AV28 potential in the singlet S channel so that we could reproduce the triton binding energy due to the appropriate amount of the three-body force effects.

We report on the first results of a full three-body calculation of the NN-πYN amplitude for the K⁻d → πΣn reaction, and examine how the Λ(1405) resonance manifests itself in the neutron energy distributions of K⁻d → πΣn reactions. The amplitudes are computed using the NN-πYN coupled-channels Alt-Grassberger-Sandhas (AGS) equations. Two types of models are considered for the two-body meson-baryon interactions: an energy-independent interaction and an energy-dependent one, both derived from the leading order chiral SU(3) Lagrangian. These two models have different off-shell properties that cause correspondingly different behaviors in the three-body system. As a remarkable result of this investigation, it is found that the neutron energy spectrum, reflecting the A(1405) mass distribution and width, depends quite sensitively on the (energy-dependent or energy-independent) model used. Hence accurate measurements of the πΣ mass distribution have the potential to discriminate between possible mechanisms at work in the formation of the Λ(1405).

We have carried out an experiment to produce the neutron-rich hypernucleus ⁶_ΛH by the (π⁻,K⁺) reaction on ⁶Li target at the pion beam momentum of 1.2 GeV/c (J-PARC E10). In order to calibrate the scale of the missing-mass or of the A binding energy of the hypernucleus, we also measured the ¹²C(π⁺,K⁺)¹²_ΛC, p(π⁺K⁺)Σ⁻ and p(π⁺,K +)E+ reactions. The experiment was performed at the K1.8 beam line of J-PARC Hadron Experimental Facility. The overall collected data sample corresponds to an integrated beam intensity of 1.4 × 10¹² pions.

The status of the light hypernuclei is reviewed, and discussed with models based either on the Nijmegen-RIKEN baryon-baryon interaction or on recent studies using chiral effective field theory. The latter suggests a significantly shorter range for the ΛΛ interaction, and this favours the formation of a Borromean state made of two neutrons and two hyperons. Various corrections are discussed, in particular the coupling of NΛ to NΣ, or of ΛΛ to NΞ, and the role of tensor forces. The new nucleus ⁴_ΛΛn = (n,n, Λ, Λ) could be produced in various reactions, in particular deuteron-deuteron scattering with the simultaneous production of two charged kaons, for which an estimate of the cross section is provided.

The J-PARC E15 experiment searches for the simplest kaonic nuclear bound state, K⁻pp, via the ³He(K⁻,n) reaction at the K1.8BR beam-line in the J-PARC hadron experimental facility. We performed the first data-taking in May, 2013, with 5 × 10⁹ incident kaons on the ³He target. The preliminary results are reported focusing on the forward-neutron spectrum, which shows a clear peak structure composed of the quasi-elastic K⁻"n" → K⁻n and the charge-exchange K⁻"p" → ⁰n reactions as expected.

The FINUDA experiment, carried out at the Frascati ϕ-factory DAΦNE, allowed to find the first experimental evidence for the existence of the neutron-rich hypernucleus ⁶_ΛH by measuring in coincidence (π⁺,π⁻) pairs from the K⁻_stop + ⁶Li → ⁶_ΛH + π⁺ production reaction, followed by the ⁶_ΛH → ⁶He + π⁻ mesonic weak decay. The production rate of ⁶_ΛH undergoing such a two-body π⁻ decay turned out to be (2.9 ± 2.0) × 10⁻⁶/K⁻_stop. A binding energy value B_Λ(⁶_ΛH) = (4.0 ± 1.1) MeV was evaluated with respect to the (⁵H + Λ) threshold by combining the information from both production and decay processes. A systematic difference of (0.98 ± 0.74) MeV observed between B_Λ values when derived separately from ⁶_ΛH formation and from its decay was tentatively assigned to the ⁶_ΛH 0⁺_g.s. → 1⁺ excitation.

With use of nuclear emulsion, double-hypernuclei have been studied for aiming to understand Λ-Λ interaction via at-rest-capture of Ξ⁻ hyperon originated by quasi-free (K⁻, K⁺) reactions, where the beam K⁻ momentum was 1.66 GeV/c. Under the process for studying them, elementary feature for not only quasi-free reaction but also production of nuclei with single and double unit(s) of strangeness have been roughly understood, even the statistics were not large. So far we have succeeded to analyze 5 events of double-hypernuclei which introduced binding energies of two A hyperons on several nuclei. However its knowledge is very limited. We have started a new experiment, J-PARC E07, to give us rich information in S = −2 world. An event which may give us a new information about Ξ-nucleus interaction shall be introduced.

The structures of the ground and low-lying states of ²¹_ΛNe and ¹²_ΛBe hypernuclei are studied with the antisymmetrized molecular dynamics. In these hypernuclei, first, the difference of the Λ binding energy on structures is discussed. Particularly, in ¹²_ΛBe, it is found that the parity-inverted ground state of ¹¹Be is reverted by adding a Λ particle. Furthermore, in ²¹_ΛNe, it is discussed that the reduction of nuclear radii is larger in the α + ¹⁶O + Λ band than the ground band and the difference appears as the difference of the B(E2) reduction.

We have investigated an essential cluster "K⁻pp", which is the simplest system of kaonic nuclei, with a coupled-channel Complex Scaling Method (ccCSM). Combining the ccCSM with Feshbach method we can handle a coupled-channel problem effectively as a singlechannel problem. As a result of a study of the K⁻pp with the ccCSM+Feshbach method using an energy-dependent chiral-theory based potential, it is found that the K⁻pp is shallowly bound with the binding energy of around 20-35 MeV. The mesonic decay width is rather dependent on the interaction parameters and ansatz; the half decay width is ranging from 20 to 65 MeV.

The heavy quark baryon spectroscopy is a key way to understand what the building block of hadrons is. The diquark correlation which is expectedly an essential degree of freedom to describe the hadron structure can be investigated from the spectroscopy of charmed baryons. An experiment to observe and investigate the charmed baryons was proposed at the J-PARC high- momentum beam line. The missing mass spectroscopy experiment via the π⁻p → Y^*+_cD^*− reaction at 20 GeV/c will be performed for the systematic measurement of the excitation energy, the production rates and the decay products of charmed baryons. In addition, the properties of the strange baryons can also be measured systematically by using the same experimental setup. From the systematic study of both charmed baryons and hyperons, the diquark correlation can be revealed which is expectedly an essential degree of freedom to describe the hadron structure.

Heavy-ion collisions in the incident energy region from several ten to several hundred MeV/nucleon are closely related to the properties of nuclear matter under various conditions of the density, the temperature and the neutron-proton asymmetry. The emission of a large number of clusters in collisions implies strong cluster correlations in nuclear matter that is expanding and breaking up into many fragments. The antisymmetrized molecular dynamics approach has been extended in order to describe the cluster emissions properly. Calculations show that the formation of α clusters affects strongly the observables, such as the ³H/³He spectrum ratio, that are usually considered as probes of the density dependence of nuclear symmetry energy.

We pick up two studies on the nuclear responses from the recent experiments of high-resolution proton inelastic scattering at the Research Center for Nuclear Physics, Osaka University; 1) study of the nuclear symmetry and the neutron skin thickness by the measurement of energy electric dipole (El) response of ²⁰⁸Pb, and 2) study of the tensor correlation in the ground state by the measurement of the spin-Ml responses of even-even self-conjugate nuclei in the sd-shell nuclei.

Cluster correlations are an important feature in strongly interacting matter at subsaturation densities. They modify the chemical composition of the system and the thermodynamic properties, which are encoded in the equation of state. The formation and dissolution of clusters can be described in a generalized relativistic density functional approach. Clusters are included as explicit degrees of freedom with medium-dependent properties. They are considered as quasiparticles with scalar and vector self-energies that represent the effective in-medium interaction. Essential ingredients in the self-energies are rearrangement contributions, which guarantee the thermodynamic consistency of the model, and mass shifts of composite particles, which take into account the effects of the Pauli exclusion principle. They cause the dissolution of clusters at high densities. The occurence of α-particle clusters on the surface of heavy nuclei can be considered by adapting the generalized relativistic density functional approach to nuclear structure calculations. A systematic variation of the α-particle abundance and neutron skin thickness with the neutron excess of the nucleus and the strength of the isovector contribution to the effective interaction is observed. The surface a clustering affects the correlation of the neutron skin thickness of heavy nuclei with the density dependence of the symmetry energy, which is relevant for calculations of neutron star structure.

This paper discusses the characterization of the cluster nature of resonances in ¹²C+¹²C and ¹²C+¹⁶O by measuring their γ decay. Results from resonant radiative capture measurements in these systems are presented. Spin attributions as well as specificities of the decay pattern are described. For the ¹²C+¹²C system, identification of γ transitions within the molecular band are discussed as well as a new method to measure the eventual persistence of the resonant behaviour down to astrophysical energies.

Clustering in nuclei is traditionally explored through reaction studies but observation of electromagnetic transitions can be of high value in establishing, for example, that highly-excited states with candidate cluster structure do indeed form rotational sequences. A topical example is given of the identification of a candidate super deformed band in ²⁸Si where super deformation in this nucleus has been described as originating from ²⁴Mg+α clustering.

Resonances observed in the ¹²C + ¹²C collisions are studied with a molecular model. At high spins J = 12–16, a stable dinuclear configuration is found to be an equator- equator touching one as is obtained in the ²⁸Si + ²⁸Si system. With K-quantum number being specified as rotation-vibration model, normal modes have been solved around the equilibrium, firstly. Furthermore, Coriolis coupling has been investigated by diagonalization among low- lying normal-mode states with K = 0 and K-excitation. It is found that the Coriolis coupling introduces about 30% of K-mixing into the K = 0 molecular ground states of J = 12–16. The analyses of the angular momentum coupling show up a dominance of the lowest L in the inelastic channel of the molecular ground state newly obtained. Thus alignments appear strongly in the inelastic channel, which is in agreement with the explanation by the band crossing model. Discussion is given on "why disalignments appear in the ²⁸Si + ²⁸Si system, in contrast to the above results".

This text summarizes the talks presented at the 3rd International Workshop on State of the Art in Nuclear Cluster Physics (SOTANCP3) held in Yokohama (Japan) from 26 to 30 May 2014. Some personal opinions are also expressed on two much debated topics: the ¹²C spectrum in the continuum and conflicting interpretations of cluster wave functions.