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We study the symmetric nuclear matter using bare nucleon-nucleon ($NN$) interactions with finite particle-number approach within finite cubic boxes. Due to the $NN$ correlations originating from bare $NN$ interaction, two nucleons can be excited to the high-momentum region, leading to the increase of the kinetic energy in nuclear matter. We further consider the spin excitations in the nucleon pairs, where the spin of the two nucleons are changed, and this excitation is important for the tensor correlation. The unitary correlation operator method (UCOM) is used to treat the short-range correlation. The tail correction coming from the neighbouring boxes is also included. We demonstrate the contributions of various excitations of nucleon pairs as well as the tail correction to the total energy at the normal density. We also discuss the effects of UCOM and correlated nucleon pairs on the density dependence of the total energy. We calculate the equations of state of symmetric nuclear matter using two kinds of the Argonne potentials and the results agree with those from other many-body theories. The density dependences of the Hamiltonian components are also shown., Comment: 12 pages, 11figures, 1 table

We propose a new many-body method based on the correlation functions, in which the multiple products of the correlation functions are expanded into the many-body diagrams using the cluster expansion method and every diagram is independently optimized in the total-energy variation. We apply this idea to the tensor-optimized antisymmetrized molecular dynamics (TOAMD) using the bare nucleon-nucleon interaction and show the results of the $s$-shell nuclei within the triple products of the correlation functions of tensor and central-types. We evaluate the effect of the independent optimization of the many-body diagrams on the solutions. It is found that the triple products provides the sizable effect in the present scheme, which results in the good reproduction of the total energy and the Hamiltonian components of nuclei with respect to the few-body calculations., 12 pages, 13 figures

We study many-body resonances in the neuron-rich $^{8}\mathrm{He}$ and the mirror proton-rich $^{8}\mathrm{C}$ using the $^{4}\mathrm{He}+N+N+N+N$ five-body model with the isospin $T=2$ system. Resonances are described with the complex energy eigenvalues as the Gamow states using the complex scaling method. In $^{8}\mathrm{He}$, we obtain five states in which four states are resonances, and in $^{8}\mathrm{C}$ all five states are resonances. We discuss the isospin-symmetry breaking dynamically induced by the Coulomb interaction in the energy spectra and decay widths of the resonances in two mirror nuclei. We predict the resonance energies and decay widths for the future experiments. We also investigate the configurations of valence nucleons above $^{4}\mathrm{He}$ in two nuclei with the $jj$ coupling scheme, and all the states dominantly have the $p$-shell configurations. From the configuration mixing, $^{8}\mathrm{He}$ and $^{8}\mathrm{C}$ give the similar results, which indicates the good symmetry in two nuclei.

We extend high-momentum antisymmetrized molecular dynamics (HMAMD) by incorporating the short-range part of the unitary correlation operator method (UCOM) as the variational method of finite nuclei. In this HMAMD+UCOM calculation of light nuclei, HMAMD is mainly in charge of the tensor correlation with up to four-body correlation, while the short-range correlation is further improved by using UCOM. The binding energies of the $^3$H and $^4$He nuclei are calculated with HMAMD+UCOM using the AV8$'$ bare nucleon–nucleon ($NN$) interaction. The different roles of the short-range and tensor correlations from HMAMD and UCOM are analyzed in the numerical results. Compared with previous calculations based on different variational methods, this newly extended HMAMD+UCOM method can almost provide consistent results with ab initio results.

We study $^5$He variationally as the first $p$-shell nucleus in the tensor-optimized antisymmetrized molecular dynamics (TOAMD) using the bare nucleon--nucleon interaction without any renormalization. In TOAMD, the central and tensor correlation operators promote the AMD's Gaussian wave function to a sophisticated many-body state including the short-range and tensor correlations with high-momentum nucleon pairs. We develop a successive approach by applying these operators successively with up to double correlation operators to get converging results. We obtain satisfactory results for $^5$He, not only for the ground state but also for the excited state, and discuss explicitly the correlated Hamiltonian components in each state. We also show the importance of the independent optimization of the correlation functions in the variation of the total energy beyond the condition assuming common correlation forms used in the Jastrow approach., 14 pages, 6 figures, published in Progress of Theoretical and Experimental Physics

We investigate the evolution of clustering structure through the momentum distributions in the $^{8\text{--}10}\mathrm{Be}$ isotopes. The nucleon dynamics within the intercluster antisymmetrization are discussed via the momentum distribution of a Brink type $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}$ wave function. For the state with a small $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}$ distance, we observe a significant depression with a dip structure at zero momentum and an enhanced tail in a relatively higher momentum region. In addition, we find the ``cluster structure'' in the intrinsic frame of momentum space, which is complementary to its significant $\ensuremath{\alpha}$-cluster dissolution in the coordinate space because of the strong antisymmetrization. For the physical $^{8\text{--}10}\mathrm{Be}$ isotopes, the Tohsaki-Horiuchi-Schuck-R\"opke (THSR) wave functions are adopted. The evolution from the dilute clustering state to the compact one is demonstrated by a successive depression at zero momentum of nucleon distribution for the two $\ensuremath{\alpha}$ clusters within $^{8\text{--}10}\mathrm{Be}$ isotopes. For the compact $^{10}\mathrm{Be}$ nucleus, the momentum distribution of all nucleons shows significant depression at zero momentum with a dip structure, which is found to be contributed by both the intercluster antisymmetrization and the $p$-orbit occupation of the valence neutrons. This study proposes a new window for the investigations of the $\ensuremath{\alpha}$-clustering effects via the low-momentum components of nuclei, which is expected to be extended to the heavier nuclear clustering states.

In this article, we review our study of the K− pp, which is a prototype system of kaonic nuclei, with a fully coupled-channel complex scaling method (Full ccCSM). In the present study, i) the K−pp is treated as a resonant state of a K¯NN-πΣN-πΛN coupled-channel system, ii) a chiral SU(3)-based potential as well as a phenomenological potential is examined as a K¯N-πY potential, and iii) property of the K− pp is investigated by analyzing the wave function obtained with the Full ccCSM calculation. It is noted that the energy dependence involved in a chiral SU(3)-based potential is taken into account by considering the self-consistency for the meson-baryon energy. As a result, we have successfully found a resonant pole corresponding to the K− pp on the complex energy plane, and compared it with the latest experimental result reported by J-PARC E15 group. Furthermore, we have considered an energy-fixed case of a chiral SU(3) potential and also the effect of kinematics of mesons by examining the semi-relativistic calculation.

High-momentum components of nuclei are essential for understanding the underlying inter-nucleon correlations in nuclei. We perform the comprehensive analysis for the origin of the high-momentum components of $^4$He in the framework of Tensor-optimized High-momentum Antisymmetrized Molecular Dynamics (TO-HMAMD), which is a completely variational approach as an $ab$ $initio$ theory starting from the bare nucleon-nucleon ($NN$) interaction. The analytical derivations are provided for the nucleon momentum distribution of the Antisymmetrized Momentum Dynamics (AMD) wave functions, with subtraction of center-of-mass motion. The nucleon momentum distribution for $^4$He is calculated by applying a new expansion technique to our $ab$ $initio$ wave function, and agrees with the values extracted from experimental data up to the high-momentum region. Fine-grained analysis is performed for the high-momentum components in $^4$He with respect to different nucleon correlations. Contributions from tensor, central with short-range, and many-body correlations are extracted from the nucleon momentum distributions. The manifestation of tensor correlation around 2 fm$^{-1}$ region is explicitly confirmed by comparing the momentum distributions predicted using different types of $NN$ interactions with and without the tensor force., 7 pages, 6 figures, under review in Phys. Lett. B

The decomposition of scattering phase shifts in single-channel systems is extended to coupled-channels systems in the complex scaling method. The present method describes the contribution of the resonant states to the phase shift separately from the background in each channel phase shift of the coupled-channels system. We apply this method to the ($^{3}\mathrm{H}+p)+(^{3}\mathrm{He}+n)$ model for $^{4}\mathrm{He}$, and show that the decomposition of phase shifts in coupled-channels systems provides useful information about the structure of scattering states.

The tensor-optimized Fermi sphere (TOFS) theory is applied first for the study of the property of nuclear matter using the Argonne V4$^\prime$$NN$ potential. In the TOFS theory, the correlated nuclear matter wave function is taken to be a power-series type of the correlation function $F$, where $F$ can induce central, spin–isospin, tensor, etc. correlations. This expression has been ensured by a linked cluster expansion theorem established in the TOFS theory. We take into account the contributions from all the many-body terms arising from the product of the nuclear matter Hamiltonian $\mathcal{H}$ and $F$. The correlation function is optimally determined in the variation of the total energy of nuclear matter. It is found that the density dependence of the energy per particle in nuclear matter is reasonably reproduced up to the nuclear matter density $\rho \simeq 0.20$ fm$^{-3}$ in the present numerical calculation, in comparison with other methods such as the Brueckner–Hartree–Fock approach.

The high-momentum antisymmetrized molecular dynamics (HMAMD) is a new promising framework with significant analytical simplicity and efficiency inherited from its antisymmetrized molecular dynamics in describing the high momentum correlations in various nuclear states. In the aim of further improving the numerical efficiency for the description of nucleon-nucleon correlation, we introduce a new formulation by including a new Gaussian weighted basis of high momentum pairs in the HMAMD wave function, with which very rapid convergence is obtained in numerical calculation. It is surprising that the very high-momentum components in the new HMAMD basis are found to be almost equivalent to the contact representation of the nucleon-nucleon pairs with very small nucleon-nucleon distance. The explicit formulation for the contact term significantly improves the numerical efficiency of the HMAMD method, which shows the importance of the contact correlation in the formulation of light nuclei.

Nuclear systems with antikaons, so-called kaonic nuclei, have been a longstanding issue in strange nuclear physics and hadron physics, because they might have exotic nature; In particular, they could be a doorway to the dense matter due to the strong attraction between antikaon and nucleon. Among kaonic nuclei, the three-body system composed of two protons and a single K− meson, K− pp, is the most essential. In this article, we will report on the recent situation of K− pp studies in both theoretical and experimental sides. Afterwards, we will explain our latest study of the K− pp with a fully coupled-channel complex scaling method (Full ccCSM) using a chiral SU(3)-based KN(-πY) potential. In Full ccCSM, the K− pp is completely treated as a resonant state of a KNN-πΣN-πΛN coupled-channel system. The energy dependence involved in the chiral potential is handled with a self-consistent calculation in which two extreme ansatzes are examined: field picture and particle picture. With our chiral SU(3)-based potential constrained by the precise data of kaonic hydrogen atom (SIDDHARTA experiment), the K− pp resonance is obtained as a shallowly bound state measured from the KNN threshold with a narrow width, if the field picture is employed in the calculation: the binding energy is 14 – 28 MeV and the half value of the mesonic decay width is 8 – 15 MeV. On the other hand, if the particle picture is employed, it is found that the binding energy could be as large as about 50 MeV, even though such a chiral potential is used. Based on these results of Full ccCSM calculation, we have discussed on the possibility for kaonic nuclei to form a dense matter and on the latest experimental result reported by J-PARC E15 collaboration.

We propose a new variational method for describing nuclear matter from nucleon-nucleon interaction. We use the unitary correlation operator method (UCOM) for central correlation to treat the short-range repulsion and further include the two-particle two-hole (2p2h) excitations of nucleon pair involving a large relative momentum, which is called 'high-momentum pair'(HM). We describe nuclear matter in finite size with finite particle number on periodic boundary condition and increase the 2p2h configurations until we get the convergence of the total energy per particle. We demonstrate the validity of this 'UCOM+HM' framework by applying it to the symmetric nuclear and neutron matters with the Argonne V4$^\prime$ potential having short-range repulsion. The nuclear equations of state obtained in UCOM+HM are fairly consistent to those of other calculations such as Brueckner-Hartree-Fock and auxiliary field diffusion Monte Carlo in the overall density region., Comment: 12 pages, 24 figures

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 complex scaling method (CSM) is one of the most powerful methods of describing the resonances with complex energy eigenstates, based on non-Hermitian quantum mechanics. We present the basic application of CSM to the properties of the unbound phenomena of light nuclei. In particular, we focus on many-body resonant and non-resonant continuum states observed in unstable nuclei. We also investigate the continuum level density (CLD) in the scattering problem in terms of the Green's function with CSM. We discuss the explicit effects of resonant and non-resonant contributions in CLD and transition strength functions., 38 pages, 33 figures, to be published in Progress of Theoretical and Experimental Physics

By using bare Argonne V4' (AV4'), V6' (AV6'), and V8' (AV8') nucleon-nucleon (NN) interactions respectively, the nuclear equations of state (EOSs) for neutron matter are calculated with the unitary correlation operator and high-momentum pair methods. The neutron matter is described under a finite particle number approach with magic number $N=66$ under a periodic boundary condition. The central short-range correlation coming from the short-range repulsion in the NN interaction is treated by the unitary correlation operator method (UCOM) and the tensor correlation and spin-orbit effects are described by the two-particle two-hole (2p2h) excitations of nucleon pairs, in which the two nucleons with a large relative momentum are regarded as a high-momentum pair (HM). With the 2p2h configurations increasing, the total energy per particle of neutron matter is well converged under this UCOM+HM framework. By comparing the results calculated with AV4', AV6', and AV8' NN interactions, the effects of the short-range correlation, the tensor correlation, and the spin-orbit coupling on the density dependence of the total energy per particle of neutron matter are demonstrated. Moreover, the contribution of each Hamiltonian component to the total energy per particle is discussed. The EOSs of neutron matter calculated within the present UCOM+HM framework agree with the calculations of six different microscopic many-body theories, especially in agreement with the auxiliary field diffusion Monte Carlo calculations., Comment: 13 pages, 6 figures, 3 tables

PROCEEDINGS OF THE 4TH INTERNATIONAL WORKSHOP ON “STATE OF THE ART IN NUCLEAR CLUSTER PHYSICS” (SOTANCP4) 13–18 May 2018 Texas, USA, A virtual state plays an important role in reaction cross sections just above the breakup threshold energy, such as producing the peak behaviour. However, the virtual state cannot be directly obtained as an isolated pole solution in the complex scaling method (CSM) because of a limit of the scaling angle in the CSM. Recently, we proposed a useful approach to find the pole position of the virtual state using the continuum level density (CLD), the scattering phase shift, and scattering length calculated in the CSM [4]. On the basis of the proposed method, we investigate the photo-disintegration cross sections of resonance and virtual states above the threshold energy to see their differences.

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...

We propose a new variational method for treating short-range repulsion of bare nuclear force for nuclei in antisymmetrized molecular dynamics (AMD). In AMD, the short-range correlation is described in terms of large imaginary centroids of Gaussian wave packets of nucleon pairs in opposite signs, causing high-momentum components in nucleon pair. We superpose these AMD basis states and name this method "high-momentum AMD" (HM-AMD), which is capable of describing strong tensor correlation (Prog. Theor. Exp. Phys. (2017) 111D01). In this paper, we extend HM-AMD by including up to two kinds of nucleon pairs in each AMD basis state utilizing the cluster expansion, which produces many-body correlations involving high-momentum components. We investigate how much HM-AMD describes the short-range correlation by showing the results for $^3$H using the Argonne V4$^\prime$ central potential. It is found that HM-AMD reproduces the results of few-body calculations and also the tensor-optimized AMD. This means that HM-AMD is a powerful approach to describe the short-range correlation in nuclei. In HM-AMD, momentum directions of nucleon pairs isotropically contribute to the short-range correlation, which is different from the tensor correlation., 11 pages, 7 figures

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

In association with the property of the $1/{2}^{+}$ state observed just above the $^{8}\mathrm{Be}({0}^{+})+n$ threshold energy in $^{9}\mathrm{Be}$, we investigate the photodisintegration cross section of an $s$ state in a simple schematic two-body model using the complex scaling method. The photodisintegration cross section, continuum level density, scattering phase shifts, and scattering length are discussed in relation with the virtual state. These scattering observables show strong divergences when a virtual state is located near the physical scattering region.

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

The excited hyperon Λ ( 1405 ) is the important building block for kaonic nuclei which are a nuclear many-body system with anti-kaons. We have been investigating the Λ ( 1405 ) resonance with the coupled-channel Complex Scaling Method (ccCSM) in which the Λ ( 1405 ) is treated as a hadron-molecular state of a K ¯ N – πΣ coupled system. We use a K ¯ N (– πY ) potential based on the chiral SU(3) theory. In this article, we report the double-pole nature of the Λ ( 1405 ) , which is a characteristic property predicted by many studies with chiral SU(3)-based models. With the help of the complex-range Gaussian basis in ccCSM, we have found successfully another pole besides a pole near the K ¯ N threshold (called higher pole) which was found in our previous work with the real-range Gaussian basis. The new pole (called lower pole) is found far below K ¯ N threshold: ( M , − Γ / 2 ) = ( 1395 , − 138 ) MeV when f π = 110 MeV . In spite of so broad width of the lower-pole state, the state is clearly identified with good separation from continuum states, since the oscillatory behavior of the continuum states is improved owing to the complex-range Gaussian basis. Analyzing the ccCSM wave function of the lower pole, we have revealed explicitly that the lower-pole state is dominated by the πΣ component rather than the K ¯ N component. We have confirmed that the ccCSM wave function is correctly connected to the asymptotic form of the resonance wave function. Estimating the meson–baryon mean distance for the lower-pole state which involves a large decay width, the obtained value has a large imaginary part comparable to a real part. Therefore, the mean-distance of the lower-pole state is difficult to be interpreted intuitively. Such a nature of the lower pole is different from that of the higher pole. In addition, we have investigated the origin of the appearance of the lower pole. The lower pole is confirmed to be generated by the energy dependence attributed to the chiral dynamics, by comparing the result of an energy-independent potential.

The s-wave photodisintegration cross sections observed just above the neutron breakup threshold energy are calculated for resonant and virtual states by using a complex-scaled two-body model, which simulates the 9Be nucleus with a 8Be+ns-wave channel. We investigate the differences between behaviors of the resonance and virtual states in the photodisintegration cross sections near threshold energy in detail. It is shown that, in the present two-body model, resonant states very near the threshold energy produce a peak structure in the photodisintegration cross section that is similar that of the virtual state.

We have measured the 16O(p, d) reaction using 198-, 295- and 392-MeV proton beams to search for a direct evidence on an effect of the tensor interactions in light nucleus. Differential cross sections of the one-neutron transfer reaction populating the ground states and several low-lying excited states in 15O were measured. Comparing the ratios of the cross sections for each excited state to the one for the ground state 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 initial ground-state configurations due to the tensor interactions.

We have applied the coupled-channel complex scaling method (ccCSM) to K ¯ N – π Y system. One advantage of ccCSM is that resonant states as well as scattering states can be treated in the same framework. For the interactions in the system, we have constructed a meson–baryon potential-matrix by basing on the chiral SU(3) theory and respecting the K ¯ N scattering length obtained in the Martinʼs analysis. For future purpose to apply it more complicated system such as K ¯ N N , we adopt a local Gaussian form in the r-space. We have investigated both the non-relativistic (NR) and the semi-relativistic (SR) kinematics. In the SR case, two types of the potentials are obtained. To test the constructed potentials, we have calculated scattering amplitudes and searched resonances. One resonance pole, corresponding to Λ ( 1405 ) , is found in isospin I = 0 system around ( 1419 , − 20 ) MeV ( ( 1425 , − 25 ) or ( 1419 , − 13 ) MeV ) on complex-energy plane with the NR (SR) kinematics. Mean distance between meson and baryon in the resonant state is 1.3 − i 0.3 fm ( 1.2 − i 0.5 fm ) for NR (SR), in which the states are treated as Gamow states. In addition, we have observed a signature of another pole in lower-energy region involving large decay width, although they are unstable against the change of scaling angle θ. This may correspond to the lower pole of the double-pole of Λ ( 1405 ) discussed in literature today.

The photodisintegration of $^{9}\mathrm{Be}$ in the energy region lower than ${E}_{\ensuremath{\gamma}}=16$ MeV is investigated by using the $\ensuremath{\alpha} + \ensuremath{\alpha} + n$ three-body model and the complex scaling method. The cross section exhibits two aspects in two different energy regions. In the low-energy region up to ${E}_{\ensuremath{\gamma}}=6$ MeV, the cross section is explained by the transition strengths into the excited resonant states of $^{9}\mathrm{Be}$, while the dipole transition into the nonresonant continuum states of $^{8}\mathrm{Be}({2}^{+}) + n$ dominates the cross section in the energy region of $6\ensuremath{\le}{E}_{\ensuremath{\gamma}}\ensuremath{\le}16$ MeV. Furthermore, it is shown that the dipole strength at ${E}_{\ensuremath{\gamma}}\ensuremath{\sim}8$ MeV is understood to be caused by the single-neutron excitation from the $^{8}\mathrm{Be}({2}^{+})\ensuremath{\bigotimes} \ensuremath{\nu}{p}_{3/2}$ configuration in the ground state.

In strange nuclear physics and hadron physics, kaonic nuclei (nuclear system with anti-kaons (K)) have been a hot topic since the formation of dense state are interestingly expected due to the strong KN attraction. To reveal the nature of kaonic nuclei, which could be an exotic system, lots of efforts have been devoted to the study of a prototype system of kaonic nuclei, “Kpp”. Especially, now is the very exciting time because new experimental results are being reported from two groups of J-PARC (E15 and E27). We are theoretically investigating the Kpp with a coupled-channel Complex Scaling Method (ccCSM) which was proposed in our previous work [1]. This method can treat simultaneously coupled-channel problem and resonance problem which are important ingredients in the study of Kpp. Recently, we have developed a handy method, so-called ccCSM+Feshbach method. The Kpp is actually a coupled-channel system of KNN-πΣ N-πΛ N. However, we can treat it as a single-channel problem of KNN by a tricky use of ccCSM. As a result of careful calculation with the ccCSM+Feshbach method using an energy-dependent potential based on chiral SU(3) theory [1], we find that the Kpp is not so deeply bound with ~30 MeV binding. The decay width depends on a parameter and ansatz for the treatment of energy dependence; 20~60 MeV. Analyzing the ccCSM wave function, we find that the mean distance of two nucleons in the Kpp is found to be ~2.2 fm which is almost equal to the NN distance in normal nuclear matter. (In the figure, a result obtained with non-relativistic kinematics is shown.) In the talk, we will report further results obtained with other versions of KN potential and those in the semi-relativistic kinematics. We hope to discuss on comparison of our result and the J-PARC experimental results.

We study the character of the first excited $1/{2}^{+}$ state of $^{9}\mathrm{Be}$, which is observed as a low-lying sharp peak in the cross section of $^{9}\mathrm{Be}(\ensuremath{\gamma},n)2^{4}\mathrm{He}$ just above the $^{8}\mathrm{Be}+n$ threshold. Using the $\ensuremath{\alpha}+\ensuremath{\alpha}+n$ three-body model, we describe the ground and excited unbound states of $^{9}\mathrm{Be}$ above the $\ensuremath{\alpha}+\ensuremath{\alpha}+n$ threshold. Applying the complex scaling method to the three-body model, we find no $1/{2}^{+}$ resonant solutions with the scaling angle of $\ensuremath{\theta}\ensuremath{\le}{15}^{\ensuremath{\circ}}$, while the low-lying peak in the photodisintegration cross section is reproduced in the present calculation. It is found that the $^{8}\mathrm{Be}+n$ continuum states dominate the low-lying peak in the cross section. Furthermore, using the analytical continuation of the coupling constant of the three-body interaction for the $\ensuremath{\alpha}+\ensuremath{\alpha}+n$ system, we discuss the virtual-state character of the $1/{2}^{+}$ state.

We study the resonance spectroscopy of the He isotopes and their mirror nuclei with an α + N + N + N + N cluster model. Many-body Gamow states are treated with the correct boundary condition using the complex scaling method. The spectrum agrees with the experiment systematically for energies and decay widths and we predict several resonances. We discuss the mirror symmetry breaking of He isotopes and their mirror nuclei for the configurations and the radii.

The structure of neutron-rich $\Lambda$ hypernucleus, $^7_{\Lambda}$He is studied within the framework of an $\alpha +\Lambda +n+n$ four-body cluster model. We predict second $3/2^+$ and $5/2^+$ states, corresponding to a $0s$ $\Lambda$ coupled to the second $2^+$ state of $^6$He, as narrow resonant states with widths $\Gamma \sim 1$ MeV to be at 0.03 MeV and 0.07 MeV respect to the $\alpha +\Lambda +n+n$ threshold. From an estimation of the differential cross section for the $^7{\rm Li} (\gamma,K^+) ^7_{\Lambda}$He reaction, there is a possibility to observe these state at JLab in the future. We also calculate the second $2^+$ state of $^6$He as resonant state within the framework of an $\alpha +n+n$ three-body cluster model. Our result is $2.81$ MeV with $\Gamma =$4.63 MeV with respect to the $\alpha +n+n$ threshold. This energy position is $\sim 1$ MeV higher, and with a much broader decay width, than the recent SPIRAL data. It is suggested that an experiment at JLab to search for the second $3/2^+$ and $5/2^+$ states of $^7_{\Lambda}$He would provide an opportunity to confirm the second $2^+$ state of the core nucleus $^6$He.

We have investigated a prototype of kaonic nuclei, "$K^-pp$", with a coupled-channel Complex Scaling Method (ccCSM). Combining the ccCSM with Feshbach projection method, we can handle a coupled-channel problem effectively as a single-channel problem. By using an energy-dependent chiral SU(3)-based $\bar{K}N$ potential, the $K^-pp$ ($J^\pi=0^-$ and $T=1/2$) is obtained to be shallowly bound with the binding energy of 20-30 MeV. The mesonic decay width depends on the interaction parameters and ansatz; the decay width is ranging from 20 to 65 MeV. In case of $J^\pi=1^-$ state, no three-body $\bar{K}NN$ resonant states are found., Comment: 6 pages, 3 figures, Proceedings of "International Conference on Exotic Atoms and Related Topics (EXA2014)", Vienna, Austria, Sept. 15-19, 2014, to be published in Hyperfine Interactions

We investigate the tensor correlation in He isotopes. We extend the model space of 4 He with the shell model approach to incorporate the tensor correlation, and π meson-like 0 - particle-hole correlation is favoured. Based on the 'tensor-correlated 4 He+n(+n)' model, it is found that the tensor correlation affects the LS splitting in 5 He and the 0 + 2 state of 6 He due to the strong Pauli blocking for the p 1/2 orbit of neutrons. We also obtain a reliable 4 He-n interaction including the tensor correlation, which improves the behaviour of the d- and f-wave phase shifts in the 4 He+n system.