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We provide a global density-dependent $^4$He-nucleon (DD-$\alpha N$) interaction to construct the $\alpha$-nucleus optical model potential (OMP) in a wide range of incident energies. The global parametrization for the DD-$\alpha N$ interaction is obtained based on the proton-$^4$He OMP which reproduces the elastic scattering cross-section data very well in the incident energies of 12.04--500 MeV per nucleon. We derive the $\alpha$-nucleus potential by a folding procedure with the point-nucleon density obtained by a microscopic mean-field model using the present DD-$\alpha N$ interaction. The density dependence of the DD-$\alpha N$ interaction is fixed phenomenologically to reproduce the $\alpha$-nucleus elastic scattering cross-section data by the $^{16}$O, $^{40}$Ca, $^{58}$Ni, $^{90}$Zr, and $^{208}$Pb targets at $E/A =$ 10--342.5 MeV. We also show the total reaction cross sections, which are helpful in fixing one free parameter, the renormalization factor for the imaginary part of the $\alpha$-nucleus potential. Lastly, we show some examples, which clearly demonstrate the validity and power of the present DD-$\alpha N$ approach., Comment: 20 pages, 11 figures

We systematically investigate the relation between the nuclear structure and reaction in the $^{10}$Be nucleus using a theoretical framework. The structure of the $^{10}$Be nucleus is constructed with a cluster model based on a microscopic viewpoint. In this paper, the $^{10}$Be nucleus with different structures is prepared by manipulating the parameters of an effective nucleon-nucleon interaction. The nuclear structure and expectation values of physical quantities are drastically changed by the modification. We summarize such changes and show the effects on the elastic and inelastic scatterings for the proton and $^{12}$C targets in the microscopic coupled-channel calculation. Especially, we recently reported the visualization of dineutron correlation in $^{10}$Be on proton inelastic scattering in [Phys. Rev. C104, 034613 (2021)]. In this preceding work, we found that the changing the degree of dineutron correlation in $^{10}$Be leads to drastic changes of the inelastic cross section for the 2$_2^+$ state. The development (or breaking) of the dineutron correlation is governed by the strength of the spin-orbit interaction of the structure calculation. However, in the previous work, some of the realistic physical points were missing, for example, the binding energy. Therefore, we reconstruct the $^{10}$Be nucleus by adjusting the effective nucleon-nucleon interaction to obtain the reasonable binding energy of the ground state. With this improvement, we again discuss the dineutron correlation in the $^{10}$Be nucleus. We reconfirm the way to measure the degree of the development (or breaking) of dineutron cluster structure; the sensitivity to the inelastic cross section of the ground state to the 2$_2^+$ state of $^{10}$Be., Comment: 33 pages, 16 figures, 5 tables. arXiv admin note: text overlap with arXiv:2105.03025

Complex transition density can be constructed by a nuclear structure model with a complex basis and/or complex coefficient. In general, the complex transition density is converted to the real one with phase factor. In this study, we apply the complex transition density directly to the microscopic reaction model. We compare with scattering cross sections calculated with the real and complex transition densities in the frameworks of the optical model, the distorted wave Born approximation, and the coupled-channel (CC) calculation, respectively. In addition, we investigate the dependence of the phase factor for the transition density in the elastic and inelastic cross sections. The effect of the phase factor on the elastic and inelastic cross sections can be seen in the CC calculation. Finally, we found an important role of the phase factor in the nuclear elastic and inelastic scatterings., Comment: I found a mistake. The sign of the phase depends on the direction of the transition. However, the calculation and formulation in this manuscript do not incorporate that dependence. Since the results and conclusions change, this manuscript is withdrawn

We investigated the development and breaking of the dineutron correlation in $^{10}$Be by analyzing the elastic and inelastic scatterings with a framework combing the microscopic structure and reaction models. For studying the structure, the $^{10}$Be nucleus was constructed under the assumption of a four-body ($\alpha + \alpha + n + n$) cluster model. In this work, we focused on the change in the inner structure for the 0$_1^+$, 2$_1^+$, and 2$_2^+$ states when the strength of the spin-orbit interaction is varied. The inner structure, including various physical quantities such as energy, radius, and transition strength, is drastically influenced by the strength of the spin-orbit interaction. In particular, the development and breaking of the dineutron correlation is governed by the spin-orbit strength. The differences in the inner structure can be manifested by applying the obtained wave functions to elastic and inelastic scatterings with a proton target at $E/A =$ 59.4 and 200 MeV. Although the 0$_1^+$ and 2$_1^+$ states are significantly influenced by the spin-orbit strength of the nuclear structure calculation, the elastic and inelastic cross sections are not much affected. On the other hand, the inelastic cross section of the 2$_2^+$ state depends greatly on the spin-orbit strength of the structure calculation. Thus, we discovered a way to measure the degree of the development of dineutron cluster structure based on its sensitivity to the inelastic cross section of the 2$_2^+$ state of $^{10}$Be., Comment: 22 pages, 7 figures, accepted for publication in Physical Review C

We calculate proton elastic and inelastic scatterings with a microscopic coupled channel (MCC) calculation. The localized diagonal and coupling potentials including the spin-orbit part are obtained by folding a complex $G$-matrix effective nucleon-nucleon interaction with a transition density. This is the first time that the present folding prescription for the spin-orbit part is applied to the proton inelastic scattering, while for the monopole transition only. We apply the MCC calculation to the proton elastic and inelastic (0$^+_2$) scatterings by $^{12}$C target at $E_p$ = 65 and 200 MeV. The role of diagonal and coupling potentials for the central and spin-orbit parts is checked. In addition, the relation between the transition density and the proton inelastic scattering is investigated with the modified wave function and the modified transition density. Namely, we perform the investigation with the artificial drastic change rather than fine structural change. The inelastic cross section is sensitive to the strength and shape of the transition density, but the inelastic analyzing power is sensitive only to the shape of that. Finally, we make clear the property of the inelastic analyzing power derived from the transition density without an ambiguity., Comment: 20 pages, 12 figures, accepted in Physical Review C

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

The existence of neutron stars with $2M_\odot$ requires the strong stiffness of the equation of state (EoS) of neutron-star matter. We introduce a multi-pomeron exchange potential (MPP) working universally among 3- and 4-baryons to stiffen the EoS. Its strength is restricted by analyzing the nucleus-nucleus scattering with the G-matrix folding model. The EoSs are derived using the Brueckner-Hartree-Fock (BHF) and the cluster variational method (CVM) with the nuclear interactions ESC and AV18. The mass-radius relations are derived by solving the Tolmann-Oppenheimer-Volkoff (TOV) equation, where the maximum masses over $2M_\odot$ are obtained on the basis of the terrestrial data. Neutron-star radii $R$ at a typical mass $1.5M_\odot$ are predicted to be $12.3\!\sim\!13.0$ km. The uncertainty of calculated radii is mainly from the ratio of 3- and 4-pomeron coupling constants, which cannot be fixed by any terrestrial experiment. Though values of $R(1.5M_\odot)$ are not influenced by hyperon-mixing effects, finely-observed values for them indicate degrees of EoS softening by hyperon mixing in the region of $M\!\sim\!2M_\odot$. If $R(1.5M_\odot)$ is less than about 12.4 km, the softening of EoS by hyperon mixing has to be weak. Useful information can be expected by the space mission NICER offering precise measurements for neutron-star radii within $\pm 5\%$., Comment: 8 pages, 7 figures

We investigate the property of the high-density nuclear matter probed by the nucleus-nucleus elastic scattering in the framework of the double-folding (DF) model with the complex $G$-matrix interaction. The medium effect including three-body-force (TBF) effect is investigated with present two methods based on the frozen density approximation (FDA). The medium effect is clearly seen on the potential and the elastic cross section for the $^{16}$O + $^{16}$O system at $E/A =$ 70 MeV. The crucial role of the medium effect is also confirmed with other effective nucleon-nucleon ($NN$) interactions. In addition, the present methods are applied to other heavy-ion elastic scattering systems. Again, the medium effect is clearly seen in the heavy-ion elastic cross section. The medium effect on the elastic cross section becomes invisible with the increase of the target mass and the incident energy (up to $E/A =$ 200 MeV). However, the medium effect is again important to fix the heavy-ion scattering over $E/A =$ 200 MeV. Finally, we make clear the crucial role of the TBF effect up to $k_F =$ 1.6 fm$^{-1}$ in the nucleus-nucleus elastic scattering., Comment: 29 pages, 11 figures, accepted in Physical Review C. arXiv admin note: substantial text overlap with arXiv:1406.3718

Neutron stars with large masses $\sim 2M_{\odot}$ require the hard stiffness of equation of state (EoS) of neutron-star matter. On the other hand, hyperon mixing brings about remarkable softening of EoS. In order to solve this problem, a multi-pomeron exchange potential (MPP) is introduced as a model for the universal many-body repulsion in baryonic systems on the basis of the Extended Soft Core (ESC) baryon-baryon interaction. The strength of MPP is determined by analyzing the nucleus-nucleus scattering with the G-matrix folding model. The interactions in $\Lambda\!N$, $\Sigma\!N$ and $\Xi\!N$ channels are shown to be consistent with experimental indications. The EoS in neutron-star matter with hyperon mixing is obtained from ESC in addition of MPP, and mass-radius relations of neutron stars are derived. The maximum mass is shown to reach $2M_{\odot}$ even in the case of including hyperon mixing on the basis of model-parameters determined by terrestrial experiments., Comment: prepared for the 2015 EPJA Topical Issue on "Exotic Matter in Neutron Stars"

A multi-pomeron exchange potential (MPP) is proposed as a model for the universal many-body repulsion in baryonic systems on the basis of the Extended Soft Core (ESC) bryon-baryon interaction. The strength of MPP is determined by analyzing the nucleus-nucleus scattering with the G-matrix folding model. The interaction in $\Lambda N$ channels is shown to reproduce well the experimental $\Lambda$ binding energies. The equation of state (EoS) in neutron matter with hyperon mixing is obtained including the MPP contribution, and mass-radius relations of neutron stars are derived. It is shown that the maximum mass can be larger than the observed one $2M_{\odot}$ even in the case of including hyperon mixing on the basis of model-parameters determined by terrestrial experiments.

We investigate the sensitivity of the medium effect in the high-density region on the nucleus-nucleus elastic scattering in the framework of the double-folding (DF) model with the complex $G$-matrix interaction. The medium effect including three-body-force (TBF) effect is investigated with two methods. In the both methods, the medium effect is clearly seen on the potential and the elastic cross section. Finally, we make clear the crucial role of the TBF effect up to $k_F =$ 1.6 fm$^{-1}$ in the nucleus-nucleus elastic scattering., Comment: 12 pages, 4 figures, accepted as Rapid Communication in Physical Review C

A multi-pomeron exchange potential (MPP) is proposed as a model for the three-body repulsion indicated in neutron-star matter, which works universally among three- and four-baryons. Its strength is determined by analyzing the nucleus-nucleus scattering with the G-matrix folding model. The EoS in neutron matter is obtained including the MPP contribution. The neutron-star mass is calculated by solving the TOV equation. The maximum mass is obtained to be larger than the observed one $1.97 M_{solar}$ on the basis of the experimental data.

The low-lying states of the $^{9}$Li nucleus are investigated with a unified framework of microscopic structure and reaction models. In the structure model, the wave function is fully antisymmetrized and the $^{9}$Li nucleus is described as an $\alpha$ + $t$ + $n$ + $n$ four-body system, and low-lying 1/2$^{-}$, 3/2$^{-}$, 5/2$^{-}$, and 7/2$^{-}$ states are obtained by the stochastic multi-configuration mixing method. Using these wave functions, the quasi-elastic cross section at $E/A$ = 60 MeV and the elastic and inelastic cross sections at $E/A$ = 50 MeV on the $^{12}$C target are calculated in the framework of the microscopic coupled channel (MCC) method. The characteristic inelastic angular distribution is seen in the 3/2$_{2}^{-}$ state, whose $\alpha+t$ cluster structure and valence neutron configurations are discussed in detail. We find the possibility of triaxial deformation and mixing of di-neutron components in the $^{9}$Li nucleus., Comment: 10 pages, 11 figures, 5 tables

The reduced transition probability B(E2) of the first excited 2+ state in the nucleus 104Sn was measured via Coulomb excitation in inverse kinematics at intermediate energies. A value of 0.163(26) e^2b^2 was extracted from the absolute cross-section on a Pb target, while the method itself was verified with the stable 112Sn isotope. Our result deviates significantly from the earlier reported value of 0.10(4) e^2b^2 and corresponds to a moderate decrease of excitation strength relative to the almost constant values observed in the proton-rich, even-A 106-114Sn isotopes. Present state-of-the-art shell-model predictions, which include proton and neutron excitations across the N=Z=50 shell closures as well as standard polarization charges, underestimate the experimental findings

We discuss the exotic hadron structure and hadron-hadron interactions in view of heavy ion collisions. First, we demonstrate that a hadronic molecule with a large spatial size would be produced more abundantly in the coalescence model compared with the statistical model result. Secondly, we constrain the Lambda-Lambda interaction by using the recently measured Lambda-Lambda correlation data. We find that the RHIC-STAR data favor the Lambda-Lambda scattering parameters in the range 1/a_0 <= -0.8 fm^{-1} and r_{eff} >= 3 fm., Comment: 8 pages, 5 figures. Talk presented at the 11th International Conference on Hypernuclear and Strange Particle Physics (HYP2012), Oct.1-5, 2012, Barcelona, Spain

The recent works by the present authors and their collaborator predicted that the real part of heavy-ion optical potentials changes its character from attraction to repulsion around the incident energy per nucleon $E =$ 200 -- 300 MeV/u on the basis of the complex $G$-matrix interaction and the double-folding model (DFM) and revealed that the three-body force plays an important role there. In the present paper, we have analyzed the energy dependence of the coupling effect with the Microscopic Coupled Channel (MCC) method and its relation to the elastic and inelastic-scattering angular distributions in detail in the case of the $^{12}$C + $^{12}$C system in the energy range of $E =$ 100 -- 400 MeV/u. The large channel coupling effect is clearly seen in the elastic cross section although the incident energies are enough high. The dynamical polarization potential is derived to investigate the channel coupling effect. Moreover, we analyze the effect of imaginary part of the coupling potential on elastic and inelastic cross sections., Comment: 13 pages, 15 figures, accepted in Physical Review C

We present a new global optical potential (GOP) for nucleus-nucleus systems, including neutron-rich and proton-rich isotopes, in the energy range of $50 \sim 400$ MeV/u. The GOP is derived from the microscopic folding model with the complex $G$-matrix interaction CEG07 and the global density presented by S{\~ a}o Paulo group. The folding model well accounts for realistic complex optical potentials of nucleus-nucleus systems and reproduces the existing elastic scattering data for stable heavy-ion projectiles at incident energies above 50 MeV/u. We then calculate the folding-model potentials (FMPs) for projectiles of even-even isotopes, $^{8-22}$C, $^{12-24}$O, $^{16-38}$Ne, $^{20-40}$Mg, $^{22-48}$Si, $^{26-52}$S, $^{30-62}$Ar, and $^{34-70}$Ca, scattered by stable target nuclei of $^{12}$C, $^{16}$O, $^{28}$Si, $^{40}$Ca $^{58}$Ni, $^{90}$Zr, $^{120}$Sn, and $^{208}$Pb at the incident energy of 50, 60, 70, 80, 100, 120, 140, 160, 180, 200, 250, 300, 350, and 400 MeV/u. The calculated FMP is represented, with a sufficient accuracy, by a linear combination of 10-range Gaussian functions. The expansion coefficients depend on the incident energy, the projectile and target mass numbers and the projectile atomic number, while the range parameters are taken to depend only on the projectile and target mass numbers. The adequate mass region of the present GOP by the global density is inspected in comparison with FMP by realistic density. The full set of the range parameters and the coefficients for all the projectile-target combinations at each incident energy are provided on a permanent open-access website together with a Fortran program for calculating the microscopic-basis GOP (MGOP) for a desired projectile nucleus by the spline interpolation over the incident energy and the target mass number., Comment: 25 pages, 13 figures

We focus on a characteristic non-alpha cluster structure in light neutron-rich nuclei; three triton structure in 9Li. This is an analogy to the case of three alpha state in 12C (Hoyle state). The alpha clusters behave as bosons. however tritons have Fermionic nature, and how the three cluster structure is different from 12C is an intriguing problem. For this purpose, we introduce three triton wave functions. In addition, alpha+t+n+n wave functions are prepared to describe other low-lying states of 9Li, and the coupling effect between them is taken into account. The states with dominantly the three triton components appear below the three triton threshold energy, where three triton correlation is important, however the root mean square radius is not enhanced contrary to the alpha gas states in 12C and 16O., Comment: 5 pages, 4 figures

The recent works by the present authors predicted that the real part of heavy-ion optical potentials changes its character from attraction to repulsion around the incident energy per nucleon E/A = 200 - 300 MeV on the basis of the complex G-matrix interaction and the double-folding model (DFM) and revealed that the three-body force plays an important role there. In the present paper, we have precisely analyzed the energy dependence of the calculated DFM potentials and its relation to the elastic-scattering angular distributions in detail in the case of the $^{12}$C + $^{12}$C system in the energy range of E/A = 100 - 400 MeV. The tensor force contributes substantially to the energy dependence of the real part of the DFM potentials and plays an important role to lower the attractive-to-repulsive transition energy. The nearside and farside (N/F) decomposition of the elastic-scattering amplitudes clarifies the close relation between the attractive-to-repulsive transition of the potentials and the characteristic evolution of the calculated angular distributions with the increase of the incident energy. Based on the present analysis, we propose experimental measurements of the predicted strong diffraction phenomena of the elastic-scattering angular distribution caused by the N/F interference around the attractive-to-repulsive transition energy together with the reduced diffractions below and above the transition energy., Comment: 35 pages, 13 figures, accepted for publication in Phys. Rev. C