# K. Hagino's research while affiliated with Kyoto University and other places

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## Publications (394)

The generator coordinate method (GCM) has been a well-known method to describe nuclear collective motions. In this method, one specifies a priori the relevant collective degrees of freedom as input of the method, based on empirical and/or phenomenological assumptions. We here propose a new extension of the GCM, in which both the basis Slater determ...

Over the past decade, machine learning has been successfully applied in various fields of science. In this study, we employ a deep learning method to analyze a Skyrme energy density functional (Skyrme-EDF), which is a Kohn-Sham type functional commonly used in nuclear physics. Our goal is to construct an orbital-free functional that reproduces the...

In the present work the fusion cross section of the ¹² C+ ²⁴ Mg system has been measured down to energies far below the coulomb barrier around 4μ b . This system is slightly heavier than those of astrophysical interest, like ¹² C+ ¹² C and ¹⁶ O+ ¹⁶ O. The data points highlight the presence of hindrance in ¹² C+ ²⁴ Mg because the excitation function...

The generator coordinate method (GCM) has been a well-known method to describe nuclear collective motions. In this method, one specifies {\it a priori} the relevant collective degrees of freedom as input of the method, based on empirical and/or phenomenological assumptions. We here propose a new extension of the GCM, in which both the basis Slater...

We model fission at barrier-top energies in a simplified model space that permits comparison of different components of the residual nucleon-nucleon interaction. The model space is built on particle-hole excitations of reference configurations. These are Slater determinants of uniformly spaced orbitals characterized only by their quantum numbers an...

Over the past decade, machine learning has been successfully applied in various fields of science. In this study, we employ a deep learning method to analyze a Skyrme energy density functional (Skyrme-EDF), that is a Kohn-Sham type functional commonly used in nuclear physics. Our goal is to construct an orbital-free functional that reproduces the r...

A configuration-interaction model is presented for the barrier region of induced fission. The configuration space is composed of seniority-zero configurations constructed from self-consistent mean-field wave functions. The Hamiltonian matrix elements between configurations include diabatic and pairing interactions between particles. Other aspects o...

We model fission at barrier-top energies in a simplified model space that permits comparison of different components of the residual nucleon-nucleon interaction. The model space is built on particle-hole excitations of reference configurations. These are Slater determinants of uniformly spaced orbitals characterized only by their quantum numbers an...

Quasi-elastic (QEL) scattering measurements have been performed using $^{28}$Si projectile off a $^{90}$Zr target at energies around the Coulomb barrier. A Bayesian analysis within the framework of coupled channels (CC) calculations is performed in a large parameter space of quadrupole and hexadecapole deformations ($\beta_{2}$ and $\beta_{4}$) of...

A configuration-interaction model is presented for the barrier region of induced fission. The configuration space is composed of seniority-zero configurations constructed from self-consistent mean-field wave functions. The Hamiltonian matrix elements between configurations include diabatic and pairing interactions between particles. Other aspects o...

We study the spatial correlation of a particle-hole pair in the isovector channel in Co56 and K40 nuclei. To this end, we employ the Hartree-Fock+Tamm-Dancoff approximation with the Skyrme interaction. We find a large concentration of the two-body density at positions where the neutron particle and the proton hole states locate on the opposite side...

A recent experiment on ¹² C + ²⁴ Mg sub-barrier fusion was performed. Standard coupled-channels calculations clearly over-estimated the low energy cross sections and there was indication of a maximum of the astrophysical S factor vs energy. In the present work further measurements have been performed on the same system, and we extended the excitati...

We apply the dynamical generator coordinate method (DGCM) with a conjugate momentum to a nuclear collective excitation. To this end, we first discuss how to construct a numerically workable scheme of the DGCM for a general one-body operator. We then apply the DGCM to the quadrupole vibration of O16 using the Gogny D1S interaction. We show that both...

We apply the dynamical generator coordinate method (DGCM) with a conjugate momentum to a nuclear collective excitation. To this end, we first discuss how to construct a numerically workable scheme of the DGCM for a general one-body operator. We then apply the DGCM to the quadrupole vibration of $^{16}$O using the Gogny D1S interaction. We show that...

Since its beginnings, fission theory has assumed that low-energy induced fission takes place through transition-state channels at the barrier tops. Nevertheless, up to now there is no microscopic theory applicable to those conditions. We suggest that modern reaction theory is suitable for this purpose, and propose a methodology based on a configura...

Background: While many phenomenological models for nuclear fission have been developed, a microscopic understanding of fission has remained one of the most challenging problems in nuclear physics.

With a view to applying the generator coordinate method to large configuration spaces, we propose a simple approximate formula to compute diabatic many-body matrix elements without having to evaluate two-body interaction matrix elements. The method is illustrated with two analytically solvable Hamiltonians based on the harmonic oscillator.

Atomic nuclei are composite systems, and they may be dynamically excited during nuclear reactions. Such excitations are not only relevant to inelastic scattering but they also affect other reaction processes such as elastic scattering and fusion. The coupled-channels approach is a framework which can describe these reaction processes in a unified m...

We reply to the criticisms of our publication (N. Hasegawa, K. Hagino, and Y. Tanimura, Phys. Lett. B808, 135693 (2020)) made by A. Ono in his recent article, arXiv:2201.02966.

Atomic nuclei are composite systems, and they may be dynamically excited during nuclear reactions. Such excitations are not only relevant to inelastic scattering but they also affect other reaction processes such as elastic scattering and fusion. The coupled-channels approach is a framework which can describe these reaction processes in a unified m...

The concept of compound nucleus was proposed by Niels Bohr in 1936 to explain narrow resonances observed in scattering of a slow neutron off atomic nuclei. A compound nucleus is a metastable state with a long lifetime, in which all the degrees of freedom are in a sort of thermal equilibrium. Fusion reactions are defined as reactions to form such co...

With a view to applying the Generator Coordinate Method to large configuration spaces, we propose a simple approximate formula to compute diabatic many-body matrix elements without having to evaluate two-body interaction matrix elements. The method is illustrated with two analytically solvable Hamiltonians based on the harmonic oscillator.

Background: While many phenomenological models for nuclear fission have been developed, a microscopic understanding of fission has remained one of the most challenging problems in nuclear physics. Purpose: We investigate the applicability of the generator coordinate method (GCM) as a microscopic theory for cluster radioactivities of heavy nuclei, w...

The existence of transition channels across the fission barrier has been central to the theory of induced fission, but there has been no microscopic theory applicable to energies at the barrier top. We propose a microscopic treatment motivated by the Generator Coordinate Method (GCM) and Gaussian Overlap Approximation (GOA) to parameterize both the...

The Gaussian orthogonal ensemble (GOE) of random matrices has been widely employed to describe diverse phenomena in strongly coupled quantum systems. In particular, it has often been invoked to explain the fluctuations in decay rates that follow the χ-squared distribution for one degree of freedom, as originally proposed by Brink and by Porter and...

A large variety of periodic tables of the chemical elements have been proposed. It was Mendeleev who proposed a periodic table based on the extensive periodic law and predicted a number of unknown elements at that time. The periodic table currently used worldwide is of a long form pioneered by Werner in 1905. As the first topic, we describe the wor...

The study of fusion reactions at extreme sub-barrier energies has seen an increased interest in recent years, although difficult to measure due to their very small cross sections. Such reactions are extremely important for our understanding of the production of heavy elements in various environments. In this article, the status of the field is revi...

The Gaussian Orthogonal Ensemble (GOE) of random matrices has been widely employed to describe diverse phenomena in strongly coupled quantum systems. An important prediction is that the decay rates of the GOE eigenstates fluctuate according to the distribution for one degree of freedom, derived by Brink and by Porter and Thomas. However, we find th...

A model is proposed for studying the reaction dynamics in complex quantum systems in which the complete mixing of states is hindered by an internal barrier. Such systems are often treated by the transition-state theory, also known in chemistry as RRKM theory, but the validity of the theory is questionable when there is no identifiable coordinate as...

It is known that nuclear deformation plays an important role in inducing the halo structure in neutron-rich nuclei by mixing several angular momentum components. While previous theoretical studies on this problem in the literature assume axially symmetric deformation, we here consider non-axially symmetric deformations. With triaxial deformation, t...

It is known that nuclear deformation plays an important role in inducing the halo structure in neutron-rich nuclei by mixing several angular momentum components. While previous theoretical studies on this problem in the literature assume axially symmetric deformation, we here consider nonaxially symmetric deformations. With triaxial deformation, th...

We discuss an extension of the generator coordinate method (GCM) by taking simultaneously a collective coordinate and its conjugate momentum as generator coordinates. To this end, we follow the idea of the dynamical GCM (DGCM) proposed by Goeke and Reinhard. We first show that the DGCM method can be regarded as an extension of the double projection...

We discuss the role of deformation of the target nucleus in the fusion reaction of the C15+Th232 system at energies around the Coulomb barrier, in which C15 is a well-known one-neutron halo nucleus. To this end, we construct the potential between C15 and Th232 with the double folding procedure, assuming that the projectile nucleus is composed of th...

We propose a configuration-interaction (CI) representation to calculate induced nuclear fission with explicit inclusion of nucleon-nucleon interactions in the Hamiltonian. The framework is designed for easy modeling of schematic interactions but still permits a straightforward extension to realistic ones. As a first application, the model is applie...

A semi-classical approximation has been a powerful tool in understanding the dynamics of low-energy heavy-ion reactions. Here we discuss two topics in this regard, for which Mahir Hussein was a world leading pioneer. The first topic is heavy-ion fusion reactions of neutron-rich nuclei, in which the breakup process of the projectile nucleus plays a...

We discuss an extension of the generator coordinate method (GCM) by taking simultaneously a collective coordinate and its conjugate momentum as generator coordinates. To this end, we follow the idea of the dynamical GCM (DGCM) proposed by Goeke and Reinhard. We first show that the DGCM method can be regarded as an extension of the double projection...

We discuss the role of deformation of the target nucleus in the fusion reaction of the $^{15}$C + $^{232}$Th system at energies around the Coulomb barrier, for which $^{15}$C is a well-known one-neutron halo nucleus. To this end, we construct the potential between $^{15}$C and $^{232}$Th with the double folding procedure, assuming that the projecti...

A semi-classical approximation has been a powerful tool in understanding the dynamics of low-energy heavy-ion reactions. Here we discuss two topics in this regard, for which Mahir Hussein was a world leading pioneer. The first topic is heavy-ion fusion reactions of neutron-rich nuclei, in which the breakup process of the projectile nucleus plays a...

Atomic nuclei can be spontaneously deformed into non-spherical shapes as many-nucleon systems. We discuss to what extent a similar deformation takes place in many-electron systems. To this end, we employ several many-body methods, such as the unrestricted Hartree-Fock method, post-Hartree-Fock methods, and the density functional theory, to compute...

We investigate the dynamics of spontaneous fission in a configuration-interaction (CI) approach. In that formalism the decay rate is governed by an effective interaction coupling the ground-state configuration and a fission doorway configuration, with the interaction strength determined by inverting a high-dimensioned CI Hamiltonian matrix that may...

A large variety of periodic tables of the chemical elements have been proposed. It was Mendeleev who proposed a periodic table based on the extensive periodic law and predicted a number of unknown elements at that time. The periodic table currently used worldwide is of a long form pioneered by Werner in 1905. As the first topic, we describe the wor...

It has been known that the time-dependent Hartree-Fock (TDHF) method, or the time-dependent density functional theory (TDDFT), fails to describe many-body quantum tunneling. We overcome this problem by superposing a few time-dependent Slater determinants with the time-dependent generator coordinate method (TDGCM). We apply this method to scattering...

There has been much recent interest in nuclear fission, due in part to a new appreciation of its relevance to astrophysics, stability of superheavy elements, and fundamental theory of neutrino interactions. At the same time, there have been important developments on a conceptual and computational level for the theory. The promising new theoretical...

There has been plenty of empirical evidence which shows that the single-particle picture holds to a good approximation in atomic nuclei. In this picture, protons and neutrons move independently inside a mean-field potential generated by an interaction among the nucleons. This leads to the concept of nuclear shells, similar to the electronic shells...

We investigate microscopically the tunneling dynamics in spontaneous fission of atomic nuclei. To this end, we employ a schematic solvable model with a pairing-plus-quadrupole interaction. The spontaneous decay of a system is simulated by introducing a small imaginary part to the energy of a fission doorway state. We show that the many-body Hamilto...

We investigate the dynamics of spontaneous fission in a configuration-interaction (CI) approach. In that formalism the decay rate is governed by an effective interaction coupling the ground-state configuration and a fission doorway configuration, with the interaction strength determined by inverting a high-dimensioned CI Hamiltonian matrix that may...

It has been known that the time-dependent Hartree-Fock (TDHF) method, or the time-dependent density functional theory (TDDFT), fails to describe many-body quantum tunneling. We overcome this problem by superposing a few time-dependent Slater determinants with the time-dependent generator coordinate method (TDGCM). We apply this method to scattering...

The heaviest bound isotope of boron ^{19}B has been investigated using exclusive measurements of its Coulomb dissociation, into ^{17}B and two neutrons, in collisions with Pb at 220 MeV/nucleon. Enhanced electric dipole (E1) strength is observed just above the two-neutron decay threshold with an integrated E1 strength of B(E1)=1.64±0.06(stat)±0.12(...

There has been much recent interest in nuclear fission, due in part to a new appreciation of its relevance to astrophysics, stability of superheavy elements, and fundamental theory of neutrino interactions. At the same time, there have been important developments on a conceptual and computational level for the theory. The promising new theoretical...

Quasi-elastic scattering measurements have been performed using ¹⁶O and ²⁴Mg projectiles off ⁹⁰Zr at energies around the Coulomb barrier. Experimental data have been analyzed in the framework of coupled channels (CC) calculations using the code CCFULL. The quasi-elastic scattering excitation function and derived barrier distribution for ¹⁶O + ⁹⁰Zr...

There have been many empirical evindences which show that the single-particle picture holds to a good approximation in atomic nuclei. In this picture, protons and neutrons move independently inside a mean-field potential generated by an interaction among the nucleons. This leads to the concept of nuclear shells, similar to the electronic shells in...

We investigate microscopically the tunneling dynamics in spontaneous fission of atomic nuclei. To this end, we employ a schematic solvable model with a pairing-plus-quadrupole interaction. The spontaneous decay of a system is simulated by introducing a small imaginary part to the energy of a fission doorway state. We show that the many-body Hamilto...

Couplings of a system to other degrees of freedom (that is, environmental degrees of freedom) lead to energy dissipation when the number of environmental degrees of freedom is large enough. Here, we discuss quantal treatments for such energy dissipation. To this end, we discuss two different time-dependent methods. One is to introduce an effective...

The excitation functions for quasielastic scattering of Ne22+Cm248, Mg26+Cm248, and Ca48+U238 are measured using a gas-filled recoil ion separator. The quasielastic barrier distributions are extracted for these systems and are compared with coupled-channel calculations. The results indicate that the barrier distribution is affected dominantly by de...

We give an account of the main achievements of the scientific career of Andrea Vitturi so far, that have recently been discussed during the workshop “Theoretical Nuclear Physics in Padova” on the occasion of his retirement from full professor at the University of Padova. He has oftentimes been the driving force behind numerous contributions to nucl...

We derive a compact formula for the width of a multi-channel resonance state. To this end, we use a deformed square-well potential and solve the coupled-channels equations. We obtain the $S$-matrix in the Breit–Wigner form, from which partial widths can be extracted. We apply the resultant formula to a deformed nucleus and discuss the behavior of p...

We discuss heavy-ion fusion reactions of a well-deformed odd-mass nucleus at energies around the Coulomb barrier. To this end, we consider the O16+Ho165 reaction and take into account the effect of deformation of Ho165 using the orientation average formula. We show that fusion cross sections are sensitive to magnetic substates of the target nucleus...

We give an account of the main achievements of the scientific career of Andrea Vitturi so far, that have recently been discussed during the workshop "Theoretical Nuclear Physics in Padova" on the occasion of his retirement from full professor at the University of Padova. He has oftentimes been the driving force behind numerous contributions to nucl...

We use an underground counting lab with an extremely low background to perform an activity measurement for the C12+13C system with energies down to Ec.m.=2.323 MeV, at which the 12C(13C,p)24Na cross section is found to be 0.22(7) nb. The C12+13C fusion cross section is derived with a statistical model calibrated using experimental data. Our new res...

Couplings of a system to other degrees of freedom (that is, environmental degrees of freedom) lead to energy dissipation when the number of environmental degrees of freedom is large enough. Here we discuss quantal treatments for such energy dissipation. To this end, we discuss two different time-dependent methods. One is to introduce an effective t...

We discuss heavy-ion fusion reactions of a well-deformed odd-mass nucleus at energies around the Coulomb barrier. To this end, we consider the $^{16}$O+$^{165}$Ho reaction and take into account the effect of deformation of $^{165}$Ho using the orientation average formula. We show that fusion cross sections are sensitive to magnetic substates of the...

To investigate a system coupled to a harmonic oscillator bath, we propose a new approach based on a phonon number representation of the bath. Compared to the method of the hierarchical equations of motion, the new approach is computationally much less expensive in a sense that a reduced density matrix is obtained by calculating the time evolution o...

To investigate a system coupled to a harmonic oscillator bath, we propose a new approach based on a phonon number representation of the bath. Compared to the method of the hierarchical equations of motion, the new approach is computationally much less expensive in a sense that a reduced density matrix is obtained by calculating the time evolution o...

We use an underground counting lab with an extremely low background to perform an activity measurement for the $^{12}$C+$^{13}$C system with energies down to $E\rm_{c.m.}$=2.323 MeV, at which the $^{12}$C($^{13}$C,$p$)$^{24}$Na cross section is found to be 0.22(7) nb. The $^{12}$C+$^{13}$C fusion cross section is derived with a statistical model ca...

Influence of couplings to collective excitations on fusion process has been well established experimentally and theoretically. Much less is known about the influence of dissipation caused by transfer reactions, even less due to noncollective excitations. In this paper, we report the results of the comparison of experimental barrier distributions wi...

We report the recent progress in relativistic mean-field (RMF) and beyond approaches for the low-energy structure of deformed hypernuclei. We show that the Λ hyperon with orbital angular momentum ℓ = 0 (or ℓ > 1) generally reduces (enhances) nuclear quadrupole collectivity. The beyond mean-field studies of hypernuclear low-lying states demonstrate...

Sub-barrier fusion of the two near-by systems ³⁶S + ⁵⁰Ti, ⁵¹V has been measured at the Laboratori Nazionali di Legnaro (INFN). Motivation for the experiment came from the possible effect of the non-zero spin of the ground state of the ⁵¹V nucleus on the sub-barrier excitation function, and in particular on the shape of the barrier distribution. No...

The barrier distribution, originated from channel coupling effects in heavy-ion fusion reactions, has been extracted experimentally for many systems using either a fusion excitation function or an excitation function of large-angle quasi-elastic scattering. In this article, we discuss an application of the latter method to the ⁴⁸ Ca+ ²⁴⁸ Cm system,...

The potential model for nuclear astrophysical reactions requires a considerably shallow nuclear potential when a square-well potential is employed to fit experimental data. We discuss the origin of this apparently different behavior from that obtained with a smooth Woods-Saxon potential, for which a deep potential is often employed. We argue that d...

We develop a novel approach to fusion reactions for synthesis of superheavy elements, which combines the time-dependent Hartree-Fock (TDHF) method with a dynamical diffusion model based on the Langevin equation. In this approach, the distance of the closest approach for the capture process is estimated within the TDHF approach, which is then plugge...

We develop a novel approach to fusion reactions for syntheses of superheavy elements, which combines the time-dependent Hartree-Fock (TDHF) method with a dynamical diffusion model based on the Langevin equation. In this approach, the distance of the closest approach for the capture process is estimated within the TDHF approach, which is then plugge...

The potential model for nuclear astrophysical reactions requires a considerably shallow nuclear potential when a square-well potential is employed to fit experimental data. We discuss the origin of this apparently different behavior from that obtained with a smooth Woods-Saxon potential, for which a deep potential is often employed. We argue that d...

We derive a simple formula for the width of a multi-channel resonance state. To this end, we use a deformed square-well potential and solve the coupled-channels equations. We obtain the $S$-matrix in the Breit-Wigner form, from which partial widths can be extracted. We apply the resultant formula to a deformed nucleus and discuss the behavior of pa...

A detailed comparative study of the sub-barrier fusion of the two near-by systems ³⁶ S+ ⁵⁰ Ti, ⁵¹ V was performed at the National Laboratories of Legnaro (INFN). Aim of the experiment was the investigation of possible effects of the non-zero spin of the ground state of the ⁵¹ V nucleus on the sub-barrier excitation function, and in particular on th...

Hexadecapole ($\beta_{4}$) deformation of the light-mass nucleus $^{24}$Mg has been determined from quasi-elastic measurements at backward angles using $^{16}$O and $^{24}$Mg beams and $^{90}$Zr target. Experimental data were compared with coupled channel calculations using the code CCQEL.Considering $^{16}$O as an inert partner, the strength of vi...

We report the recent progress in relativistic mean-field (RMF) and beyond approaches for the low-energy structure of deformed hypernuclei. We show that the $\Lambda$ hyperon with orbital angular momentum $\ell=0$ (or $\ell>1$) generally reduces (enhances) nuclear quadrupole collectivity. The beyond mean-field studies of hypernuclear low-lying state...