arXiv subjects

K. Hagino

Publications and source records attributed to K. Hagino.

At least 55 records · Page 3Linked to original sources

arXiv2021

Role of triaxiality in deformed halo nuclei

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, the $Ω$ quantum number is admixed in a single-particle wave function, where $Ω$ is the projection of the single-particle angular momentum on the symmetric axis, and the halo structure may arise even when it is absent with the axially symmetric deformation. In this way, the area of halo nuclei may be extended when triaxial deformation is considered. We demonstrate this idea using a deformed Woods-Saxon potential for nuclei with neutron number N=13 and 43.

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arXiv2021

Transition-state dynamics in complex quantum systems

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 associated with the barrier. The model consists of two Gaussian Orthogonal Ensembles (GOE) of internal levels coupled to each other and to the wave functions in the entrance and decay channels. We find that the transition-state formula can be derived from the model under some easily justifiable approximations. In particular, the assumption in transition-state theory that the reaction rates are insensitive to the decay widths of the internal states on the far side of the barrier is fulfilled for broad range of Hamiltonian parameters. More doubtful is the common assumption that the transmission factor $T$ across the barrier is unity or can be modeled by a one-dimensional Hamiltonian giving $T$ close to unity above the barrier. This is not the case in the model; we find that the transmission factor only approaches one under special conditions that are not likely to be fulfilled without a strong collective component in the Hamiltonian.

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arXiv2021

Configuration-interaction approach to nuclear fission

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 applied to branching ratios between fission and capture in the decay modes of excited fissile nuclei. The ratios are compared with the Bohr-Wheeler transition-state theory to explore its domain of validity. The Bohr-Wheeler theory assumes that the rates are insensitive to the final-state scission dynamics; the insensitivity is rather easily achieved in the CI parameterizations. The CI modeling is also capable of reproducing the branching ratios of the transition-state hypothesis which is one of the key ingredients in the present-day theory of induced fission.

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arXiv2021

Fusion reaction of a weakly-bound nucleus with a deformed target

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 projectile nucleus is composed of the core nucleus, $^{14}$C, and a valance neutron. By taking into account the halo nature of the projectile nucleus as well as the deformation of the target nucleus, we simultaneously reproduce the fusion cross sections for the $^{14}$C + $^{232}$Th and the $^{15}$C + $^{232}$Th systems. Our calculation indicates that the net effect of the breakup and the transfer channels is small for this system.

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arXiv2020

Generator coordinate method with a conjugate momentum: application to the particle number projection

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 method for the center of mass motion. As an application of DGCM, we then investigate the particle number projection, for which we not only carry out an integral over the gauge angle as in the usual particle number projection but also take a linear superposition of BCS states which have different mean particle numbers. We show that the ground state energy is significantly lowered by such effect, especially for magic nuclei for which the pairing gap is zero in the BCS approximation. This suggests that the present method makes a good alternative to the variation after projection (VAP) method, as the method is much simpler than the VAP.

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arXiv2020

Semi-classical approaches to heavy-ion reactions: fusion, rainbow, and glory

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 crucial role. The second is rainbow and glory scattering, for which characteristic oscillatory patterns in differential cross sections can be well understood in terms of intereferences among several semi-classical trajectories.

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arXiv2020

Least action and the maximum-coupling approximations in the theory of spontaneous fission

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 have a block-tridiagonal structure. It is shown that the decay rate decreases exponentially with the number of blocks at a rate determined by the largest eigenvalue of a matrix in the block space for Hamiltonians with identical off-diagonal blocks. The theory is greatly simplified by approximations similar in spirit to the adiabatic and the least-action approximations in continuum representations. Here each block is replaced by a single matrix element. While the adiabatic reduction underestimates the coupling, a reduction based on a maximum-coupling approximation works well in a schematic CI model.

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arXiv2020

Time-Dependent Generator Coordinate Method for Many-Particle Tunneling

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 of two $α$ particles in one dimension, and demonstrate that the TDGCM method yields a finite tunneling probability even at energies below the Coulomb barrier, at which the tunneling probability is exactly zero in the TDHF. This is the first case in which a many-particle tunneling is simulated with a microscopic real-time approach.

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arXiv2020

A microscopic model for spontaneous fission: validity of the adiabatic approximation

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 Hamiltonian can be reduced to an effective 2$\times$2 Hamiltonian, from which one can derive a simple approximate formula for the decay width. We particularly investigate the applicability of the adiabatic approximation, which has often been used in the literature. With typical value of the parameters, we find that the adiabatic approximation works within a factor of around 5 for the decay width.

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arXiv2020

Determination of hexadecapole ($β_{4}$) deformation of the light-mass nucleus $^{24}$Mg using quasi-elastic measurement

Quasi-elastic scattering measurements have been performed using $^{16}$O and $^{24}$Mg projectiles off $^{90}$Zr 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 $^{16}$O + $^{90}$Zr reaction are well reproduced by the CC calculations using the vibrational coupling strengths for $^{90}$Zr reported in the literature. Using these vibrational coupling strengths, a Bayesian analysis is carried out for $^{24}$Mg + $^{90}$Zr reaction. The $β_{2}$ and $β_{4}$ values for $^{24}$Mg are determined to be $+0.43 \pm 0.02$ and $ - 0.11 \pm 0.02$, respectively. The $β_{2}$ parameter determined in the present work is in good agreement with results obtained using inelastic scattering probes. The hexadecapole deformation of $^{24}$Mg has been measured very precisely for the first time. Present results establish that quasi-elastic scattering could provide a useful probe to determine the ground state deformation of atomic nuclei.

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arXiv2020

A Nuclear Periodic Table

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 atoms. In particular, the magic numbers due to closures of the nucleonic shells, corresponding to noble gases in elements, have been known to play an important role in nuclear physics. Here we propose a periodic table for atomic nuclei, in which the elements are arranged according to the known nucleonic shells. The nuclear periodic table clearly indicates that nuclei in the vicinity of the magic numbers can be understood in terms of a shell closure with one or two additional nucleons or nucleon holes, while nuclei far from the magic numbers are characterized by nuclear deformation.

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arXiv2019

An overview of the scientific contribution of Andrea Vitturi to Nuclear Physics (being an account of the recent TNP19 meeting held in Padova)

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 nuclear structure and nuclear reactions that are here reviewed: giant resonances, pairing correlations, collective modes, algebraic models, inelastic excitations, electromagnetic response, break-up and transfer reactions, coupled-channel formalism, clustering, subbarrier fusion processes, etc. Among these topics several inspirational works and ideas can be found that we would like to highlight.

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arXiv2019

Resonance width for a particle-core coupling model with a square-well potential

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 partial width for an $s$-wave channel.

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arXiv2019

Time-dependent approaches to open quantum systems

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 time-dependent Hamiltonian, which leads to a classical equation of motion as a relationship among expectation values of quantum operators. We apply this method to a heavy-ion fusion reaction and discuss the role of dissipation on the penetrability of the Coulomb barrier. The other method is to start with a Hamiltonian with environmental degrees of freedom and derive an equation which the system degree of freedom obeys. For this, we present a new efficient method to solve coupled-channels equations, which can be easily applied even when the dimension of the coupled-channels equations is huge.

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arXiv2019

Subbarrier fusion reactions of an aligned deformed nucleus

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 target nucleus, and cross sections for the side collision, which are relevant to a synthesis of superheavy elements, may be enhanced by a factor of around two by aligning the deformed target nuclei. We also discuss the effect of alignment on the fusion barrier distribution. We find that, for a particular choice of alignment, the shape of barrier distribution becomes similar to a typical shape of barrier distribution for a deformed nucleus with a negative hexadecapole deformation parameter, $β_4$, even if the intrinsic $β_4$ is positive in the target nucleus.

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arXiv2019

A new approach for open quantum systems based on a phonon number representation of a harmonic oscillator bath

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 of vectors, instead of matrices, which enables one to deal with large dimensional systems. As a benchmark test, we consider a quantum damped harmonic oscillator, and show that the exact results can be well reproduced. In addition to the reduced density matrix, our approach also provides a link to the total wave function by introducing new boson operators.

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arXiv2019

Constraining the $^{12}$C+$^{12}$C astrophysical S-factors with the $^{12}$C+$^{13}$C measurements at very low energies

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 calibrated using experimental data. Our new result of the $^{12}$C+$^{13}$C fusion cross section is the first decisive evidence in the carbon isotope systems which rules out the existence of the astrophysical S-factor maximum predicted by the phenomenological hindrance model, while confirming the rising trend of the S-factor towards lower energies predicted by other models, such as CC-M3Y+Rep, DC-TDHF, KNS, SPP and ESW. After normalizing the model predictions with our data, a more reliable upper limit is established for the $^{12}$C+$^{12}$C fusion cross sections at stellar energies.

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arXiv2019

Sub-pixel Response of Double-SOI Pixel Sensors for X-ray Astronomy

We have been developing the X-ray silicon-on-insulator (SOI) pixel sensor called XRPIX for future astrophysical satellites. XRPIX is a monolithic active pixel sensor consisting of a high-resistivity Si sensor, thin SiO$_2$ insulator, and CMOS pixel circuits that utilize SOI technology. Since XRPIX is capable of event-driven readouts, it can achieve high timing resolution greater than $\sim 10{\rm ~μs}$, which enables low background observation by adopting the anti-coincidence technique. One of the major issues in the development of XRPIX is the electrical interference between the sensor layer and circuit layer, which causes nonuniform detection efficiency at the pixel boundaries. In order to reduce the interference, we introduce a Double-SOI (D-SOI) structure, in which a thin Si layer (middle Si) is added to the insulator layer of the SOI structure. In this structure, the middle Si layer works as an electrical shield to decouple the sensor layer and circuit layer. We measured the detector response of the XRPIX with D-SOI structure at KEK. We irradiated the X-ray beam collimated with $4{\rm ~μmϕ}$ pinhole, and scanned the device with $6{\rm ~μm}$ pitch, which is 1/6 of the pixel size. In this paper, we present the improvement in the uniformity of the detection efficiency in D-SOI sensors, and discuss the detailed X-ray response and its physical origins.

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