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Takashi Nakatsukasa

Publications and source records attributed to Takashi Nakatsukasa.

At least 37 records · Page 2Linked to original sources
arXiv2018

Nuclear reaction path and requantization of TDDFT

Using a theory of large amplitude collective motion, the adiabatic self-consistent collective coordinate method, we derive reaction path for the fusion process at sub-barrier energies. The collective Hamiltonian to describe the fusion process is constructed, based on the obtained reaction path and canonical variables. We study the reaction of N=Z stable nuclei, alpha+16O, 16O+16O, and alpha+12C. The results suggest that, after two nuclei touch, the reaction path is significantly deviated from the simple relative motion, which may affect the deep sub-barrier fusion cross section.

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arXiv2017

Isospin-symmetry breaking in masses of $N\simeq Z$ nuclei

Effects of the isospin-symmetry breaking (ISB) beyond mean-field Coulomb terms are systematically studied in nuclear masses near the $N=Z$ line. The Coulomb exchange contributions are calculated exactly. We use extended Skyrme energy density functionals (EDFs) with proton-neutron-mixed densities, to which we add new terms breaking the isospin symmetry. Two parameters associated with the new terms are determined by fitting mirror and triplet displacement energies (MDEs and TDEs) of isospin multiplets. The new EDFs reproduce MDEs for the $T=\frac12$ doublets and $T=1$ triplets, and TDEs for the $T=1$ triplets. Relative strengths of the obtained isospin-symmetry-breaking terms {\em are not} consistent with the differences in the $NN$ scattering lengths, $a_{nn}$, $a_{pp}$, and $a_{np}$. Based on low-energy experimental data, it seems thus impossible to delineate the strong-force ISB effects from beyond-mean-field Coulomb-energy corrections.

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arXiv2017

Multipole modes of excitation in triaxially deformed superfluid nuclei

The five-dimensional quadrupole collective model based on energy density functionals (EDF) has often been employed to treat long-range correlations associated with shape fluctuations in nuclei. Our goal is to derive the collective inertial functions in the collective Hamiltonian by the local quasiparticle random phase approximation (QRPA) that correctly takes into account time-odd mean-field effects. Currently, practical framework to perform the QRPA calculation with the modern EDFs on the $(β,γ)$ deformation space is not available. Toward this goal, we develop an efficient numerical method to perform the QRPA calculation on the $(β,γ)$ deformation space based on the Skyrme EDF. We use the finite amplitude method (FAM) for efficient calculation of QRPA strength functions for multipole external fields. We construct a computational code of FAM-QRPA in the three-dimensional Cartesian coordinate space to handle triaxially deformed superfluid nuclei. We validate our new code by comparing our results with former QRPA calculations for axially symmetric nuclei. Isoscalar quadrupole strength functions in triaxial superfluid nuclei, ${}^{110}$Ru and ${}^{190}$Pt, are obtained within a reasonable computational cost. QRPA calculations for triaxially deformed superfluid nuclei based on the Skyrme EDF are achieved with the help of FAM. This is an important step toward the microscopic calculation of collective inertial functions of the local QRPA.

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arXiv2017

Octupole deformation in the nuclear chart based on the 3D Skyrme Hartree-Fock plus BCS model

We have performed a systematic study of the ground state for even-even 1,002 nuclei in which 28 octupole-deformed nuclei are found. The interplay between the spatial deformation and the pairing correlation, plays important roles in nuclear structure. Our model is based on the Skyrme Hartree-Fock plus BCS model represented in the three-dimensional Cartesian coordinate space which can describe any kind of nuclear shape. The quadrupole and octupole deformed nuclei appear in the mass region with characteristic neutron and proton numbers which are consistent with previous studies. In our results, there appear only pear shape ($β_{30}$) in the octupole deformed nuclei. We investigate the potential energy surfaces as functions of the octupole deformations ($β_{3m}, m = 0, 1, 2, 3$), which tells us that. $^{220}$Rn has also local minima in the $β_{31}$ and $β_{32}$ potential energy surfaces.

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arXiv2017

Adiabatic self-consistent collective path in nuclear fusion reactions

Collective reaction paths for fusion reactions, $^{16}$O+$α$ $\rightarrow$ $^{20}$Ne and $^{16}$O+$^{16}$O $\rightarrow$ $^{32}$S, are microscopically determined, on the basis of the adiabatic self-consistent collective coordinate (ASCC) method. The collective path is maximally decoupled from other intrinsic degrees of freedom. The reaction paths turn out to deviate from those obtained with standard mean-field calculations with constraints on quadrupole and octupole moments. The potentials and inertial masses defined in the ASCC method are calculated along the reaction paths. The sub-barrier fusion cross sections are calculated for these systems. Inertial mass inside the Coulomb barrier may have a significant influence on the fusion cross section at the deep sub-barrier energy.

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arXiv2016

Mirror and triplet displacement energies within nuclear DFT: numerical stability

Isospin-symmetry-violating class II and III contact terms are introduced into the Skyrme energy density functional to account for charge dependence of the strong nuclear interaction. The two new coupling constants are adjusted to available experimental data on triplet and mirror displacement energies, respectively. We present preliminary results of the fit, focusing on its numerical stability with respect to the basis size.

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arXiv2016

Self-consistent collective coordinate for reaction path and inertial mass

We propose a numerical method to determine the optimal collective reaction path for the nucleus-nucleus collision, based on the adiabatic self-consistent collective coordinate (ASCC) method. We use an iterative method combining the imaginary-time evolution and the finite amplitude method, for the solution of the ASCC coupled equations. It is applied to the simplest case, the $α-α$ scattering. We determine the collective path, the potential, and the inertial mass. The results are compared with other methods, such as the constrained Hartree-Fock method, the Inglis's cranking formula, and the adiabatic time-dependent Hartree-Fock (ATDHF) method.

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arXiv2016

Microscopic derivation of the Bohr-Mottelson collective Hamiltonian and its application to quadrupole shape dynamics

We discuss the nature of the low-frequency quadrupole vibrations from small-amplitude to large-amplitude regimes. We consider full five-dimensional quadrupole dynamics including three-dimensional rotations restoring the broken symmetries as well as axially symmetric and asymmetric shape fluctuations. Assuming that the time-evolution of the self-consistent mean field is determined by five pairs of collective coordinates and collective momenta, we microscopically derive the collective Hamiltonian of Bohr and Mottelson, which describes low-frequency quadrupole dynamics. We show that the five-dimensional collective Schrödinger equation is capable of describing large-amplitude quadrupole shape dynamics seen as shape coexistence/mixing phenomena. We summarize the modern concepts of microscopic theory of large-amplitude collective motion, which is underlying the microscopic derivation of the Bohr-Mottelson collective Hamiltonian.

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arXiv2016

Time-dependent density-functional description of nuclear dynamics

We present the basic concepts and recent developments in the time-dependent density functional theory (TDDFT) for describing nuclear dynamics at low energy. The symmetry breaking is inherent in nuclear energy density functionals (EDFs), which provides a practical description of important correlations at the ground state. Properties of elementary modes of excitation are strongly influenced by the symmetry breaking and can be studied with TDDFT. In particular, a number of recent developments in the linear response calculation have demonstrated their usefulness in description of collective modes of excitation in nuclei. Unrestricted real-time calculations have also become available in recent years, with new developments for quantitative description of nuclear collision phenomena. There are, however, limitations in the real-time approach; for instance, it cannot describe the many-body quantum tunneling. Thus, we treat the quantum fluctuations associated with slow collective motions assuming that time evolution of densities are determined by a few collective coordinates and momenta. The concept of collective submanifold is introduced in the phase space associated with the TDDFT and used to quantize the collective dynamics. Selected applications are presented to demonstrate the usefulness and quality of the new approaches. Finally, conceptual differences between nuclear and electronic TDDFT are discussed, with some recent applications to studies of electron dynamics in the linear response and under a strong laser field.

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arXiv2016

Quantal rotation and its coupling to intrinsic motion in nuclei

Symmetry breaking is an importance concept in nuclear physics and other fields of physics. Self-consistent coupling between the mean-field potential and the single-particle motion is a key ingredient in the unified model of Bohr and Mottelson, which could lead to a deformed nucleus as a consequence of spontaneous breaking of the rotational symmetry. Some remarks on the finite-size quantum effects are given. In finite nuclei, the deformation inevitably introduces the rotation as a symmetry-restoring collective motion (Anderson-Nambu-Goldstone mode), and the rotation affects the intrinsic motion. In order to investigate the interplay between the rotational and intrinsic motions in a variety of collective phenomena, we use the cranking prescription together with the quasiparticle random phase approximation. At low spin, the coupling effect can be seen in the generalized intensity relation. A feasible quantization of the cranking model is presented, which provides a microscopic approach to the higher-order intensity relation. At high spin, the semiclassical cranking prescription works well. We discuss properties of collective vibrational motions under rapid rotation and/or large deformation. The superdeformed shell structure plays a key role in emergence of a new soft mode which could lead to instability toward the $K^π=1^-$ octupole shape. A wobbling mode of excitation, which is a clear signature of the triviality, is discussed in terms of a microscopic point of view. A crucial role played by the quasiparticle alignment is presented.

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arXiv2016

Multiple period states of the superfluid Fermi gas in an optical lattice

We study multiple period states of a two-component unpolarized superfluid Fermi gas in an optical lattice along the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover. The existence of states whose period is a multiple of the lattice spacing is a direct consequence of the non-linear behavior of the gas, which is due to the presence of the order parameter associated with superfluidity. By solving Bogoliubov-de Gennes equations for a superfluid flow with finite quasimomentum, we find that, in the BCS side of the crossover, the multiple period states can be energetically favorable compared to the normal Bloch states and their survival time against dynamical instability drastically increases, suggesting that these states can be accessible in current experiments, in sharp contrast to the situation in BECs.

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arXiv2015

Time-dependent density functional studies of nuclear quantum dynamics in large amplitudes

The time-dependent density functional theory (TDDFT) provides a unified description of the structure and reaction. The linear approximation leads to the random-phase approximation (RPA) which is capable of describing a variety of collective motion in a harmonic regime. Beyond the linear regime, we present applications of the TDDFT to nuclear fusion and fission reaction. In particular, the extraction of the internuclear potential and the inertial mass parameter is performed using two different methods. A fusion hindrance mechanism for heavy systems is investigated from the microscopic point of view. The canonical collective variables are determined by the adiabatic self-consistent collective coordinate method. Preliminary results of the spontaneous fission path, the potential, and the collective mass parameter are shown for 8Be --> alpha+alpha.

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arXiv2015

Microscopic derivation of the quadrupole collective Hamiltonian for shape coexistence/mixing dynamics

Assuming that the time-evolution of the self-consistent mean field is determined by five pairs of collective coordinate and collective momentum, we microscopically derive the collective Hamiltonian for low-frequency quadrupole modes of excitation. We show that the five-dimensional collective Schrödinger equation is capable of describing large-amplitude quadrupole shape dynamics seen as shape coexistence/mixing phenomena. We focus on basic ideas and recent advances of the approaches based on the time-dependent mean-field theory, but relations to other time-independent approaches are also briefly discussed.

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arXiv2014

Mean-Field Calculation Based on Proton-Neutron Mixed Energy Density Functionals

We have performed calculations based on the Skyrme energy density functional (EDF) that includes arbitrary mixing between protons and neutrons. In this framework, single-particle states are generalized as mixtures of proton and neutron components. The model assumes that the Skyrme EDF is invariant under the rotation in isospin space and the Coulomb force is the only source of the isospin symmetry breaking. To control the isospin of the system, we employ the isocranking method, which is analogous to the standard cranking approach used for describing high-spin states. Here, we present results of the isocranking calculations performed for the isobaric analog states in $A = 40$ and $A = 54$ nuclei.

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arXiv2014

Finite amplitude method in linear response TDDFT calculations

The finite amplitude method is a feasible and efficient method for the linear response calculation based on the time-dependent density functional theory. It was originally proposed as a method to calculate the strength functions. Recently, new techniques have been developed for computation of normal modes (eigenmodes) of the quasiparticle-random-phase approximation. Recent advances associated with the finite amplitude method are reviewed.

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arXiv2014

Repulsive aspects of pairing correlation in nuclear fusion reaction

Numerical simulation on nuclear collisions are performed using the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory (Cb-TDHFB) in the three-dimensional coordinate space. Comparing results of the Cb-TDHFB and the conventional time-dependent Hartree-Fock (TDHF) calculations, we study effects of the pairing correlation on fusion reaction of $^{22}$O+$^{22}$O, $^{52}$Ca+$^{52}$Ca, and $^{22}$O+$^{52}$Ca, using the Skyrme SkM$^*$ functional and a contact-type pairing energy functional. Although current results are yet preliminary, they may suggest that the pairing correlation could hinder the fusion probability at energies in the vicinity of the Coulomb barrier height. We also perform a calculation for heavier nuclei, $^{96}$Zn+$^{124}$Sn, which seems to suggest a similar hindrance effect.

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arXiv2014

Systematic investigation of low-lying dipole modes using the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory

Systematic investigations of the electric dipole (E1) modes of excitation are performed using the canonical-basis time-dependent Hartree-Fock-Bogoliubov (Cb-TDHFB) theory. The Cb-TDHFB is able to describe dynamical pairing correlations in excited states of nuclear systems. We apply the method to the real-time calculation of linear response in even-even nuclei with Skyrme functionals. Effects of shell structure, neutron skin, deformation, and neutron chemical potential (separation energy) are studied in a systematic way. This reveals a number of characteristic features of the low-energy E1 modes. We also find a universal behavior in the low-energy E1 modes for heavy neutron-rich isotopes, which suggests the emergence of decoupled E1 peaks beyond N = 82.

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