Search

The exact-exchange relativistic density functional theory (Ex-RDFT) of atomic nuclei has been solved in three-dimensional lattice space for the first time. The exchange energy is treated within the framework of the orbital-dependent relativistic Kohn-Sham density functional theory, wherein the local Lorentz scalar and vector potentials are derived using the relativistic optimized effective potential method. The solutions of binding energies, charge radii, and density distributions are benchmarked against the traditional relativistic Hartree-Fock approach for spherical and axially deformed nuclei. Furthermore, the triaxial neutron-rich $^{104-120}\text{Ru}$ isotopes are investigated with the exchange correlations, which is beyond the current capacity of the traditional relativistic Hartree-Fock approach. The results notably indicate the $\gamma$-softness of these neutron-rich nuclei, which is consistent with experimental observations. This novel approach establishes a foundation for the study of nuclei without imposing any symmetry restrictions employing relativistic density functional with exchange correlations., Comment: 8 pages, 3 figures

[Background] Nuclear pairing is a well-established many-body correlation, particularly among like particles in a spin-singlet state. However, the strength of spin-triplet proton-neutron (pn) pairing in nuclei has remained a long-standing and unresolved issue. [Purpose] The relative strength of spin-triplet pn pairing compared to spin-singlet one is investigated by introducing and analyzing the polarizability of the response to pn pair transfers. [Method] The nuclear energy-density functional method is employed. The ground state of the target nucleus is described using the Hartree-Fock-Bogoliubov approximation, which accounts for the conventional superfluidity of like-particle pairs. The response to pn pair transfers is then analyzed using the pn quasiparticle random-phase approximation. [Results] The spin-singlet pn-pair correlation is strongest at $N=Z$ and decreases monotonically with the increasing number of excess neutrons, whereas the spin-triplet pn-pair correlation is shown to depend non-monotonically on the neutron number and can be enhanced in cases where the pn-pair transfers involving the $\pi j_> \otimes \nu j_<$ configuration occur at low energy. [Conclusions] The shell effect, which uniquely appears in spin-triplet pn-pair correlation, serves as a key indicator of the strength of pn-pair correlations., Comment: 8 pages, 5 figures

Background: The isoscalar giant monopole resonance (ISGMR) splits into two peaks in prolately deformed nuclei. When a nucleus is triaxially deformed, a peak appears in the middle between the two peaks. Purpose: We investigate the mechanism of the appearance of the middle peak in the ISGMR in triaxial nuclei. Method: We perform the constrained Skyrme-Hartree-Fock-Bogoliubov (CHFB) calculation for arbitrary triaxial shapes in $^{100}$Mo. We calculate the strength functions of the isoscalar monopole (ISM) and IS quadrupole modes on the CHFB states. Furthermore, we investigate vibrations of matter distributions in $x$, $y$, and $z$ directions induced by the external ISM field, with the $z$ axis being the longest axis of the triaxial shape. Results: The middle peak in the ISM strength evolves from the triaxial degree $\gamma=0^\circ$ to $60^\circ$. This is because the difference between the vibration in $x$ direction and that in $y$ direction is evident with an increase in $\gamma$ and the quadrupole $K=2$ component of the induced density of the ISM at the middle peak increases as $\gamma$ increases, where $K$ denotes the $z$ component of the angular momentum. This property is also obtained in the unperturbed ISM strength without the residual fields. Conclusions: The mixing between the monopole and quadrupole modes is primarily determined by the ground-state deformation. Therefore, the ISM strength of the middle peak becomes strong as the triaxial degree in the ground state increases., Comment: 7 pages, 7 figures

Background: The appearance of the pairing condensate is an essential feature of many-fermion systems. There are two possible types of pairing: spin-singlet and spin-triplet. However, an open question remains as to whether the spin-triplet pairing condensate emerges in finite nuclei. Purpose: The aim of this work is to examine the coexistence of the spin-singlet and spin-triplet like-particle pairing condensates in nuclei. We also discuss the dependence on the type of pairing functional. Method: The Hartree-Fock-Bogoliubov calculations with a Skyrme $+$ local-pair energy-density functional (EDF) are performed to investigate the pairing condensate in the spherical ground states of Ca and Sn isotopes. Results: The spin-singlet pair EDF induces not only the spin-singlet but also the spin-triplet pairing condensates due to a strong spin-orbit splitting. By discarding the spin-orbit EDF, only the spin-singlet pairing condensate appears. The spin-triplet pair EDF, however, induces the spin-orbit splitting and accordingly the spin-singlet pairing condensate. Conclusions: The spin-orbit splitting plays an essential role in the coexistence of the spin-singlet and spin-triplet pairing condensates in nuclei., Comment: 9 pages, 6 figures

[Background] $\beta$-decay half-life is sensitive to the shell structure near the Fermi levels. Nuclear deformation thus impacts the $\beta$-decay properties. [Purpose] A first-order shape-phase transition in neutron-rich Zr isotopes is predicted by some models. We investigate the $\beta$-decay half-lives of neutron-rich nuclei around $^{110}$Zr, where the shape-phase transition is predicted to occur, to see if the $\beta$-decay half-life can be an indicator of the shape changes. [Method] The proton-neutron quasiparticle random-phase approximation (RPA) is adopted to calculate the Gamow-Teller transitions. In addition, we apply the quasiparticle phonon-vibrational coupling (PVC) to consider the phonon couplings. [Results] The spherical and oblate configurations give similar half-lives but shorter ones than the prolate configuration at the RPA level. The PVC effect further reduces the half-lives in general, but the effect is smaller for the deformed configuration than that for the spherical one. As a result, it makes the shape change from the oblate configuration to the spherical configuration visible. Therefore, a sudden shortening of $\beta$-decay half-lives is always found at the nuclear shape changes. [Conclusions] $\beta$-decay half-life is an indicator of the shape-phase transition. The shape mixing and the roles of the triaxial deformation are subject to study in the future., Comment: 7 pages, 4 figures

Background: Non-yrast states in neutron-rich nuclei are being investigated experimentally. These states reveal various aspects and details of the nuclear structure, such as the fluctuation around the axially symmetric shape. Purpose: The beyond-mean-field effects in neutron-rich nuclei with $N \simeq 28$ are investigated. We focus on the role of collective mass in triaxial-shape dynamics. Method: We employ the five-dimensional quadrupole collective Hamiltonian method with the potential obtained in a constrained Hartree--Fock--Bogoliubov approach with a Skyrme energy-density functional and the collective-mass functions obtained by the cranking approximation. The method includes triaxial deformations. Results: We find that $^{42}$Mg, $^{40}$Si, $^{44}$S, and $^{46}$S show $\gamma$-soft: A flat behavior in the potential energy surface along the triaxial deformation. Their low-lying spectra show a strong nucleus dependence, while those obtained with a collective mass assumed as constant are similar to each other. The energy ratio $E(0_2^+)/E(2_1^+)$ and the $B(E2)$ ratio $B(E2;0_2^+\to 2_1^+)/B(E2;2_1^+\to 0_1^+)$ show a unique property of the $0_2^+$ state, while the energy and $B(E2)$ ratios in neutron-deficient $\gamma$-soft nuclei with $N=78$ do not depend on nucleus so much. Conclusions: Low-lying spectra are determined by not only the potential energy but also the collective mass. We clarify the important role of the collective mass in low-energy dynamics in the neutron-rich $N\sim28$ nuclei., Comment: 8 pages, 9 figures, accepted for publication in Phys. Rev. C

Background: Nuclear energy-density functional (EDF) approach has been widely used to describe nuclear-matter equations of state (EoS) and properties of finite nuclei. Recent advancements in neutron-star (NS) observations have put constraints on the nuclear EoS. The Korea-IBS-Daegu-SKKU (KIDS) functional has been then developed to satisfy the NS observations and applied to homogeneous nuclear matter and spherical nuclei. Purpose: We examine the performance of the KIDS functional by calculating the masses and charge radii of even-even nuclei towards the drip lines. Method: The Kohn-Sham-Bogoliubov equation is solved by taking into account the axial deformation. Results: The root-mean-square deviation of the binding energy and the charge radius for the KIDS functional is 4.5--5.1 MeV and 0.03--0.04 fm, which is comparable to that for existing EDFs. The emergence and development of nuclear deformation in open-shell nuclei are well described. The location of the neutron drip line is according to the nuclear-matter parameter characterizing the low-mass NS. Conclusions: The NS-observation-inspired EDF offers a reasonable reproduction of the structures of finite nuclei. A future global optimization including more nuclear data will give better accuracy and high predictive power of neutron-rich nuclei., Comment: 9 pages, 6 figures, and 2 tables

Ground-state moments of inertia (MoI) are investigated for about 1700 even-even nuclei from the proton drip line to the neutron drip line up to $Z=120$ and $N=184$. The cranked Skyrme-Hartree-Fock-Bogoliubov equation is solved in the coordinate space. This model describes well the available experimental data of more than 300 nuclides possessing an appreciable deformation. I find that the MoI greatly increase near the drip line whereas the deformation is not as strong as estimated by the empirical relation. Systematic measurements of the excitation energy and the transition probability to the first $I^\pi=2^+$ state in neutron-rich nuclei not only reveal the evolution of deformation but can also constrain an effective pair interaction., Comment: 7 pages, including 4 figures and 1 table

To describe the yrast states in weakly bound nuclei, I directly solve the coordinate-space cranked Skyrme-Hartree-Fock-Bogoliubov equation on a three-dimensional lattice with the continuum states discretized in a box. After the numerical demonstration for the ground-state band in a medium-mass nucleus, I apply the newly-developed method to neutron-rich even-$N$ Mg isotopes. I find that the appearance of the significantly low $I^\pi=2^+$ state in $^{40}$Mg is mainly due to the suppression of pairing. The calculation predicts that the $2^+$ state in $^{42}$Mg appears as high in energy as in $^{34\text{-}38}$Mg whereas the triaxial deformation is enhanced in non-zero spin states. The present numerical framework offers a practical approach for investigating the near yrast states systematically and revealing structures unique in drip-line nuclei., Comment: 7 pages, 5 figures; accepted version

Background: The observation of the superdeformed (SD) bands in $^{60,62}$Zn indicates that the particle number 30 is a magic particle number, where two and four neutron single-particles are considered to be promoted to the intruder $1g_{9/2}$ shell. However, the SD-yrast band in $^{62}$Zn is assigned negative parity. Purpose: I investigate various SD configurations in the rapidly rotating $^{60,62}$Zn and $^{64}$Ge, and attempt elucidating the different roles of the energy gaps at particle numbers 30 and 32. Method: I employ a nuclear energy-density functional (EDF) method: the configuration-constrained cranked Skyrme-Kohn-Sham approach is used to describe the rotational bands near the yrast line. Results: The negative-parity SD bands appear higher in energy than the positive-parity SD-yrast band in $^{60}$Zn by about 4 MeV, which is indicative of the SD doubly-magic nucleus. However, the energy gap in $^{64}$Ge is smaller $\sim 2\text{-}3$ MeV, though the quadrupole deformation of the SD states in $^{64}$Ge is greater than that of $^{60}$Zn. The present calculation predicts the occurrence of the hyperdeformed state in $^{60}$Zn and $^{64}$Ge at a high rotational frequency $\sim 2.0$ MeV$/\hbar$ due to the occupation of the $h_{11/2}$ shell. Conclusions: An SD-shell gap at particle number 30 and 32 appears at different deformations and the energy gap at particle number 32 is low, which make the SD structures of $^{62}$Zn unique, where the negative-parity SD states appear lower in energy than the positive-parity one., Comment: 12 pages, 11 figures; accepted version

[Background] Giant resonance (GR) is a typical collective mode of vibration. The deformation splitting of the isovector (IV) giant dipole resonance is well established. However, the splitting of GRs with other multipolarities is not well understood. [Purpose] I explore the IV monopole and quadrupole excitations and attempt to obtain the generic features of IV giant resonances in deformed nuclei by investigating the neutral and charge-exchange channels simultaneously. [Method] I employ a nuclear energy-density functional (EDF) method: the Skyrme-Kohn-Sham-Bogoliubov and the quasiparticle random-phase approximation are used to describe the ground state and the transition to excited states. [Results] I find the concentration of the monopole strengths in the energy region of the isobaric analog or Gamow-Teller resonance irrespective of nuclear deformation, and the appearance of a high-energy giant resonance composed of the particle-hole configurations of $2\hbar \omega_0$ excitation. Splitting of the distribution of the strength occurs in the giant monopole and quadrupole resonances due to deformation. The lower $K$ states of quadrupole resonances appear lower in energy and possess the enhanced strengths in the prolate configuration, and vice versa in the oblate configuration, while the energy ordering depending on $K$ is not clear for the $J=1$ and $J=2$ spin-quadrupole resonances. [Conclusions] The deformation splitting occurs generously in the giant monopole and quadrupole resonances. The $K$-dependence of the quadrupole transition strengths is largely understood by the anisotropy of density distribution.

Background: The $K^\pi=2^-$ excited band emerges systematically in $N=150$ isotones raging from Pu to No with even-$Z$ numbers, and a sharp drop in energies was observed in Cf. Purpose: I attempt to uncover the microscopic mechanism for the appearance of such a low-energy $2^-$ state in $^{248}$Cf. Furthermore, I investigate the possible occurrence of the low-energy $K^\pi=2^+$ state to elucidate the mechanism that prefers the simultaneous breaking of the reflection and axial symmetry to the breaking of the axial symmetry alone in this mass region. Method: I employ a nuclear EDF method: the Skyrme-Kohn-Sham-Bogoliubov and the quasiparticle random-phase approximation are used to describe the ground state and the transition to excited states. Results: The Skyrme-type SkM* and SLy4 functionals reproduce the fall in energy, but not the absolute value, of the $K^\pi=2^-$ state at $Z=98$, where the proton 2qp excitation $[633]7/2 \otimes [521]3/2$ plays a decisive role for the peculiar isotonic dependence. I find interweaving roles by the pairing correlation of protons and the deformed shell closure at $Z=98$. The SkM* model predicts the $K^\pi=2^-$ state appears lower in energy in $^{246}$Cf than in $^{248}$Cf as the Fermi level of neutrons is located in between the $[622]5/2$ and $[734]9/2$ orbitals. Except for $^{250}$Fm in the SkM* calculation, the $K^\pi=2^+$ state is predicted to appear higher in energy than the $K^\pi=2^-$ state because the quasi-proton $[521]1/2$ orbital is located above the $[633]7/2$ orbital. Conclusions: A systematic study of low-lying collective states in heavy actinide nuclei provides a rigorous testing ground for microscopic nuclear models. The present study shows a need for improvements in the EDFs to describe pairing correlations and shell structures in heavy nuclei, that are indispensable in predicting the heaviest nuclei.

Background: Spin-triplet ($S=1$) proton-neutron (pn) pairing in nuclei has been under debate. It is well known that the dynamical pairing affects the nuclear matrix element of the Gamow-Teller (GT) transition and the double beta decay. Purpose: We investigate the effect of the pn-pair interaction in the $T=0, S=1$ channel on the low-lying spin-dipole (SD) transition. We then aim at clarifying the distinction of the role in between the SD and GT transitions. Method: We perform a three-body model calculation for the transition ${}^{80}\mathrm{Ni}\to{}^{80}\mathrm{Cu}$, where ${}^{78}\mathrm{Ni}$ is taken as a core. The strength of the pair interaction is varied to see the effect on the SD transition-strength distribution. To fortify the finding obtained by the three-body model, we employ the nuclear energy-density functional method for the SD transitions in several nuclei, where one can expect a strong effect. Results: The effect of the $S=1$ pn-pair interaction depends on the spatial overlap of the pn pair and the angular momentum of the valence nucleons; the higher the angular momentum of the orbitals, the more significant the effect. Conclusions: The dynamical $S=1$ pairing is effective even for SD states although the spatial overlap of the pn pair can be smaller than GT states. The SD transition involving high-$\ell$ orbitals with the same principal quantum number is strongly affected by the dynamical $S=1$ pairing.

Background: A global description of the ground-state properties of nuclei in a wide mass range in a unified manner is desirable not only for understanding exotic nuclei but for providing nuclear data for applications. Purpose: We demonstrate the KIDS functional describes the ground states appropriately with respect to the existing data and predictions for a possible application of the functional to all the nuclei by taking Nd isotopes as examples. Method: The Kohn-Sham-Bogoliubov equation is solved for the Nd isotopes with the neutron numbers ranging from 60 to 160 by employing the KIDS functionals constructed to satisfy both neutron-matter equation of state or neutron star observation and selected nuclear data. Results: Considering the nuclear deformation improves the description of the binding energies and radii. We find that the discrepancy from the experimental data is more significant for neutron-rich/deficient isotopes and this can be made isotope independent by changing the slope parameter of the symmetry energy. Conclusions: The KIDS functional is applied to the mid-shell nuclei for the first time. The onset and evolution of deformation are nicely described for the Nd isotopes. The KIDS functional is competent to a global fitting for a better description of nuclear properties in the nuclear chart.

Background: Response to spin-dependent operators has been investigated in the magnetic dipole and Gamow-Teller transitions, which provides magnetic properties of a nuclear system. Purpose: I investigate an isotopic dependence of the collectivity generated by the spin-dependent interactions in the Ca and Ni isotopes through the isovector (IV) spin-flip excitations. The responses in the neutral $(t_z)$ and charge-exchange $(t_{\pm})$ channels are considered in a unified way. Method: A nuclear energy-density functional approach is employed for calculating the response functions based on the Skyrme-Kohn-Sham-Bogoliubov method and the quasiparticle-random-phase approximation (QRPA). I adopt the like-particle QRPA and the proton-neutron QRPA for the neutral and charge-exchange channels, respectively. I consider the fluctuation of the proton-neutron pair fields. Results: The collective shift due to RPA correlations for the response in the neutral channel is explained by the occupation probability of neutrons in the $j_>=\ell+1/2$ orbital. Many particle-hole or two-quasiparticle excitations have a coherent contribution to form a giant resonance in neutron-rich nuclei for the charge-exchange channel. The IV spin susceptibility displays the isotopic evolution of the collectivity and the underlying shell structure. Conclusions: A repulsive character of the residual interaction in the spin-isospin channel diminishes the IV spin susceptibility due to the collectivity, while the dynamic ${}^{3}S$ pairing appearing in the charge-exchange channel opposes the reduction., Comment: Revised version and accepted to PRC; comparison with available experimental data, numerical results, and discussion were added

Density-functional theory for superfluid systems is developed in the framework of the functional renormalization group based on the effective action formalism. We introduce the effective action for the particle-number and nonlocal pairing densities and demonstrate that the Hohenberg-Kohn theorem for superfluid systems is established in terms of the effective action. The flow equation for the effective action is then derived, where the flow parameter runs from $0$ to $1$, corresponding to the non-interacting and interacting systems. From the flow equation and the variational equation that the equilibrium density satisfies, we obtain the exact expression for the Kohn-Sham potential generalized to including the pairing potentials. The resultant Kohn-Sham potential has a nice feature that it expresses the microscopic formulae of the external, Hartree, pairing, and exchange-correlation terms, separately. It is shown that our Kohn-Sham potential gives the ground-state energy of the Hartree-Fock-Bogoliubov theory by neglecting the correlations. An advantage of our exact formalism lies in the fact that it provides ways to systematically improve the correlation part., Comment: 26 pages, 1 figure, v2: sentences added to abstract & introduction, symbols unified

Background: The electric giant-dipole resonance (GDR) is the most established collective vibrational mode of excitation. A charge-exchange analog, however, has been poorly studied in comparison with the spin (magnetic) dipole resonance (SDR). Purpose: I investigate the role of deformation on the charge-exchange dipole excitations and explore the generic features as an isovector mode of excitation. Methods: The nuclear energy-density functional method is employed for calculating the response functions based on the Skyrme--Kohn--Sham--Bogoliubov method and the proton-neuton quasiparticle-random-phase approximation. Results: The deformation splitting into $K=0$ and $K=\pm 1$ components occurs in the charge-changing channels and is proportional to the magnitude of deformation as is well known for the GDR. For the SDR, however, a simple assertion based on geometry of a nucleus cannot be applied for explaining the vibrational frequencies of each $K$-component. A qualitative argument on the strength distributions for each component is given based on the non-energy-weighted sum rules taking nuclear deformation into account. The concentration of the electric dipole strengths in low energy and below the giant resonance is found in neutron-rich unstable nuclei. Conclusions: The deformation splitting occurs generically for the charge-exchange dipole excitions as in the neutral channel. The analog pygmy dipole resonance can emerge in deformed neutron-rich nuclei as well as in spherical systems., Comment: 10 pages, 7 figures

The isoscalar $pn$ pair is expected to emerge in nuclei having the similar proton and neutron numbers but there is no clear experimental evidence for it. We aim to clarify the correspondence between the $pn$ pairing strength in many-body calculation and the triple differential cross section (TDX) of proton-induced deuteron knockout ($p,pd$) reaction on $^{16}$O. The radial wave function of the isoscalar $pn$ pair with respect to the center of $^{16}$O is calculated with the energy density functional (EDF) approach and is implemented in the distorted wave impulse approximation (DWIA) framework. The $pn$ pairing strength $V_0$ in the EDF calculation is varied and the corresponding change in the TDX is investigated. A clear $V_0$ dependence of the TDX is found for the $^{16}$O($p,pd$)$^{14}$N($1_2^+$) at $101.3$ MeV. The nuclear distortion is found to make the $V_0$ dependence stronger. Because of the clear $V_0$-TDX correspondence, the ($p,pd$) reaction will be a promising probe for the isoscalar $pn$ pair in nuclei. For quantitative discussion, further modification of the description of the reaction process will be necessary., Comment: 7 pages, 8 figures

We show that the lowest-energy solution of the Hartree-Fock-Bogoliubov (HFB) equation has the even particle-number parity as long as the time-reversal symmetry is conserved in the HFB Hamiltonian without null eigenvalues. Based on this finding, we give a rigorous foundation of a method for solving the HFB equation to describe the ground state of odd-mass nuclei by employing a time-reversal anti-symmetric constraint operator to the Hamiltonian, where one obtains directly the ground state as a self-consistent solution of the cranked-HFB-type equation. Numerical analysis is done for the neutron-rich Mg isotopes with a reasonable choice for the operator, and it is demonstrated that the anomalous increase in the matter radius of $^{37}$Mg is well described when the last neutron occupies a low angular-momentum orbital in the framework of the nuclear energy-density-functional method, revealing the deformed halo structure., Comment: 34 pages, 4 figures, to appear in PTEP

We investigate the possible occurrence of the highly-elongated shapes near the yrast line in $^{40}$Ca and $^{41}$Ca at high spins on the basis of the nuclear energy-density functional method. Not only the superdeformed (SD) yrast configuration but the yrare configurations on top of the SD band are described by solving the cranked Skyme-Kohn-Sham equation in the three-dimensional coordinate-space representation. It is suggested that some of the excited SD bands undergo band crossings and develop to the hyperdeformation (HD) beyond $J \simeq 25 \hbar$ in $^{40}$Ca. We find that the change of triaxiality in response to rotation plays a decisive role for the shape evolution towards HD, and that this is governed by the signature quantum number of the last occupied orbital at low spins. This mechanism can be verified in an experimental observation of the positive-parity SD yrast signature-partner bands in $^{41}$Ca, one of which ($\alpha=+1/2$) undergoes crossings with the HD band while the other ($\alpha=-1/2$) shows the smooth evolution from the collective rotation at low spins to the non-collective rotation with oblate shape at the termination.

$\beta$-decay rates play a decisive role in understanding the nucleosynthesis of heavy elements and are governed by microscopic nuclear-structure information. A sudden shortening of the half-lives of Ni isotopes beyond $N=50$ was observed at the RIKEN-RIBF. This is considered due to the persistence of the neutron magic number $N=50$ in the very neutron-rich Ni isotopes. By systematically studying the $\beta$-decay rates and strength distributions in the neutron-rich Ni isotopes around $N=50$, I try to understand the microscopic mechanism for the observed sudden shortening of the half-lives. The $\beta$-strength distributions in the neutron-rich nuclei are described in the framework of nuclear density-functional theory. I employ the Skyrme energy-density functionals (EDF) in the Hartree-Fock-Bogoliubov calculation for the ground states and in the proton-neutron Quasiparticle Random-Phase Approximation (pnQRPA) for the transitions. Not only the allowed but the first-forbidden (FF) transitions are considered. The experimentally observed sudden shortening of the half-lives beyond $N=50$ is reproduced well by the calculations employing the Skyrme SkM* and SLy4 functionals. The sudden shortening of the half-lives is due to the shell gap at $N=50$ and cooperatively with the high-energy transitions to the low-lying $0^-$ and $1^-$ states in the daughter nuclei. The onset of FF transitions pointed out around $N=82$ and 126 is preserved in the lower-mass nuclei around $N=50$. This study suggests that needed is a microscopic calculation where the shell structure in neutron-rich nuclei and its associated effects on the FF transitions are selfconsistenly taken into account for predicting $\beta$-decay rates of exotic nuclei in unknown region., Comment: 8 pages, 7 figures and 1 table

We demonstrate for the first time that a functional-renormalization-group aided density-functional theory (FRG-DFT) describes well the characteristic features of the excited states as well as the ground state of an interacting many-body system with infinite number of particles in a unified manner. The FRG-DFT is applied to a $(1+1)$-dimensional spinless nuclear matter. For the excited states, the density--density spectral function is calculated at the saturation point obtained in the framework of FRG-DFT, and it is found that our result reproduces a notable feature of the density--density spectral function of the non-linear Tomonaga-Luttinger liquid: The spectral function has a singularity at the edge of its support of the lower-energy side. These findings suggest that the FRG-DFT is a promising first-principle scheme to analyze the excited states as well as the ground states of quantum many-body systems starting from the inter-particle interaction., Comment: 10 pages, 3 figures, v2: two figures removed, sentences modified, title changed, to appear in PTEP letter

We present the first successful functional renormalization group(FRG)-aided density-functional (DFT) calculation of the equation of state (EOS) of an infinite nuclear matter (NM) in (1+1)-dimensions composed of spinless nucleons. We give a formulation to describe infinite matters in which the 'flowing' chemical potential is introduced to control the particle number during the flow. The resultant saturation energy of the NM coincides with that obtained by the Monte-Carlo method within a few percent. Our result demonstrates that the FRG-aided DFT can be as powerful as any other methods in quantum many-body theory., Comment: 9 pages, 3 figures, v3: revised for submission as regular article

The occurrence of the low-lying charge-exchange non spin-flip dipole modes below the giant resonance in neutron-rich nuclei is predicted on the basis of nuclear density functional theory. The ground and excited states are described in the framework of the self-consistent Hartree-Fock-Bogoliubov and the proton-neutron quasiparticle-random-phase approximation employing a Skyrme-type energy density functional. The model calculations are performed for the spherical neutron-rich Ca, Ni, and Sn isotopes. It is found that the low-lying states appear sensitively to the shell structure associated with the $-1 \hbar \omega_0$ excitation below the Gamow-Teller states. Furthermore, the pygmy resonance emerges below the giant resonance when the neutrons occupy the low-$\ell (\ell \leq 2 -3)$ orbitals analogous to the pygmy resonance seen in the electric dipole response., Comment: 5 pages, 5 figures