For study of dipole excitations, a new method of variation after $K$-projection in the framework of antisymmetrized molecular dynamics (AMD) with the deformation $β$ constraint was proposed. The method was applied to $^{10}$Be and $^{16}$O to describe low-energy dipole excitations and found to be a useful and economical approach for dipole excitations. In the application to $^{10}$Be, two dipole states in low-energy region were described. For $^{16}$O, the $1_1^-$ and $1_2^-$ states with remarkable dipole strengths were obtained. The $1_1^-$ state is characterized by significant toroidal dipole (TD) and compressional dipole strengths, whereas the $1_2^-$ has significant TD strength and shows a developed $α+ {}^{16}$O cluster structure. Dipole properties in $^{16}$O were discussed by analysis of current densities of the dipole transitions.
Low-energy dipole (LED) excitations in $^{18}$O were investigated using a combination of the variation after $K$-projection in the framework of antisymmetrized molecular dynamics with $β$-constraint with the generator coordinate method. We obtained two LED states, namely, the $1_1^-$ state with a dominant shell-model structure and the $1_2^-$ state with a large $^{14}\textrm{C}+α$ cluster component. Both these states had significant toroidal dipole (TD) and compressive dipole (CD) strengths, indicating that the TD and CD modes are not separated but mixed in the LED excitations of $^{18}$O. Thi…
In order to study isovector dipole response of neutron-rich nuclei, we have applied a time-dependent method of antisymmetrized molecular dynamics. The dipole resonances in Be, B and C isotopes have been investigated. In $^{10}$Be, $^{15}$B, $^{16}$C, collective modes of the vibration between a core and valence neutrons cause soft resonances at the excitation energy $E_x=10-15$ MeV below the giant dipole resonance(GDR). In $^{16}$C, we found that a remarkable peak at $E_x=14$ MeV corresponds to coherent motion of four valence neutrons against a $^{12}$C core, while the GDR arises from the core …
In order to study the structure of excited states we perform a variational calculation after spin parity projection (VAP) within the framework of Antisymmetrized Molecular Dynamics (AMD). The framework is proven to be a new powerful approach for the study of the various structures of excited states because it is free from model assumptions such as inert cores, existence of clusters, and the axial symmetry. By using finite range interactions with a density dependent term we reproduce well all the energy levels below 15 MeV in $^{12}$C. This is the first theoretical model that reproduces many $E…
Isovector and isoscalar dipole excitations in $^9$Be and $^{10}$Be are investigated in the framework of antisymmetrized molecular dynamics, in which angular-momentum and parity projections are performed. In the present method, 1p-1h excitations on the ground state and large amplitude $α$-cluster mode are incorporated. The isovector giant dipole resonance (GDR) in $E>20$ MeV shows the two peak structure which is understood by the dipole excitation in the 2$α$ core part with the prolate deformation. Because of valence neutron modes against the $2α$ core, low-energy E1 resonances appear in $E<20$…
Low-energy dipole (LED) excitations in $^{20}$O were investigated by variation after $K$-projection of deformation($β$)-constraint antisymmetrized molecular dynamics combined with the generator coordinate method. We obtained two LED states, namely, the $1_1^-$ state with one-proton excitation on the relatively weak deformation and the $1_2^-$ state with a parity asymmetric structure of the normal deformation. The former is characterized by a toroidal dipole (TD) mode with vortical nuclear current, whereas the latter is associated with a low-energy $E1$ mode caused by surface neutron oscillatio…
The cluster states in $^{13}{\rm C}$ are investigated by antisymmetrized molecular dynamics. By investigating the spectroscopic factors, the cluster configurations of the excited states are discussed. It is found that the $1/2^+_2$ state is dominantly composed of the $^{12}{\rm C}(0^+_2)\otimes s_{1/2}$ configuration and can be regarded as a Hoyle analogue state. On the other hand, the p-wave states ($3/2^-$ and $1/2^-$) do not have such structure, because of the coupling with other configurations. The isoscalar monopole and dipole transition strengths from the ground to the excited states are…
We study structure of excited states of 10Be with the method of variation after spin parity projection in the framework of antisymmetrized molecular dynamics. Present calculations describe many excited states and reproduce the experimental data of E2 and E1 transitions and the new data of the $β$ transition strength successfully. We make systematic discussions on the molecule-like structures of light unstable nuclei and the important role of the valence neutrons based on the results obtained with the framework which is free from such model assumptions as the existence of inert cores and cluste…
To investigate $pn$ pair correlations in $N=Z=\textrm{odd}$ nuclei, we develop a new framework based on the generator coordinate method of the $βγ$ constraint antisymmetrized molecular dynamics. In the framework, the isospin projection is performed before the energy variation to obtain the wave function optimized for each isospin. We apply the method to ${}^{10} \textrm{B}$ and show that it works well to describe coexistence of $T=0$ and $T=1$ states in low-energy spectra. Structures of low-lying states and $pn$ correlations are investigated. Strong $M1$($0^+_1\rightarrow 1^+_1$) and $E2$($1^+…
Structures of light unstable nuclei, Li, Be, B, and C isotopes are systematically studied with a microscopic method of antisymmetrized molecular dynamics. The theoretical method is found to be very useful to study ground and excited states of various nuclei covering unstable nuclei. The calculations succeed to reproduce many experimental data for nuclear structures; energies, radii, magnetic dipole moments, electric quadrupole moments, transition strength. In the theoretical results it is found that various exotic phenomena in unstable nuclei such as molecular-like structures, neutron skin, an…
Revisiting neutron-skin thickness and dipole polarizability constraints on the symmetry energy in Antisymmetrized Molecular Dynamics
China Institute of Atomic Energy（中国原子能科学研究院）；Tohoku University（东北大学）；Guangxi Normal University（广西师范大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）
Constraining the nuclear symmetry energy with electric dipole polarizability and neutron skin characteristics in \texorpdfstring{$^{208}\mathrm{Pb}$}{208Pb} within antisymmetrized molecular dynamics
China Institute of Atomic Energy（中国原子能科学研究院）；Department of Physics, Graduate School of Science, Tohoku University（东北大学理学研究科物理学系）；Guangxi Key Laboratory of Nuclear Physics and Technology, Guangxi Normal University（广西师范大学核物理与技术重点实验室）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）
We investigated cluster correlation and nuclear voricity in low-lying $1^-$ states of $^{24}$Mg within antisymmetrized molecular dynamics framework. We found that the toroidal and compressional dipole modes separately appear as the $K=1$ and $K=0$ states. The $1^-$ ($K=1$) state is the toroidal dipole state with the strong nuclear vorticity but no prominent cluster structure, and the $1^-$ ($K=0$) state is the compressional dipole state having enhanced cluster structure but has the weaker vorticity.
Isoscalar (IS) monopole and dipole excitations in $^{16}$O were investigated by the method of shifted basis antisymmetrized molecular dynamics combined with the generator coordinate method. Significant strengths of the IS monopole and dipole transitions were obtained in the low-energy region below the giant resonances. In addition to the compressive mode, which mainly contributes to the high-energy strengths for the IS dipole giant resonance, we obtained a variety of low-energy dipole modes such as the vortical dipole mode in the $1^-_1$ state of the vibrating tetrahedral $4α$ and the $^{12}$C…
The low-lying spectra of $^{24,25,26}{\rm Ne}$ and the structure of the pygmy dipole resonance (PDR) in $^{26}{\rm Ne}$ have been theoretically studied by the antisymmetrized molecular dynamics (AMD) and its extended version called shifted-basis AMD. The calculated energy and strength of the PDR reasonably agree with the observation, and the analysis of the wave function shows that the PDR is dominated by neutron excitation coupled to the quadrupole excited core nucleus $^{25}{\rm Ne}$, which explains the observed unexpected decay of PDR to the excited states of $^{25}{\rm Ne}$. The large isos…
We present a review of recent works on clustering phenomena in unstable nuclei studied by antisymmetrized molecular dynamics (AMD). The AMD studies in these decades have uncovered novel types of clustering phenomena brought about by the excess neutrons. Among them, this review focuses on the molecule-like structure of unstable nuclei. One of the earliest discussions on the clustering in unstable nuclei was made for neutron-rich Be and B isotopes. AMD calculations predicted that the ground state clustering is enhanced or reduced depending on the number of excess neutrons. Today, the experiments…
We investigated cluster and toroidal aspects of isoscalar dipole excitations in $^{12}$C based on the shifted basis antisymmetrized molecular dynamics combined with the generator coordinate method, which can describes 1p-1h excitations and $3α$ dynamics. In the $E=10-15$ MeV region, we found two low-energy dipole modes separating from the giant dipole resonance. One is the developed $3α$-cluster state and the other is the toroidal dipole mode. The cluster state is characterized by the large amplitude cluster motion beyond the 1p-1h model space, whereas the toroidal dipole mode is predominantly…
We studied dipole excitations in $^{10}$Be based on an extended version of the antisymmetrized molecular dynamics, which can describe 1p-1h excitations and large amplitude cluster modes. Toroidal and compressive dipole operators are found to be good proves to separate the low-energy and high-energy parts of the isoscalar dipole excitations, respectively. Two low-energy $1^-$ states, the toroidal dominant $1^-_1$ state at $E\sim 8$ MeV and the $E1$ dominant $1^-_2$ state at $E\sim 16$ MeV, were obtained. By analysis of transition current densities, the $1^-_1$ states is understood as a toroidal…
On the basis of an extended antisymmetrized molecular dynamics calculation, we study the cluster structure and the of the 0+ and 1- states of 18O. We discuss that several different kinds of cluster states appear in the excitation spectrum, and their monopole and dipole transitions are interesting fingerprints of unique cluster structure. We show that the monopole/dipole transitions are enhanced for the 14C+alpha cluster states, while they are hindered for the molecular-orbit state. We also point out that the ratio of the electric and isoscalar monopole transition strengths gives a good hint fo…
Structure of $^{13}$Be was investigated with antisymmetrized molecular dynamics. The variation after spin and parity projections was performed. An unnatural parity $1/2^-$ state was suggested to be lower than $5/2^+$ state indicating that vanishing of the N=8 magic number occurs in $^{13}$Be. A low-lying $3/2^+$ state with a $2\hbarω$ configuration was also suggested. Developed cluster structures were found in the intruder states. Lowering mechanism of the intruder states was discussed in terms of molecular orbitals around a $2α$ core.
We have developed a new framework of Antisymmetrized Molecular Dynamics (AMD), to adequately treat the I=0 KN interaction, which is essential to study kaonic nuclei. The improved points are 1) pK$^-$/nK$^0$ mixing and 2) total spin and isospin projections. These improvements enable us to investigate various kaonic nuclei (ppnK$^-$, pppK$^-$, pppnK$^-$, $^6$BeK$^-$ and $^9$BK$^-$) systematically. We have found that they are deeply bound and extremely dense with a variety of shapes.
Procedures for projecting angular momentum in a model describing a hot nucleus that takes into account large-amplitude quadrupole fluctuations are discussed. Particular attention is paid to the effect angular-momentum projection has on the observables associated with the $γ$-decay of the giant-dipole resonance (GDR). We also elaborate on which of the different projection methods provides the best overall description of the GDR, including angular distributions. The main consequence of angular-momentum projection is the appearance of an effective volume element in the integrals associated with t…
Background: The sharp $1^-$ resonances with enhanced isoscalar dipole transition strengths are observed in many light nuclei at relatively small excitation energies, but their nature was unclear. Purpose: We show those resonances can be attributed to the cluster states with asymmetric configurations such as $α$+$^{16}{\rm O}$. We explain why asymmetric cluster states are strongly excited by the isoscalar dipole transition. We also provide a theoretical prediction of the isoscalar dipole transitions in $^{20}{\rm Ne}$ and $^{44}{\rm Ti}$. Method: The transition matrix is analytically derived to…
The isoscalar monopole(ISM) and dipole(ISD) excitations in $^{12}$C are theoretically investigated with the shifted antisymmetrized molecular dynamics(AMD) plus $3α$-cluster generator coordinate method(GCM). The small amplitude vibration modes are described by coherent one-particle one-hole excitations expressed by small shift of single-nucleon Gaussian wave functions within the AMD framework, whereas the large amplitude cluster modes are incorporated by superposing $3α$-cluster wave functions in the GCM. The coupling of the excitations in the intrinsic frame with the rotation and parity trans…
Superdeformed (SD) states in $^{40}$Ar have been studied using the deformed-basis antisymmetrized molecular dynamics. Low energy states were calculated by the parity and angular momentum projection (AMP) and the generator coordinate method (GCM). Basis wave functions were obtained by the energy variation with a constraint on the quadrupole deformation parameter $β$, while other quantities such as triaxiality $γ$ were optimized by the energy variation. By the GCM calculation, an SD band was obtained just above the ground state (GS) band. The SD band involves a $K^π= 2^+$ side band due to the tr…
The effect of nuclear deformation on the isoscalar toroidal and compression dipole modes in prolate $^{170}$Yb is studied in the framework of the random-phase-approximation method with a representative set of Skyrme forces (SV-bas, SLy6, SkM$^*$ and SkI3). It is shown that the deformation crucially redistributes the strength of both modes. The compression mode has the same sequence of $μ$=0 and 1 branches as the isovector giant dipole resonance where for prolate nuclei the $μ=0$ mode is lower in energy ($μ$ being the projection of the axial momentum of the mode). Instead, the toroidal mode exh…
The radiative neutron capture reaction rates of the r-process nucleosynthesis are immensely affected by the microscopic structure of the low-energy spectra of compound nuclei. The relativistic (quasiparticle) time blocking approximation (R(Q)TBA) has successfully provided a good description of the low-energy strength, in particular, the strength associated with pygmy dipole resonance, describing transitions from and to the nuclear ground state. The finite-temperature generalization of this method is designed for thermally excited compound nuclei and has the potential to enrich the fine structu…
The many-body states in an extended Fermionic Molecular Dynamics approach are flexible enough to allow the description of nuclei with shell model nature as well as nuclei with cluster and halo structures. Different many-body configurations are obtained by minimizing the energy under constraints on collective variables like radius, dipole, quadrupole and octupole deformations. In the sense of the Generator Coordinate Method we perform variation after projection and multiconfiguration calculations. The same effective interaction derived from realistic interactions by means of the Unitary Correla…
A low-energy magnetic dipole $(M1)$ spin-scissors resonance (SSR) located just below the ordinary orbital scissors resonance (OSR) was recently predicted in deformed nuclei within the Wigner Function Moments (WFM) approach. We analyze this prediction using fully self-consistent Skyrme Quasiparticle Random Phase Approximation (QRPA) method. Skyrme forces SkM*, SVbas and SG2 are implemented to explore SSR and OSR in $^{160,162,164}$Dy and $^{232}$Th. Accuracy of the method is justified by a good description of M1 spin-flip giant resonance. The calculations show that isotopes $^{160,162,164}$Dy i…
