$ΛN$ spin-spin and spin-orbit splittings in low-lying excitation spectra are investigated for $p$-shell $Λ$ hypernuclei on the basis of the microscopic structure calculation within the antisymmetrized molecular dynamics, where the $ΛN$ $G$-matrix interaction derived from the baryon-baryon interaction model ESC (extended soft core) is used. It is found that the ground-state spin-parity is systematically reproduced in the $p$-shell $Λ$ hypernuclei by tuning the $ΛN$ spin-spin and spin-orbit interactions so as to reproduce the experimental data of $^{4}_Λ$H, $^{7}_Λ$Li and $^9_Λ$Be. Furthermore, we also focus on the excitation energies of the excited doublets as well as the energy shifts of them by the addition of a $Λ$ particle.
The response to the addition of a $Λ$ hyperon is investigated for the deformed states such as superdeformation in $^{41}_Λ$Ca, $^{46}_Λ$Sc and $^{48}_Λ$Sc. In the present study, we use the antisymmetrized molecular dynamics (AMD) model. It is pointed out that many kinds of deformed bands appear in $^{45}$Sc and $^{47}$Sc. Especially, it is found that there exists superdeformed states in $^{45}$Sc. By the addition of a $Λ$ particle to $^{40}$Ca, $^{45}$Sc and $^{47}$Sc, it is predicted, for the first time, that the superdeformed states exist in the hypernuclei $^{41}_Λ$Ca and $^{46}_Λ$Sc. The m…
An extended version of the antisymmetrized molecular dynamics to study structure of $p$-$sd$ shell hypernuclei is developed. By using an effective $ΛN$ interaction, we investigate energy curves of $^9_Λ$Be, $^{13}_Λ$C and $^{20,21}_Λ$Ne as function of nuclear quadrupole deformation. Change of nuclear deformation caused by $Λ$ particle is discussed. It is found that the $Λ$ in p-wave enhances nuclear deformation, while that in s-wave reduces it. This effect is most prominent in $^{13}_Λ$C. The possibility of the parity inversion in $^{20}_Λ$Ne is also examined.
Energy spectra of $0s$-orbit $Λ$ states in $p$-shell $Λ$ hypernuclei ($^{A}_ΛZ$) and those in $^{19}_Λ\textrm{F}$ are studied with the microscopic cluster model and antisymmetrized molecular dynamics using the $G$-matrix effective $ΛN$ ($ΛNG$) interactions. Spin-dependent terms of the ESC08a version of the $ΛNG$ interactions are tested and phenomenologically tuned to reproduce observed energy spectra in $p$-shell $^{A}_ΛZ$. Spin-dependent contributions of the $ΛN$ interactions to spin-doublet splitting and excitation energies are discussed. Energy spectra for unobserved excited states in $p$-s…
Low-lying hypernuclei $ ^3_ΛH$, $ ^3_ΣH$, $ ^3_ΛHe$, $ ^3_ΣHe$ are described by the relativistic nine-quark equations in the framework of the dispersion relation technique. The approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitudes are obtained. The relativistic nine-quark amplitudes of hypernuclei, including the quarks of three flavors ($u$, $d$, $s$) are calculated. The poles of these amplitudes determine the masses of hypernuclei. The mass of state $ ^3_ΛH$ with the isospin I=0 and the spin-parity $J^P=\frac{1}{2}^+$ is e…
Taking the hypernucleus $^{13}_{~Λ}$C as an example, we illustrate the miscroscopic particle-rotor model for low-lying spectra of hypernuclei. This approach is based on the beyond-mean-field method, with the particle number and angular momentum projections. The quantum fluctuation of the mean-field is also taken into account for the core nucleus using the generator coordinate method. We show that the impurity effect of $Λ$ hyperon, such as a change in $B(E2)$, is well described with this model. Our calculation indicates that the most important impurity effect in $sd$-shell hypernuclei is a cha…
We propose a novel method for low-lying states of hypernuclei based on the particle-rotor model, in which hypernuclear states are constructed by coupling the hyperon to low-lying states of the core nucleus. In contrast to the conventional particle-rotor model, we employ a microscopic approach for the core states, that is, the generator coordinate method (GCM) with the particle number and angular momentum projections. We apply this microscopic particle-rotor model to $^9_Λ$Be employing a point-coupling version of the relativistic mean-field Lagrangian. A reasonable agreement with the experiment…
We perform a coupled-channels study of the low-lying states in $^{13,15,17,19}_{~~~~~~~~~~~~~~~~~~~~~Λ}$C with a covariant energy density functional based microscopic particle-core coupling model. The energy differences of $1/2^-$ and $3/2^-$ states in $^{13}_Λ$C and $^{15}_Λ$C are predicted to be 0.25 MeV and 0.34 MeV, respectively. We find that configuration mixings in the $1/2^-$ and $3/2^-$ states of $^{15}_Λ$C are the weakest among those of $^{13,15,17,19}_{~~~~~~~~~~~~~~~~~~~~~Λ}$C. It indicates that $^{15}_Λ$C provides the best candidate among the carbon hypernuclei to study the spin-or…
We present a detailed formalism of the microscopic particle-rotor model for hypernuclear low-lying states based on a covariant density functional theory. In this method, the hypernuclear states are constructed by coupling a hyperon to low-lying states of the core nucleus, which are described by the generator coordinate method (GCM) with the particle number and angular momentum projections. We apply this method to study in detail the low-lying spectrum of $^{13}_{~Λ}$C and $^{21}_{~Λ}$Ne hypernuclei. We also briefly discuss the structure of $^{155}_{~~Λ}$Sm as an example of heavy deformed hyper…
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 $\ell=0$ (or $\ell>1$) generally reduces (enhances) nuclear quadrupole collectivity. The beyond mean-field studies of hypernuclear low-lying states demonstrate that there is generally a large configuration mixing between the two components $[^{A-1}Z (I^+) \otimes Λp_{1/2}]^J$ and $[^{A-1}Z (I\pm2 ^+) \otimes Λp_{3/2}]^J$ in the hypernuclear $1/2^-_1, 3/2^-_1$ states. The mixing weight increases as t…
The stiff equation of state (EoS) giving the neutron-star mass of $2M_{\odot}$ suggests the existence of strongly repulsive many-body effect (MBE) not only in nucleon channels but also in hyperonic ones. As a specific model for MBE, the repulsive multi-pomeron exchange potential (MPP) is added to the two-body interaction together with the phenomenological three-body attraction. For various versions of the Nijmegen interaction models, the MBE parts are determined so as to reproduce the observed data of $B_Λ$. The mass dependence of $B_Λ$ values is shown to be reproduced well by adding MBE with …
The structures of the ground and excited states of Be-11 were studied with a microscopic method of antisymmetrized molecular dynamics. The theoretical results reproduce the abnormal parity of the ground state and predict various kinds of excited states. We suggest a new negative-parity band with a well-developed clustering structure which reaches high-spin states. Focusing on a $2α$ clustering structure, we investigated structure of the ground and excited states. We point out that molecular orbits play important roles for the intruder ground state and the low-lying $2\hbar ω$ states. The featu…
Competitive effects of nuclear deformation and density dependence of $Λ\!N$-interaction in $Λ$ binding energies $B_Λ$ of hypernuclei are studied systematically on the basis of the baryon-baryon interaction model ESC including many-body effects. By using the $Λ\!N$ G-matrix interaction derived from ESC, we perform microscopic calculations of $B_Λ$ in $Λ$ hypernuclei within the framework of the antisymmetrized molecular dynamics under the averaged-density approximation. The calculated values of $B_Λ$ reproduce experimental data within a few hundred keV in the wide mass regions from 9 to 51. It i…
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^+…
In order to clarify the nature of hypernuclear low-lying states, we carry out a comprehensive study for the structure of $^{144-154}_{~~~~~~~~Λ}$Sm-hypernuclei, which exhibit a transition from vibrational to rotational characters as the neutron number increases. To this end, we employ a microscopic particle-core coupling scheme based on a covariant density functional theory. We find that the positive-parity ground-state band in the hypernuclei shares a similar structure to that of the corresponding core nucleus. That is, regardless of whether the core nucleus is spherical or deformed, each hyp…
[Background] The hyperon impurity effect in nuclei has been extensively studied in different mean-field models. Recently, there is a controversy about whether the $Λ$ hyperon is more tightly bound in the normal deformed (ND) states than that in the superdeformed (SD) states.[Purpose] This article is aimed to provide a beyond-mean-field study of the low-lying states of hypernuclei with shape coexistence and to shed some light on the controversy.[Method] The models of relativistic mean-field and beyond based on a relativistic point-coupling energy functional are adopted to study the low-lying st…
The impurity effect of hyperon on atomic nuclei has received a renewed interest in nuclear physics since the first experimental observation of appreciable reduction of $E2$ transition strength in low-lying states of hypernucleus $^{7}_Λ$Li. Many more data on low-lying states of $Λ$ hypernuclei will be measured soon for $sd$-shell nuclei, providing good opportunities to study the $Λ$ impurity effect on nuclear low-energy excitations. We carry out a quantitative analysis of $Λ$ hyperon impurity effect on the low-lying states of $sd$-shell nuclei at the beyond-mean-field level based on a relativi…
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.
We investigated structures of low-lying $0s$-orbit $Λ$ states in $p$-shell $Λ$ hypernuclei ($^A_ΛZ$) by applying microscopic cluster models for nuclear structure and a single-channel folding potential model for a $Λ$ particle. For $A>10$ systems, the size reduction of core nuclei is small, and the core polarization effect is regarded as a higher-order perturbation in the $Λ$ binding. The present calculation qualitatively describes the systematic trend of experimental data for excitation energy change from $^{A-1} Z$ to $^A_ΛZ$, in $A>10$ systems. The energy change shows a clear correlation wit…
The low-lying structure of $^{10}_Λ$Be and $^{11}_Λ$Be are investigated within the framework of the antisymmetrized molecular dynamics. We focus on the modifications of the excitation spectra and dynamical changes of the 2$α$ cluster structure caused by a $Λ$ particle as an impurity in these hypernuclei. It is found that the excitation energies of well-pronounced cluster states are largely shifted up by the addition of a $Λ$ particle. Furthermore, we also find that the 2$α$ cluster structure is significantly changed in the excited states, whereas it is almost unchanged in the ground states.
The nucleus $^{44}$Ti has low-lying levels of various kinds of mutually very different nuclear structure displaying the richness of the nuclear many-body dynamics. It is shown that the deformed-basis antisymmetrized molecular dynamics by the use of the Gogny D1S force reproduces successfully and unifiedly two types of coexistence phenomena in $^{44}$Ti. Namely, on one hand, the coexistence of the mean field structure and the cluster structure is confirmed by verifying the normally deformed structure of the $K^π$=$3^-_1$ band with a 1-particle-jump intrinsic configuration and the $α+ ^{40}$Ca c…
Violations of the $Δ$I=1/2 rule are investigated in the nonmesonic weak hypernuclear decay using a weak $Λ$N$\to$NN transition potential based on meson exchange. While the weak $Δ$I=3/2 matrix elements of baryons with pseudoscalar mesons are known to be very small, the same matrix elements of baryons with vector mesons, evaluated in the factorization approximation, are found to be significant. Within the uncertainties of the factorization approximation we find that the total rate increases by at most 6% lying within the error bars of the more recent experimental result. The neutron- to proton-…
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 apply the generator coordinate method (GCM) to single-$Λ$ hypernuclei in order to discuss the spectra of hypernuclear low-lying states. To this end, we use the same relativistic point-coupling energy functional both for the mean-field and the beyond-mean-field calculations. This relativistic GCM approach provides a unified description of low-lying states in ordinary nuclei and in hypernuclei, and is thus suitable for studying the $Λ$ impurity effect. We carry out an illustrative calculation for the low-lying spectrum of $^{21}_Λ$Ne, in which the interplay between the hypernuclear collective…
A Multi-Channel Algebraic Scattering (MCAS) approach has been used to analyze the spectra of two hyper-nuclear systems, Lambda-9Be and Lambda-13C. The splitting of the two odd-parity excited levels (1/2^- and 3/2^-) at 11 MeV excitation in Lambda-13C is driven mainly by the weak Lambda-nucleus spin-orbit force, but the splittings of the 3/2^+ and 5/2^+ levels in both Lambda-9Be and Lambda-13C have a different origin. These cases appear to be dominated by coupling to the collective 2+ states of the core nuclei. Using simple phenomenological potentials as input to the MCAS method, the observed s…
We discuss low-lying collective excitations of $Λ$ hypernuclei using the self-consistent mean-field approaches. We first discuss the deformation properties of $Λ$ hypernuclei in the $sd$-shell region. Based on the relativistic mean-field (RMF) approach, we show that the oblate deformation for $^{28}$Si nucleus may disappear when a $Λ$ particle is added to this nucleus. We then discuss the rotational excitations of $^{25}_Λ$Mg nucleus using the three-dimensional potential energy surface in the deformation plane obtained with the Skyrme-Hartree-Fock method. The deformation of $^{25}_Λ$Mg nucleus…
The low-lying level structure of $^{31}{\rm Mg}$ has been investigated by the antisymmetrized molecular dynamics (AMD) plus generator coordinate method (GCM) with the Gogny D1S force. It is shown that the N=20 magic number is broken and the ground state has the pure neutron $2p3h$ configuration. The coexistence of many particle and many hole states at very low excitation energy is discussed.
Shape coexistence problems in N=14 isotones are studied with a microscopic method of antisymmetrized molecular dynamics. The present calculations reproduce features of deformation in 28Si, and predict possible shape coexistence of neutron density in neutron-rich nuclei(19B and 24Ne). We also systematically study the structures of the ground and excited states, and the molecular resonances of 28Si. Besides the shape coexistence in the low-energy region, the results indicate the high-lying levels with $α$-cluster and 12C+16O molecular structures in 28Si, which are consistent with the observed sp…
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.
$0^+$, $1^-$, $2^+$, and $3^-$ excitations of $^{28}\textrm{Si}$ are investigated via proton and $α$ inelastic scattering off $^{28}\textrm{Si}$. The structure calculation of $^{28}\textrm{Si}$ is performed with the energy variation after total angular momentum and parity projections in the framework of antisymmetrized molecular dynamics (AMD). As a result of the AMD calculation, the oblate ground and prolate bands, $0^+$ and $3^-$ excitations, and the $1^-$ and $3^-$ states of the $K^π=0^-$ band are obtained. Using the matter and transition densities of $^{28}\textrm{Si}$ obtained by AMD, mic…
The low-lying states of the $^{9}$Li nucleus are investigated with a unified framework of microscopic structure and reaction models. In the structure model, the wave function is fully antisymmetrized and the $^{9}$Li nucleus is described as an $α$ + $t$ + $n$ + $n$ four-body system, and low-lying 1/2$^{-}$, 3/2$^{-}$, 5/2$^{-}$, and 7/2$^{-}$ states are obtained by the stochastic multi-configuration mixing method. Using these wave functions, the quasi-elastic cross section at $E/A$ = 60 MeV and the elastic and inelastic cross sections at $E/A$ = 50 MeV on the $^{12}$C target are calculated in …
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…
The structures of excited states in $^{34}$S are investigated using the antisymmetrized molecular dynamics and generator coordinate method (GCM). The GCM basis wave functions are calculated via energy variation with a constraint on the quadrupole deformation parameter $β$. By applying the GCM after parity and angular momentum projections, the coexistence of two positive- and one negative-parity superdeformed (SD) bands are predicted, and low-lying states and other deformed bands are obtained. The SD bands have structures of $^{16}$O + $^{16}$O + two valence neutrons in molecular orbitals aroun…
According to microscopic calculations with antisymmetrized molecular dynamics, we studied cluster features in stable and unstable nuclei. A variety of structure was found in stable and unstable nuclei in the $p$-shell and $sd$-shell regions. The structure of excited states of $^{12}$Be was investigated, while in $sd$-shell nuclei we focused on molecular states and deformed states. The deformed states in $^{28}$Si and $^{40}$Ca were discussed in connection with the high-lying molecular states. Appealing molecular states in $^{36}$Ar and $^{24}$Mg were suggested. The results signified that both …
The low-lying level structures of $^{26}{\rm Ne}$, $^{28}{\rm Ne}$ and $^{30}{\rm Ne}$ which are related to the breaking of the N=20 shell closure have been studied by the framework of the deformed-basis antisymmetrized molecular dynamics plus generator coordinate method using Gogny D1S force. The properties of the many-particle and many-hole states are discussed as well as that of the ground band. We predict that the negative-parity states in which neutrons are promoted into $pf$-orbit from $sd$ orbit have the small excitation energy in the cases of $^{28}{\rm Ne}$ and $^{30}{\rm Ne}$ which, …
A new approach based on antisymmetrized molecular dynamics is proposed to correctly take account of the many-body correlation. We applied it to the spectra of low-lying, light and strange baryons. The inclusion of the quark-quark correlation is vital to predict the precise spectra, and the semi-relativistic kinematics is also important to correct the level ordering. The baryon spectra calculated by the present method is as precise as the Faddeev calculation.
The coexistence of various low-lying deformed states in $^{42}$Ca and $α$--$^{38}$Ar correlations in those deformed states have been investigated using deformed-basis antisymmetrized molecular dynamics. Wave functions of the low-lying states are obtained via parity and angular momentum projections and the generator coordinate method (GCM). Basis wave functions of the GCM calculation are obtained via energy variations with constraints on the quadrupole deformation parameter $β$ and the distance between $α$ and $^{38}$Ar clusters. The rotational band built on the $J^π= 0_2^+$ (1.84 MeV) state as…
Coupling of cluster and deformed structures are important for dynamics of nuclear structure. Threshold energy has been discussed to explain cluster structures coupling to deformed states but relation between threshold energy and excitation energy has open problems. Negative-parity superdeformed (SD) states were observed by a $γ$-spectroscopy experiment in $^{35}$Cl but its detailed structure is unclear. By analyzing coupling of cluster structures in deformed states and high-lying cluster states in $^{35}$Cl, cluster structures coupling to deformed states and excitation energy of high-lying clu…
We extend the No-Core Shell Model (NCSM) methodology to incorporate strangeness degrees of freedom and apply it to single-$Λ$ hypernuclei. After discussing the transformation of the hyperon-nucleon (YN) interaction into Harmonic-Oscillator (HO) basis and the Similarity Renormalization Group transformation applied to it to improve model-space convergence, we present two complementary formulations of the NCSM, one that uses relative Jacobi coordinates and symmetry-adapted basis states to fully exploit the symmetries of the hypernuclear Hamiltonian, and one working in a Slater determinant basis o…
