70 pages, 30 figures, 2 tables. accepted for publication in Atomic Data and Nuclear Data Tables. arXiv admin note: text overlap with arXiv:1002.0907 by other authors
Since the prediction of nuclear chirality in 1997, tremendous progresses both theoretically and experimentally have been achieved. Experimentally, 59 chiral doublet bands in 47 chiral nuclei (including 8 nuclei with multiple chiral doublets) have been reported in $A\sim80,~100,~130$,~and~190 mass regions. The spins, parities, energies, ratios of the magnetic dipole transition strengths to the electric quadrupole transition strengths, and related references for these nuclei are compiled and listed in Table 1. For these nuclei with the magnetic dipole transition strengths and the electric quadrupole transition strengths measured, the corresponding results are given in Table 2. A brief discussion is provided after the presentation of energy $E$, energy difference $ΔE$, energy staggering parameter $S(I)$, rotational frequency $ω$, kinematic moment of inertia $\mathcal{J}^{(1)}$, dynamic moment of inertia $\mathcal{J}^{(2)}$, and ratio of the magnetic dipole transition strength to the electric quadrupole transition strength $B(M1)/B(E2)$ versus spin $I$ in each mass region.
A particle rotor model, which couples nucleons in four single-$j$ shells to a triaxial rotor core, is developed to investigate the five pairs of nearly degenerate doublet bands recently reported in the even-even nucleus $^{136}$Nd. The experimental energy spectra and available $B(M1)/B(E2)$ values are successfully reproduced. The angular momentum geometries of the valence nucleons and the core support the chiral rotation interpretations not only for the previously reported chiral doublet, but also for the other four candidates. Hence, $^{136}$Nd is the first even-even candidate nucleus in whic…
The chiral geometry of the multiple chiral doublet bands with identical configuration is discussed for different triaxial deformation parameters $γ$ in the particle rotor model with $πh_{11/2}\otimes νh_{11/2}^{-1}$. The energy spectra, electromagnetic transition probabilities $B(M1)$ and $B(E2)$, angular momenta, and $K$-distributions are studied. It is demonstrated that the chirality still remains not only in the yrast and yrare bands, but also in the two higher excited bands when $γ$ deviates from $30^{\circ}$. The chiral geometry relies significantly on $γ$, and the chiral geometry of the …
The open problem on whether or not the chirality exists in doublet bands M1 and M4 in light-mass even-even nucleus $^{60}$Ni is studied by adopting the recently developed fully quantal four-$j$ shells triaxial particle rotor model. The corresponding experimental energy spectra, energy differences between doublet bands, and the available $B(M1)/B(E2)$ values are successfully reproduced. The analyses on the basis of the angular momentum components, the azimuthal plots, and the $K$-plots suggest that the chiral modes exist at $I\geq 12\hbar$ in doublet bands M1 and M4.
The static quadrupole moments (SQMs) of nuclear chiral doublet bands are investigated for the first time taking the particle-hole configuration $π(1h_{11/2}) \otimes ν(1h_{11/2})^{-1}$ with triaxial deformation parameters in the range $260^\circ \leq γ\leq 270^\circ$ as examples. The behavior of the SQM as a function of spin $I$ is illustrated by analyzing the components of the total angular momentum. It is found that in the region of chiral vibrations the SQMs of doublet bands are strongly varying with $I$, whereas in the region of static chirality the SQMs of doublet bands are almost constan…
One new pair of positive-parity chiral doublet bands have been identified in the odd-$A$ nucleus $^{135}$Nd which together with the previously reported negative-parity chiral doublet bands constitute a third case of multiple chiral doublet (M$χ$D) bands in the $A\approx130$ mass region. The properties of the M$χ$D bands are well reproduced by constrained covariant density functional theory and particle rotor model calculations. The newly observed M$χ$D bands in $^{135}$Nd represents an important milestone in supporting the existence of M$χ$D in nuclei.
The pairing-plus-quadrupole Hamiltonian is diagonalized in a symmetry restored basis, i.e., the triaxial quasiparticle-states with angular momentum and particle number projections, and applied for chiral doublet bands in 128Cs. The observed energy spectra and electromagnetic transition probabilities are reproduced well without introducing any parameter. The orientation of the angular momentum in the intrinsic frame is investigated by the distributions of its components on the three principle axes as well as those of its tilted angles. The evolution of the chirality with spin is illustrated and…
The basis space in the triaxial projected shell model (TPSM) approach is generalized for odd-odd nuclei to include two-neutron and two-proton configurations on the basic one-neutron coupled to one-proton quasiparticle state. The generalization allows to investigate odd-odd nuclei beyond the band crossing region and as a first application of this development, high-spin band structures recently observed in odd-odd $^{194-200}$Tl isotopes are investigated. In some of these isotopes, the doublet band structures observed after the band crossing have been conjectured to arise from the spontaneous br…
A triaxial projected shell model including configurations with more than four quasiparticles in the configuration space is developed, and applied to investigate the recently reported five chiral doublets candidates in a single even-even nucleus $^{136}$Nd. The energy spectra and transition probability ratios $B(M1)/B(E2)$ are reproduced satisfactorily. The configuration mixing along the rotational bands is studied by analyzing the intrinsic composition of the eigenfunctions. The chiral geometry of these nearly degenerate bands is examined by the \textit{K plot} and the \textit{azimuthal plot},…
Based on the reported positive-parity doublet bands in $^{120}$I, the corresponding experimental characteristics including rotational alignment have been discussed and corresponding configuration assignment is reexamined. The self-consistent tilted axis cranking relativistic mean-field calculations indicates that this doublet bands is built on configuration $πh_{11/2}\otimes νh ^{-1}_{11/2}$. In addition, adopting the two quasiparticles coupled with a triaxial rotor model, the excitation energies, energy staggering parameter $S(I)$, $B(M1)/B(E2)$, effective angles, and $K$ $plots$ have been di…
A reflection-asymmetric triaxial particle rotor model (RAT-PRM) with a quasi-proton and a quasi-neutron coupled with a reflection-asymmetric triaxial rotor is developed and applied to investigate the multiple chiral doublet (M$χ$D) bands candidates with octupole correlations in $^{78}$Br. The calculated excited energies, energy staggering parameters, and $B(M1)/B(E2)$ ratios are in a reasonable agreement with the data of the chiral doublet bands with positive- and negative-parity. The influence of the triaxial deformation $γ$ on the calculated $B(E1)$ is found to be significant. By changing $γ…
We study the Dual Chiral Density Wave (DCDW) in nuclear matter using a hadronic model with the parity doublet structure. We first extend the ordinary DCDW ansatz so as to incorporate the effect of an explicit chiral symmetry breaking. Then via numerically evaluating and minimizing the effective potential, we determine the phase structure. We find, in addition to the ordinary DCDW phase where the space average of the chiral condensate vanishes, a new DCDW phase (sDCDW) with a nonvanishing space average depending on the value of the chiral invariant mass parameter.
A reflection-asymmetric triaxial particle rotor model with three quasiparticles and a reflection-asymmetric triaxial rotor is developed, and applied to investigate the observed multiple chiral doublets (M\c{hi}D) candidates with octupole correlations in 131Ba, i.e., two pairs of positive-parity bands D3-D4 and D5-D6, as well as one pair of negative-parity bands D7-D8. The energy spectra, the energy staggering parameters, the B(M1)/B(E2) ratios, and the B(E1)/B(E2) ratios are reproduced well. The chiral geometries for these M\c{hi}D candidates are examined by the azimuthal plots, and the evolut…
In the sequel of the present study, we have investigated the rotational motion of triaxially deformed nucleus by using the microscopic framework of angular-momentum projection. The Woods-Saxon potential and the schematic separable-type interaction are employed as a microscopic Hamiltonian. As the first example nuclear wobbling motion was studied in detail in the part~I of the series. This second part reports on another interesting rotational mode, chiral doublet bands: two prototype examples, $^{128}$Cs and $^{104}$Rh, are investigated. It is demonstrated that the doublet bands naturally appea…
Multiple chiral doublet bands (M$χ$D) in the $80$, 130 and $190$ mass regions are studied by the model of $γ$=90$^{\circ}$ triaxial rotor coupled with identical symmetric proton-neutron configurations. By selecting the suitable basis, the calculated wave functions are explicitly exhibited to be symmetric under the operator $\hat{A}$, which is defined as rotation by $90^{\circ}$ about 3-axis with the exchange of valance proton and neutron. We found that both $M1$ and $E2$ transitions are allowed between the levels with different values of $A$, while are forbidden between the levels with same va…
We construct nuclear matter based on an extended parity doublet model including four light nucleons $N(939)$, $N(1440)$, $N(1535)$, and $N(1650)$. We exclude some values of the chiral invariant masses by requiring the saturation properties of normal nuclear matter; saturation density, binding energy, incompressibility, and symmetry energy. We find further constraint to the chiral invariant masses from the tidal deformability determined by the observation of the gravitational waves from neutron star merger GW170817. Our result shows that the chiral invariant masses are larger than about $600\,$…
The Quark-Hadron Chiral Parity-Doublet model (Q$χ$P) is applied to calculate compact star properties in the presence of a deconfinement phase transition. Within this model, a consistent description of nuclear matter properties, chiral symmetry restoration, and a transition from hadronic to quark and gluonic degrees of freedom is possible within one unified approach. We find that the equation of state obtained is consistent with recent perturbative quantum chromodynamics (QCD) results and is able to accommodate observational constraints of massive and small neutron stars. Furthermore, we show t…
In this contribution, we summarize our recent studies on the chiral invariant mass and the chiral condensates in neutron star matter. We construct a unified equations of state assuming the crossover phase transition from hadronic matter described by a parity doublet model to quark matter by an Nambu--Jona-Lasinio type quark model. We first show that the chiral invariant mass is constrained to be 600 MeV $\lesssim m_0 \lesssim$ 900 MeV from recent observations of neutron stars. We then determine the density dependence of the chiral condensate in the crossover description, and show that the chir…
We construct an equation of state (EOS) for neutron stars by interpolating hadronic EOS at low density and quark EOS at high density. A hadronic model based on the parity doublet structure is used for hadronic matter and a quark model of Nambu--Jona-Lasinio type is for quark matter. We assume crossover between hadronic matter and quark matter in the the color-flavor locked phase. The nucleon mass of the parity doublet model has a mass associated with the chiral symmetry breaking, and a chiral invariant mass $m_0$ which is insensitive to the chiral condensate. The value of $m_0$ affects the nuc…
We review the chiral variant and invariant components of nucleon masses and its consequence on the chiral restoration in extreme conditions, neutron star matter in particular. We consider a model of linear realization of chiral symmetry with the nucleon parity doublet structure that permits the chiral invariant mass, $m_0$, for positive and negative parity nucleons. Nuclear matter is constructed with the parity doublet nucleon model coupled to scalar fields $σ$, vector fields $(ω, ρ)$, and to mesons with strangeness through the U(1)$_A$ anomaly. In models with large $m_0$, the nucleon mass is …
A quark-diquark model for parity doublet structure of baryons
Research Center for Nuclear Physics (RCNP), Osaka University（大阪大学核物理研究中心）；Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University（名古屋大学小林-益川粒子宇宙起源研究所）；Department of Physics, Nagoya University（名古屋大学物理系）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子能研究开发机构先进科学研究中心）
Finite-volume effects for the nucleon chiral partners are studied within the framework of the parity-doublet model. Our model includes the vacuum energy shift for nucleons, which is the Casimir effect. We find that for the antiperiodic boundary the finite-volume effect leads to chiral symmetry restoration, and the masses of the nucleon parity doublets degenerate. For the periodic boundary, the chiral symmetry breaking is enhanced, and the masses of the nucleons also increase. We also discuss the finite-temperature effect and the dependence on the number of compactified spatial dimensions.
A new transport code "DaeJeon Boltzmann-Uehling-Uhlenbeck (DJBUU)" had been developed and enables to describe the dynamics of heavy-ion collisions in low-energy region. To confirm the validity of the new code, we first calculate Au + Au collisions at Ebeam = 100 and 400A MeV and also perform the box calculation to check the detail of collisions and Pauli blocking without mean-field potential as suggested by the Transport Code Comparison Project. After confirming the validity of new transport code, we study low-energy heavy-ion collisions with an extended parity doublet model. Since the distinc…
We construct a model to describe dense hadronic matter at zero and finite temperature, based on the parity doublet model of DeTar and Kunihiro, with including the iso-singlet scalar meson $σ$ as well as $ρ$ and $ω$ mesons. We show that, by including a six-point interaction of $σ$ meson, the model reasonably reproduces the properties of the normal nuclear matter with the chiral invariant nucleon mass $m_0$ in the range from $500~{\rm MeV}$ to $900~{\rm MeV}$. Furthermore, we study the phase diagram based on the model, which shows that the value of the chiral condensate drops at the liquid-gas p…
The experimental features of positive-parity doublet bands in the odd-\emph{A} cesium isotopes $^{125,127,129,131}$Cs, including angular momentum alignment, energy staggering, $B(M1)/B(E2)$ etc. are studied systematically and compared to those of the candidate chiral bands in the adjacent odd-odd Cs isotopes. The configuration assignments and the dynamics of these bands are discussed. The self-consistent tilted axis cranking relativistic mean-field calculations are performed with configuration reassigned to these bands. The experimental level schemes of four nuclei are well reproduced, and the…
We study the chiral condensates in neutron star matter from nuclear to quark matter domain. We describe nuclear matter with a parity doublet model (PDM), quark matter with the Nambu--Jona-Lasino (NJL) model, and a matter at the intermediate density by interpolating nuclear and quark matter equations of state. The model parameters are constrained by nuclear physics and neutron star observations. Various condensates in the interpolated domain are estimated from the chemical potential dependence of the condensates at the boundaries of the interpolation. The use of the PDM with substantial chiral …
Three- and two-level mixing models are proposed to understand the doubling of states at the same spin and parity in triaxially-deformed atomic nuclei with odd numbers of protons and neutrons. The Particle-Rotor Model for such nuclei is solved using the newly proposed basis which couples angular momenta of two valence nucleons and the rotating triaxial mean-field into left-handed $|\mathcal{L}\rangle$, right-handed $|\mathcal{R}\rangle$, and planar $|\mathcal{P}\rangle$ configurations. The presence and the impact of the planar component is investigated as a function of the total spin for mass A…
We examine the role of the $U(1)_A$ anomaly in a parity doublet model of nucleons which include the chiral variant and invariant masses. Our model expresses the $U(1)_A$ anomaly by the Kobayashi-Maskawa-'t\,Hooft (KMT) interaction in the mesonic sector. After examining the roles of the KMT term in vacuum, we discuss its impacts on nuclear equations of state (EOS). The $U(1)_A$ anomaly increases the masses of the $η'$ and $σ$ mesons and enhances the chiral symmetry breaking. The $U(1)_A$ anomaly enlarges the energy difference between chiral symmetric and symmetry broken vacuum; in turn, the chi…
The observation of the two states $P_c(4380)$ and $P_c(4445)$ [Phys.Rev.Lett. 115 (2015) 072001] solids the existence of the pentaquark state in Nature. In this work, we study the spectrum of the pentaquark states including one or two heavy quarks based on the bound state approach by binding the heavy-light mesons to the nucleon as a soliton in an effective Lagrangian approach. By regarding the $H$ doublet and $G$ doublet as chiral partners to each other and coupling them to light mesons with a minimal derivative, the chiral partner structure of the pentaquark states is calculated. We find tha…
Gravitational wave spectrum from first-order QCD phase transitions based on a parity doublet model
Research Center for Nuclear Physics, Osaka University（大阪大学核物理研究中心）；University of Chinese Academy of Sciences（中国科学院大学）；Hangzhou Normal University（杭州师范大学）
Renormalization-Group Invariant Parity-Doublet Model for Nuclear and Neutron-Star Matter
Justus-Liebig-Universität（吉森大学）；Helmholtz Forschungsakademie Hessen für FAIR (HFHF)（黑森FAIR亥姆霍兹研究学院）；GSI Helmholtzzentrum für Schwerionenforschung（GSI重离子研究中心）；Technische Universität Darmstadt（达姆施塔特工业大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
The nearly degenerate triplet bands with the $πg_{9/2}^{-1}\otimes νh_{11/2} (g_{7/2},d_{5/2})$ configuration in $^{105}$Ag are studied via the relativistic mean-field (RMF) theory and the multiparticle plus rotor model (MPRM), which indicates that these bands are associated with chiral symmetry and pseudospin symmetry. The configuration-fixed constrained triaxial RMF calculations exhibit the pseudospin symmetry in single particle spectra and the triaxial shape coexistence. The experimental excitation energies and the electromagnetic transition probabilities for the triplet bands are reproduce…
The dynamics of chiral nuclei is investigated for the first time with the time-dependent and tilted axis cranking covariant density functional theories on a three-dimensional space lattice in a microscopic and self-consistent way. The experimental energies of the two pairs of the chiral doublet bands in $^{135}$Nd are well reproduced without any adjustable parameters beyond the well-defined density functional. A novel mechanism, i.e., chiral precession, is revealed from the microscopic dynamics of the total angular momentum in the body-fixed frame, whose harmonicity is associated with a transi…
A systematic investigation of the nuclear observables related to the triaxial degree of freedom is presented using the multi-quasiparticle triaxial projected shell model (TPSM) approach. These properties correspond to the observation of $γ$-bands, chiral doublet bands and the wobbling mode. In the TPSM approach, $γ$-bands are built on each quasiparticle configuration and it is demonstrated that some observations in high-spin spectroscopy that have remained unresolved for quite some time could be explained by considering $γ$-bands based on two-quasiparticle configurations. It is shown in some C…
The chirality suggested for the doublet bands B2 and B2a in $^{195}$Tl in $A\sim190$ region is reexamined. The potential-energy curves and the configurations together with the deformation parameters are obtained by the constrained covariant density functional theory. The corresponding experimental energy spectra, energy differences between doublet bands, and the available $B(M1)/B(E2)$ values are investigated by the fully quantal particle rotor model. Analysis on the basis of the angular momentum components, the $K$-plots, and the azimuthal plots suggest a planar rotation interpretation for th…
