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Two new bands have been identified in $^{137}$Nd from a high-statistics JUROGAM II gamma-ray spectroscopy experiment. Constrained density functional theory and particle rotor model calculations are used to assign configurations and investigate the band properties, which are well described and understood. It is demonstrated that these two new bands can be interpreted as chiral partners of previously known three-quasiparticle positive- and negative-parity bands. The newly observed chiral doublet bands in $^{137}$Nd represent an important support to the existence of multiple chiral bands in nuclei. The present results constitute the missing stone in the series of Nd nuclei showing multiple chiral bands, which becomes the most extended sequence of nuclei presenting multiple chiral bands in the Segr\'e chart.

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 evolution of chiral geometry with spin is clearly demonstrated. The intrinsic structure for the positive-parity bands is analyzed and the possible pseudospin-chiral quartet bands are suggested., Comment: 16 pages, 8 figures, PHYSICAL REVIEW C (in press)

Time-dependent covariant density functional theory with the successful density functional PCPK1 is developed in a three-dimensional coordinate space without any symmetry restrictions, and benchmark calculations for the 16O + 16O reaction are performed systematically. The relativistic kinematics, the conservation laws of the momentum, total energy, and particle number, as well as the time-reversal invariance are examined and confirmed to be satisfied numerically. Two primary applications including the dissipation dynamics and above-barrier fusion cross sections are illustrated. The obtained results are in good agreement with the ones given by the nonrelativistic time-dependent density functional theory and the data available. This demonstrates that the newly developed time-dependent covariant density functional theory could serve as an effective approach for the future studies of nuclear dynamical processes., Comment: 22 pages, 10 figures

The nuclear Chirality-Parity (ChP) violation, a simultaneous breaking of chiral and reflection symmetries in the intrinsic frame, is investigated with a reflection-asymmetric triaxial particle rotor model. A new symmetry for an ideal ChP violation system is found and the corresponding selection rules of the electromagnetic transitions are derived. The fingerprints for the ChP violation including the nearly degenerate quartet bands and the selection rules of the electromagnetic transitions are provided. These fingerprints are examined for ChP quartet bands by taking a two-$j$ shell $h_{11/2}$ and $d_{5/2}$ with typical energy spacing for $A=$ 130 nuclei., Comment: 12 pages, 4 figures

The $g$-factor and static quadrupole moment for the wobbling mode in the nuclide $^{133}$La are investigated as functions of the spin $I$by employing the particle rotor model. The model can reproduce the available experimental data of $g$-factor and static quadrupole moment. The properties of the $g$-factor and static quadrupole moment as functions of $I$ are interpreted by analyzing the angular momentum geometry of the collective rotor, proton-particle, and total nuclear system. It is demonstrated that the experimental value of the $g$-factor at the bandhead of the yrast band leads to the conclusion that the rotor angular momentum is $R\simeq 2$. Furthermore, the variation of the $g$-factor with the spin $I$ yields the information that the angular momenta of the proton-particle and total nuclear system are oriented parallel to each other. The negative values of the static quadrupole moment over the entire spin region are caused by an alignment of the total angular momentum mainly along the short axis. Static quadrupole moment differences between the wobbling and yrast band originate from a wobbling excitation with respect to the short axis., Comment: 6 pages, 4 figures

The static quadrupole moments (SQMs) of nuclear chiral doublet bands are investigated for the first time taking the particle-hole configuration $\pi(1h_{11/2}) \otimes \nu(1h_{11/2})^{-1}$ with triaxial deformation parameters in the range $260^\circ \leq \gamma \leq 270^\circ$ 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 constant. Hence, the measurement of SQMs provides a new criterion for distinguishing the modes of nuclear chirality. Moreover, in the high-spin region the SQMs can be approximated by an analytic formula with a proportionality to $\cos\gamma$ for both doublet bands. This provides a way to extract experimentally the triaxial deformation parameter $\gamma$ for chiral bands from the measured SQMs., Comment: 7 pages, 4 figures

The effective field theory for collective rotations of triaxially deformed nuclei is generalized to odd-mass nuclei by including the angular momentum of the valence nucleon as an additional degree of freedom. The Hamiltonian is constructed up to next-to-leading order within the effective field theory formalism. The applicability of this Hamiltonian is examined by describing the wobbling bands observed in the lutetium isotopes $^{161,163,165,167}$Lu. It is found that by taking into account the next-to-leading order corrections, quartic in the rotor angular momentum, the wobbling energies $E_{\textrm{wob}}$ and spin-rotational frequency relations $\omega(I)$ are better described than with the leading order Hamiltonian., Comment: 19 pages, 6 figures

The time-dependent covariant density functional theory in 3D lattice space has been developed and applied to investigate the microscopic dynamics of the linear-chain cluster states for carbon isotopes in the reactions $^4$He$+^8$Be and $^4$He$+^{10}$Be without any symmetry assumptions. By examining the density distribution and its time evolutions, the structure and dynamics of the linear-chain states are analyzed, and the quasiperiodic oscillations of the clusters are revealed. For $^4$He$+^8$Be, the linear-chain states evolve to a triangular configuration and then to a more compact shape. In contrast, for $^4$He$+^{10}$Be, the lifetime of the linear-chain states is much more prolonged due to the dynamical isospin effects by the valence neutrons which slow down the longitudinal oscillations of the clusters and persist the linear-chain states. The dependence of the linear chain survival time and dynamical isospin effects on impact parameters have been illustrated as well., Comment: 14 pages, 5 figures

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$\chi$D) bands in the $A\approx130$ mass region. The properties of the M$\chi$D bands are well reproduced by constrained covariant density functional theory and particle rotor model calculations. The newly observed M$\chi$D bands in $^{135}$Nd represents an important milestone in supporting the existence of M$\chi$D in nuclei.

The impact of beyond mean field effects on the ground state and fission properties of superheavy nuclei has been investigated in a five-dimensional collective Hamiltonian based on covariant density functional theory. The inclusion of dynamical correlations reduces the impact of the $Z=120$ shell closure and induces substantial collectivity for the majority of the $Z=120$ nuclei which otherwise are spherical at the mean field level (as seen in the calculations with the PC-PK1 functional). Thus, they lead to a substantial convergence of the predictions of the functionals DD-PC1 and PC-PK1 which are different at the mean field level. On the contrary, the predictions of these two functionals remain distinctly different for the $N=184$ nuclei even when dynamical correlations are included. These nuclei are mostly spherical (oblate) in the calculations with PC-PK1 (DD-PC1). Our calculations for the first time reveal significant impact of dynamical correlations on the heights of inner fission barriers of superheavy nuclei with soft potential energy surfaces, the minimum of which at the mean field level is located at spherical shape. These correlations affect the fission barriers of the nuclei, which are deformed in the ground state at the mean field level, to a lesser degree., Comment: 11 pages, 8 figures,Physical Review C, in press

The behavior of the collective rotor in the chiral motion of triaxially deformed nuclei is investigated using the particle rotor model by transforming the wave functions from the $K$-representation to the $R$-representation. After examining the energy spectra of the doublet bands and their energy differences as functions of the triaxial deformation, the angular momentum components of the rotor, proton, neutron, and the total system are investigated. Moreover, the probability distributions of the rotor angular momentum ($R$-plots) and their projections onto the three principal axes ($K_R$-plots) are analyzed. The evolution of the chiral mode from a chiral vibration at the low spins to a chiral rotation at high spins is illustrated at triaxial deformations $\gamma=20^\circ$ and $30^\circ$., Comment: 21 pages, 6 figures

The toroidal states in $^{28}$Si with spin extending to extremely high are investigated with the cranking covariant density functional theory on a 3D lattice. Thirteen toroidal states with spin $I$ ranging from 0 to 56$\hbar$ are obtained, and their stabilities against particle emissions are studied by analyzing the density distributions and potentials. The excitation energies of the toroidal states at $I=28$, 36, 44$\hbar$ reasonably reproduce the observed three resonances extracted from the 7-$\alpha$ de-excitation of $^{28}$Si. The $\alpha$ clustering of these toroidal states is supported by the $\alpha$-localization function., Comment: 14 pages, 8 figures

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}, and the evolution from the chiral vibration to the static chirality with spin is clearly demonstrated for four pairs of partner bands. From the features in the \textit{azimuthal plot}, it is difficult to interpret the other candidate as chiral partners., Comment: 4 figures

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$\chi$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 $\gamma$ on the calculated $B(E1)$ is found to be significant. By changing $\gamma$ from 16$^\circ$ to 21$^\circ$, the $B(E1)$ values will be enhanced and better agreement with the $B(E1)/B(E2)$ data is achieved. The chiral geometry based on the angular momenta for the rotor, the valence proton and valence neutron is discussed in details., Comment: 17 pages, 5 figures

New rotational bands built on the $\nu$$(h_{11/2})$ configuration have been identified in $^{105}$Pd. Two bands built on this configuration show the characteristics of transverse wobbling: the $\Delta$$I$=1 transitions between them have a predominant E2 component and the wobbling energy decreases with increasing spin. The properties of the observed wobbling bands are in good agreement with theoretical results obtained using constrained triaxial covariant density functional theory and quantum particle rotor model calculations. This provides the first experimental evidence for transverse wobbling bands based on a one-neutron configuration, and also represents the first observation of wobbling motion in the $A$$\sim$100 mass region.

The intraband electromagnetic transitions in the framework of collective Hamiltonian for chiral and wobbling modes are calculated. By going beyond the mean field approximation on the orientations of rotational axis, the collective Hamiltonian provides the descriptions on both yrast band and collective excitation bands. For a system with one $h_{11/2}$ proton particle and one $h_{11/2}$ neutron hole coupled to a triaxial rotor ($\gamma=-30^\circ$), the intraband electromagnetic transitions given by the one-dimensional and two-dimensional collective Hamiltonian are compared to the results by the tilted axis cranking approach and particle rotor model. Compared with the tilted axis cranking approach, the electromagnetic transitions given by the collective Hamiltonian have a better agreement with those by the particle rotor model, due to the consideration of the quantum fluctuations., Comment: 17 pages, 4 figures

The nuclear magnetic moment is an important physical observable and serves as a useful tool for the stringent test of nuclear models. For the past decades, the covariant density functional theory and its extension have been proved to be successful in describing the nuclear ground-states and excited states properties. However, a long-standing problem is its failure to predict magnetic moments. This article reviews the recent progress in the description of the nuclear magnetic moments within the covariant density functional theory. In particular, the magnetic moments of spherical odd-A nuclei with doubly closed shell core plus or minus one nucleon and deformed odd-A nuclei., Comment: Brief review dedicated to Prof. Akito Arima on the occasion of his 88th birthday

The projected shell model with configuration mixing for nuclear chirality is developed and applied to the observed rotational bands in the chiral nucleus $^{130}$Cs. For the chiral bands, the energy spectra and electromagnetic transition probabilities are well reproduced. The chiral geometry illustrated in the $K~plot$ and the $azithumal~plot$ is confirmed to be stable against the configuration mixing. The other rotational bands are also described in the same framework.

The stability of the linear chain structure of three $\alpha$ clusters for $^{12}$C against the bending and fission is investigated in the cranking covariant density functional theory, in which the equation of motion is solved on a 3D lattice with the inverse Hamiltonian and the Fourier spectral methods. Starting from a twisted three $\alpha$ initial configuration, it is found that the linear chain structure is stable when the rotational frequency is within the range of $\sim$2.0 MeV to $\sim$2.5 MeV. Beyond this range, the final states are not stable against fission. By examining the density distributions and the occupation of single-particle levels, however, these fissions are found to arise from the occupation of unphysical continuum with large angular momenta. To properly remove these unphysical continuum, a damping function for the cranking term is introduced. Eventually, the stable linear chain structure could survive up to the rotational frequency $\sim$3.5 MeV, but the fission still occurs when the rotational frequency approaches to $\sim$4.0 MeV., Comment: 18 pages, 9 figures

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 which the multiple chiral doublets exist. Five pairs of chiral doublet bands in a single nucleus is also a new record in the study of nuclear chirality., Comment: 15 pages, 6 figures

The paradox on the previous interpretation for the nuclear chiral geometry based on the effective angle has been clarified by reexamining the system with the particle-hole configuration $\pi (1h_{11/2})^1 \otimes \nu(1h_{11/2})^{-1}$ and rotor with deformation parameter $\gamma=30^\circ$. It is found that the paradox is caused by the fact that the angular momentum of the rotor is much smaller than those of the proton and the neutron near the bandhead. Hence, it does not support a chiral rotation interpretation near the bandhead. The nuclear chiral geometry based on the effective angle makes sense only when the angular momentum of the rotor becomes comparable with those of the proton and the neutron at the certain spin region., Comment: 14 pages, 4 figures

The effective field theory (EFT) for triaxially deformed even-even nuclei is generalized to include the vibrational degrees of freedom. The pertinent Hamiltonian is constructed up to next-to-leading order. The leading order part describes the vibrational motion, and the NLO part couples rotations to vibrations. The applicability of the EFT Hamiltonian is examined through the description of the energy spectra of the ground state bands, $\gamma$-bands, and $K=4$ bands in the $^{108, 110, 112}$Ru isotopes. It is found that by taking into account the vibrational degrees of freedom, the deviations for high-spin states in the $\gamma$-band observed in the EFT with only rotational degrees of freedom disappear. This supports the importance of including vibrational degrees of freedom in the EFT formulation for the collective motion of triaxially deformed nuclei., Comment: 23 pages, 3 figures, 1 table

Microscopic signatures of nuclear ground-state shape phase transitions in odd-mass Eu isotopes are explored starting from excitation spectra and collective wave functions obtained by diagonalization of a core-quasiparticle coupling Hamiltonian based on energy density functionals. As functions of the physical control parameter -- the number of nucleons -- theoretical low-energy spectra, two-neutron separation energies, charge isotope shifts, spectroscopic quadrupole moments, and $E2$ reduced transition matrix elements accurately reproduce available data, and exhibit more pronounced discontinuities at neutron number $N=90$, compared to the adjacent even-even Sm and Gd isotopes. The enhancement of the first-order quantum phase transition in odd-mass systems can be attributed to a shape polarization effect of the unpaired proton which, at the critical neutron number, starts predominantly coupling to Gd core nuclei that are characterized by larger quadrupole deformation and weaker proton pairing correlations compared to the corresponding Sm isotopes., Comment: 6 pages, 4 figures

The excitation function for the 7 alpha de-excitation of $^{28}$Si nuclei excited to high excitation energies in the collisions of 35 MeV/nucleon $^{28}$Si with $^{12}$C reveals resonance structures that may indicate the population of high spin toroidal isomers such as those predicted by a number of recent theoretical calculations. This interpretation is supported by extended theoretical analyses., Comment: 11 pages, 5 figures

The shell-model-like approach is implemented to treat the cranking many-body Hamiltonian based on the covariant density functional theory including pairing correlations with exact particle number conservation. The self-consistency is achieved by iterating the single-particle occupation probabilities back to the densities and currents. As an example, the rotational structures observed in the neutron-rich nucleus $^{60}$Fe are investigated and analyzed. Without introducing any \emph{ad hoc} parameters, the bandheads, the rotational spectra, and the relations between the angular momentum and rotational frequency for the positive parity band A, and negative parity bands B and C are well reproduced. The essential role of the pairing correlations is revealed. It is found that for band A, the bandcrossing is due to the change of the last two occupied neutrons from the $1f_{5/2}$ signature partners to the $1g_{9/2}$ signature partners. For the two negative parity signature partner bands B and C, the bandcrossings are due to the pseudo-crossing between the $1f_{7/2,~5/2}$ and the $1f_{5/2,~1/2}$ orbitals. Generally speaking, the deformation parameters $\beta$ for bands A, B, and C decrease with rotational frequency. For band A, the deformation jumps from $\beta\sim0.19$ to $\beta\sim0.29$ around the bandcrossing. In comparison with its signature partner band C, band B exhibits appreciable triaxial deformation.

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 chiral geometry is demonstrated in the angular momentum projected model for the first time., Comment: 12 pages, 4 figures

Effective field theory (EFT) is generalized to investigate the rotational motion of triaxially deformed even-even nuclei. A Hamiltonian, called the triaxial rotor model (TRM), is obtained up to next-to-leading order (NLO) within the EFT formalism. Its applicability is examined by comparing with a five-dimensional collective Hamiltonian (5DCH) for the description of the energy spectra of the ground state and $\gamma$ band in Ru isotopes. It is found that by taking into account the NLO corrections, the ground state band in the whole spin region and the $\gamma$ band in the low spin region are well described. The results presented here indicate that it should be possible to further generalize the EFT to triaxial nuclei with odd mass number., Comment: 21 pages, 9 figures

The ground-state properties of nuclei with 8 $\le$ Z $\le$ 120 from the proton drip line to the neutron drip line have been investigated using the relativistic continuum Hartree-Bogoliubov (RCHB) theory with the relativistic density functional PC-PK1. With the effects of the continuum included, there are totally 9035 nuclei predicted to be bound, which largely extends the existing nuclear landscapes predicted with other methods. The calculated binding energies, separation energies, neutron and proton Fermi surfaces, root-mean-square (rms) radii of neutron, proton, matter, and charge distributions, ground-state spins and parities are tabulated. The extension of the nuclear landscape obtained with RCHB is discussed in detail, in particular for the neutron-rich side, in comparison with the relativistic mean field calculations without pairing correlations and also other predicted landscapes. It is found that the coupling between the bound states and the continuum due to the pairing correlations plays an essential role in extending the nuclear landscape. The systematics of the separation energies, radii, densities, potentials and pairing energies of the RCHB calculations are also discussed. In addition, the alpha-decay energies and proton emitters based on the RCHB calculations are investigated., Comment: 192 pages, 25 figures, Atomic Data and Nuclear Data Tables, in press

Background: The discovery of neutrinoless double-beta ($0\nu\beta\beta$) decay would demonstrate the nature of neutrinos, have profound implications for our understanding of matter-antimatter mystery, and solve the mass hierarchy problem of neutrinos. The calculations for the nuclear matrix elements $M^{0\nu}$ of $0\nu\beta\beta$ decay are crucial for the interpretation of this process. Purpose: We study the effects of relativity and nucleon-nucleon short-range correlations on the nuclear matrix elements $M^{0\nu}$ by assuming the mechanism of exchanging light or heavy neutrinos for the $0\nu\beta\beta$ decay. Methods: The nuclear matrix elements $M^{0\nu}$ are calculated within the framework of covariant density functional theory, where the beyond-mean-field correlations are included in the nuclear wave functions by configuration mixing of both angular-momentum and particle-number projected quadrupole deformed mean-field states. Results: The nuclear matrix elements $M^{0\nu}$ are obtained for ten $0\nu\beta\beta$-decay candidate nuclei. The impact of relativity is illustrated by adopting relativistic or nonrelativistic decay operators. The effects of short-range correlations are evaluated. Conclusions: The effects of relativity and short-range correlations play an important role in the mechanism of exchanging heavy neutrinos though the influences are marginal for light neutrinos. Combining the nuclear matrix elements $M^{0\nu}$ with the observed lower limits on the $0\nu\beta\beta$-decay half-lives, the predicted strongest limits on the effective masses are $|\langle m_\nu\rangle|<0.06~\mathrm{eV}$ for light neutrinos and $|\langle m_{\nu_h}^{-1}\rangle|^{-1}>3.065\times 10^8~\mathrm{GeV}$ for heavy neutrinos., Comment: 24 pages, 4 figures