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As a microscopic quantal many-body system, the structure of atomic nucleus is understood by measuring and interpreting its responses to all kinds of probes. The responses manifest in different kind...

The second-phonon ( n ω = 2 ) wobbling band has been established in the nucleus 135Pr. Conclusive evidence for its wobbling nature comes from the Δ I = 1 , E2 character of the transitions between the new band and the previously identified transverse wobbler band ( n ω = 1 ) in this nucleus. Theoretical calculations in the framework of the quasiparticle triaxial rotor and triaxial projected shell models are found to be in good agreement with the experimental results.

The $g$-factor and static quadrupole moment of the nuclides $^{135}$Pr, $^{105}$Pd, and $^{187}$Au in the wobbling motion are investigated in the particle-rotor model as functions of the total spin $I$. The $g$-factor of $^{105}\mathrm{Pd}$ increases with increasing $I$, due to the negative gyromagnetic ratio of a neutron valence-neutron. This behavior is in contrast to the decreasing $g$-factor of the other two nuclides, $^{135}$Pr and $^{187}$Au, which feature a valence-proton. The static quadrupole moment $Q$ depends on all three expectation values of the total angular momentum. It is smaller in the yrast band than in the wobbling band for the transverse wobblers $^{135}$Pr and $^{105}$Pd, while larger for the longitudinal wobbler $^{187}$Au., Comment: 6 pages, 4 figures

New transitions in neutron rich $^{100}$Y have been identified in a $^9$Be+$^{238}$U experiment with mass- and Z- gates to provide full fragment identification. These transitions and high spin levels of $^{100}$Y have been investigated by analyzing the high statistics $\gamma$-$\gamma$-$\gamma$ and $\gamma$-$\gamma$-$\gamma$-$\gamma$ coincidence data from the spontaneous fission of $^{252}$Cf at the Gammasphere detector array. Two new bands, 14 new levels and 23 new transitions have been identified. The $K^{\pi}=4^+$ new band decaying to an 1s isomeric state is assigned to be the high-$K$ Gallagher-Moszkowski (GM) partner of the known $K^{\pi}=1^+$ band, with the $\pi 5/2[522] \otimes \nu 3/2[411]$ configuration. This 4$^+$ band is also proposed to be the pseudo spin partner of the new $K^{\pi}=5^+$ band with a 5$^{+}$ $\pi 5/2[422] \otimes \nu 5/2[413]$ configuration, to form a $\pi 5/2[422] \otimes \nu [312$ $5/2,3/2]$ neutron pseudospin doublet. Constrained triaxial covariant density functional theory and quantal particle rotor model calculations have been applied to interpret the band structure and available electromagnetic transition probabilities and are found in good agreement with experimental values.

The yrast lines in Kr isotopes with $N=42$, 44, and 46 are investigated in a beyond mean field framework with both prolate-oblate coexistence and quasiparticle alignment taken into account. Quasiparticle orbitals with high-$j$ and low-$\Omega$ on the oblate side are shown to be responsible for the sharp backbending observed in $^{82}$Kr, by driving the yrast shape from prolate to oblate. This suggests that quasiparticle alignment may not be neglected in the investigation of the shape evolution along the yrast line., Comment: 6 pages, 5figiures

We report the first observation of two wobbling bands in ^{183}Au, both of which were interpreted as the transverse wobbling (TW) band but with different behavior of their wobbling energies as a function of spin. It increases (decreases) with spin for the positive (negative) parity configuration. The crucial evidence for the wobbling nature of the bands, dominance of the E2 component in the ΔI=1 transitions between the partner bands, is provided by the simultaneous measurements of directional correlation from the oriented states ratio and the linear polarization of the γ rays. Particle rotor model calculations with triaxial deformation reproduce the experimental data well. A value of spin, I_{m}, has been determined for the observed TW bands below which the wobbling energy increases and above which it decreases with spin. The nucleus ^{183}Au is, so far, the only nucleus in which both the increasing and the decreasing parts are observed and thus gives the experimental evidence of the complete transverse wobbling phenomenon.

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 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 the bands B2 and B2a. Hence, it coexists with the aplanar rotation in the other doublet bands B4 and B4a in $^{195}$Tl., Comment: 7 pages, 5 figures. arXiv admin note: text overlap with arXiv:1904.12100

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

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 odd–even and even-even nuclei presenting multiple chiral bands in the Segré chart. 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 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 136Nd. The experimental energy spectra and available B ( M 1 ) / B ( E 2 ) 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, 136Nd 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.

The heavy ion fusion–evaporation reaction study for the high-spin spectroscopy of 75As has been performed via the reaction channel 70Zn(9Be, 1p3n)75As at a beam energy of 42 MeV. The collective structure especially a dipole band in 75As is established for the first time. The properties of this dipole band are investigated in terms of the self-consistent tilted axis cranking covariant density functional theory. Based on the theoretical description and the examination of the angular momentum components, this dipole band can be interpreted as a novel stapler band, where the valence neutrons in ( 1 g 9 / 2 ) orbital rather than the collective core are responsible for the closing of the stapler of angular momentum.

CITATION: Li, C. G. et al. 2019. “Stapler” mechanism for a dipole band in 79Se. Physical Review C, 100(4). doi:10.1103/PhysRevC.100.044318

The structure of the odd-$A$ isotopes $^{193,195,197}\mathrm{Pt}$, which lie along the line of stability, has been studied up to high spin through multinucleon transfer reactions. Positive- and negative-parity sequences in $^{193,195}\mathrm{Pt}$ have been considerably extended and multiple band crossings established. An isomer with ${T}_{1/2}=5.0(5)$ ns and ${I}^{\ensuremath{\pi}}=25/{2}^{\ensuremath{-}}$ is present in $^{195}\mathrm{Pt}$. The isotopes $^{193,195}\mathrm{Pt}$ are characterized by moderate oblate deformation, and angular momentum generation at high spin in the yrast, positive-parity sequences is attributed to the rotation alignment of ${i}_{13/2}$ neutrons and ${h}_{11/2}$ protons. A detailed understanding of the observed features is presented using calculations based on tilted axis cranking covariant density functional theory as well as others with the ultimate cranker code.

The nuclear chiral conundrum with crossing twin bands is investigated with three-dimensional tilted axis cranking covariant density functional theory in a fully self-consistent and microscopic way. The energy spectra and electromagnetic transition strengths for bands 1 and 2 in Ag-106 are well reproduced with two distinct configurations with two and four quasiparticles, respectively. For the four-quasiparticle configuration, a chiral vibrational band on top of band 2 is expected due to the soft Routhian curves. Therefore, it provides a microscopic and solid solution for the chiral conundrum in Ag-106. It also paves the way for understanding similar chiral structure in other nuclei in the future..

New rotational bands built on the ν(h_{11/2}) configuration have been identified in ^{105}Pd. Two bands built on this configuration show the characteristics of transverse wobbling: the ΔI=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∼100 mass region.

The band built on the Kπ = 8−, T1/2 = 9.4 ms isomer of 130Ba has been identified, filling the gap in the systematics of the dipole bands built on the 8− isomers in the N = 74 isotones from 128Xe to 138Gd. The use of the GALILEO array in conjunction with its ancillaries EUCLIDES and Neutron Wall, helped to firmly place the newly identified transitions on top of the long-lived isomer. The extracted gK and gR gyromagnetic factors are in agreement with the 7/2+[404] ⊗ 9/2−[514] two-neutron Nilsson configuration. Particle-rotor model calculations give an understanding of the limited degree of K mixing. The experimental information on the Kπ = 8− isomer of 130Ba is now the most complete among the K isomers of the N = 74 isotones.

Two new bands built on the two-quasiparticle $\pi(h_{11/2})^2$ configuration of the even-even nucleus $^{130}$Ba are investigated using constrained triaxial covariant density functional theory combined with quantum particle rotor model calculations. The energy difference between the two bands, as well as the available electromagnetic transition probabilities $B(M1)_{\textrm{out}}/B(E2)_{\textrm{in}}$ and $B(E2)_{\textrm{out}}/B(E2)_{\rm{in}}$, are well reproduced. The analysis of the angular momentum geometry reveals that the higher band represents transverse wobbling motion of a two-quasiparticle configuration. This is the first example of two-quasiparticle wobbling bands in an even-even nucleus., Comment: 5 pages, 4 figures

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

Several new bands have been identified in 130Ba, among which there is one with band-head spin 8+. Its properties are in agreement with the Fermi-aligned \nu h11/2^2 , 7/2+[523] \otimes 9/2-[514] Nilsson configuration. This is the first observation of a two-quasiparticle t-band in the A=130 mass region. The t-band is fed by a dipole band involving two additional h11/2 protons. The odd-spin partners of the proton and neutron S-bands and the ground-state band at high spins are also newly identified. The observed bands are discussed using several theoretical models, which strongly suggest the coexistence of prolate and oblate shapes polarized by rotation aligned two-proton and two-neutron configurations, as well as prolate collective rotations around axes with different orientations. With the new results, 130Ba presents one of the best and most complete sets of collective excitations that a gamma-soft nucleus can manifest at medium and high spins, revealing a diversity of shapes and rotations for the nuclei in the A = 130 mass region., Comment: 8 pages, 7 figures

The influence of triaxial deformation γ on the purely collective form of wobbling motion in even–even nuclei is discussed based on the triaxial rotor model. It is found that the harmonic approximation is realized well when the value γ = 30° is adopted for the properties of energy spectra and electric quadrupole transition probabilities, while this approximation gets worse when γ gradually deviates from 30°. Recent data from a Coulomb excitation experiment, namely 3 1 + and 2 2 + for 110Ru, are studied and might be suggested as the bandhead of the wobbling bands. In addition, two types of angular momentum geometries for wobbling motion, stemming from different γ values, are exhibited by the azimuthal plots.

The three-dimensional tilted axis cranking covariant density functional theory (3D-TAC CDFT) is used to study the chiral modes in $^{135}$Nd. By modeling the motion of the nucleus in rotating mean field as the interplay between the single-particle motions of several valence particle(s) and hole(s) and the collective motion of a core-like part, a classical Routhian is extracted. This classical Routhian gives qualitative agreement with the 3D-TAC CDFT result for the critical frequency corresponding to the transition from planar to aplanar rotation. Based on this investigation a possible understanding of tilted rotation appearing in a microscopic theory is provided., Comment: 6 pages, 4 figures

Solid experimental evidence for triaxial nuclear shape is difficult to obtain and is quite rare. Such evidence can be provided by the phenomena of chiral rotation and wobbling motion, as these can occur only in triaxially deformed nuclei. Although nuclear chirality is well documented in different mass regions, experimental evidence for multiple chiral bands as well as for wobbling motion has been reported so far only in a few nuclei. Pd and Rh nuclei in the A ≈ 100 mass region have been recently studied, and transverse wobbling motion as well as multiple chiral band structures were identified for the first time in this region. These observations provide experimental evidence for the predicted triaxial shape in this mass region, and new data which enable a better understanding of the studied phenomena.

The nuclear multiple chirality in $A\sim60$ mass region is explored by the adiabatic and configuration-fixed constrained covariant density functional theory for cobalt isotopes. The potential-energy curves and triaxiality parameters $\gamma$ as functions of the deformation parameter $\beta$ in $^{54,56,57,58,59,60}$Co are obtained. It is found that there are high-$j$ particle(s) and hole(s) configurations with prominent triaxially deformed shapes in these isotopes. This points towards that the existence of chirality or multiple chirality in $A\sim60$ mass region are highly anticipated., Comment: 13 pages, 5 figures, 1 table, accepted by Phys. Rev. C

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

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$\approx$130 nuclei with the valence h$_{11/2}$ proton particle, valence h$_{11/2}$ neutron hole and the maximum difference between principle axes allowed by the quadrupole deformation of the mean field. It is concluded that at each spin value the higher-energy member of a doublet of states is built on the anti-symmetric combination of $|\mathcal{L}\rangle$ and $|\mathcal{R}\rangle$ and is free of the $|\mathcal{P}\rangle$ component, indicating that it is of pure chiral geometry. For the lower-energy member of the doublet, the contribution of the $|\mathcal{P}\rangle$ component to the eigenfunction first decreases and then increases as a function of the total spin. This trend as well as the energy splitting between the doublet states are both determined by the Hamiltonian matrix elements between the planar ($|\mathcal{P}\rangle$) and non-planar ($|\mathcal{L}\rangle$ and $|\mathcal{R}\rangle$) subspaces of the full Hilbert space., 12 pages, 5 figures, accepted as a Rapid Communication in Physical Review C

Five-dimensional collective Hamiltonian based on the covariant density functional theory has been applied to study the the low-lying states of even-even $^{148-162}$Gd isotopes. The shape evolution from $^{148}$Gd to $^{162}$Gd is presented. The experimental energy spectra and intraband $B(E2)$ transition probabilities for the $^{148-162}$Gd isotopes are reproduced by the present calculations. The relative $B(E2)$ ratios in present calculations are also compared with the available interacting boson model results and experimental data. It is found that the occupations of neutron $1i_{13/2}$ orbital result in the well-deformed prolate shape, and are essential for Gd isotopes., 11pages, 10figures

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 $^{60}\mathrm{Fe}$ are investigated and analyzed. Without introducing any 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 band crossing is due to the change of the last two occupied neutrons from the $1{f}_{5/2}$ signature partners to the $1{g}_{9/2}$ signature partners. For the two negative-parity signature partner bands B and C, the band crossings are due to the pseudocrossing between the $1{f}_{7/2,5/2}$ and the $1{f}_{5/2,1/2}$ orbitals. Generally speaking, the deformation parameters $\ensuremath{\beta}$ for bands A, B, and C decrease with rotational frequency. For band A, the deformation jumps from $\ensuremath{\beta}\ensuremath{\approx}0.19$ to $\ensuremath{\beta}\ensuremath{\approx}0.29$ around the band crossing. In comparison with its signature partner band C, band B exhibits appreciable triaxial deformation.

The $g$ factor of the 56 ns half-life isomeric state in $^{128}\mathrm{Cs}$ has been measured using the time-differential perturbed angular distribution method. This state is the bandhead of the positive-parity chiral rotational band, which emerges when an unpaired proton, an unpaired neutron hole, and an even-even core are coupled such that their angular momentum vectors are aplanar (chiral configuration). $g$-factor measurements can give important information on the relative orientation of the three angular momentum vectors. The measured $g$ factor $g=+0.59(1)$ shows that there is an important contribution of the core rotation in the total angular momentum of the isomeric state. Moreover, a quantitative theoretical analysis supports the conclusion that the three angular momentum vectors lie almost in one plane, which suggests that the chiral configuration in $^{128}\mathrm{Cs}$ demonstrated in previous works by characteristic patterns of electromagnetic transitions appears only above some value of the total nuclear spin.

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

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 behavior of the collective rotor in wobbling motion is investigated within the particle-rotor model for the nucleus $^{135}$Pr by transforming the wave functions from the $K$-representation to the $R$-representation. After reproducing the experimental energy spectra and wobbling frequencies, the evolution of the wobbling mode in $^{135}$Pr, from transverse at low spins to longitudinal at high spins, is illustrated by the distributions of the total angular momentum in the intrinsic reference frame (azimuthal plot). Finally, the coupling schemes of the angular momenta of the rotor and the high-$j$ particle for transverse and longitudinal wobbling are obtained from the analysis of the probability distributions of the rotor angular momentum ($R$-plots) and their projections onto the three principal axes ($K_R$-plots)., Comment: 21 pages, 9 pages

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

Coexistence of different geometric shapes at low energies presents a universal structure phenomenon that occurs over the entire chart of nuclides. Studies of the shape coexistence are important for understanding the microscopic origin of collectivity and modifications of shell structure in exotic nuclei far from stability. The aim of this work is to provide a systematic analysis of characteristic signatures of coexisting nuclear shapes in different mass regions, using a global self-consistent theoretical method based on universal energy density functionals and the quadrupole collective model. The low-energy excitation spectrum and quadrupole shape invariants of the two lowest $0^{+}$ states of even-even nuclei are obtained as solutions of a five-dimensional collective Hamiltonian (5DCH) model, with parameters determined by constrained self-consistent mean-field calculations based on the relativistic energy density functional PC-PK1, and a finite-range pairing interaction. The theoretical excitation energies of the states: $2^+_1$, $4^+_1$, $0^+_2$, $2^+_2$, $2^+_3$, as well as the $B(E2; 0^+_1\to 2^+_1)$ values, are in very good agreement with the corresponding experimental values for 621 even-even nuclei. Quadrupole shape invariants have been implemented to investigate shape coexistence, and the distribution of possible shape-coexisting nuclei is consistent with results obtained in recent theoretical studies and available data. The present analysis has shown that, when based on a universal and consistent microscopic framework of nuclear density functionals, shape invariants provide distinct indicators and reliable predictions for the occurrence of low-energy coexisting shapes. This method is particularly useful for studies of shape coexistence in regions far from stability where few data are available., 13 pages, 3 figures, accepted for publication in Phys. Rev. C

A two-dimensional collective Hamiltonian (2DCH) on both azimuth and polar motions in triaxial nuclei is proposed to investigate the chiral and wobbling modes. In the 2DCH, the collective potential and the mass parameters are determined from three-dimensional tilted axis cranking (TAC) calculations. The broken chiral and signature symmetries in the TAC solutions are restored by the 2DCH. The validity of the 2DCH is illustrated with a triaxial rotor ($\gamma=-30^\circ$) coupling to one $h_{11/2}$ proton particle and one $h_{11/2}$ neutron hole. By diagonalizing the 2DCH, the angular momenta and energy spectra are obtained. These results agree with the exact solutions of the particle rotor model (PRM) at high rotational frequencies. However, at low frequencies, the energies given by the 2DCH are larger than those by the PRM due to the underestimation of the mass parameters. In addition, with increasing angular momentum, the transitions from the chiral vibration to chiral rotation and further to longitudinal wobbling motion have been presented in the 2DCH., Comment: 30 pages, 12 figures

High-spin states in $^{155}\mathrm{Yb}$ have been studied via the $^{144}\mathrm{Sm}(^{16}\mathrm{O},5n)^{155}\mathrm{Yb}$ reaction at a beam energy of 118 MeV. One negative-parity and one positive-parity cascade built on the $\ensuremath{\nu}{f}_{7/2}$ and $\ensuremath{\nu}{i}_{13/2}$ states, respectively, are established for the first time. The structures observed in $^{155}\mathrm{Yb}$ are compared with those in the neighboring $N=85$ isotones and with semiempirical shell-model (SESM) calculations. According to adiabatic and configuration-fixed constrained triaxial covariant density functional theory (CDFT) calculations, a coexistence of prolate and oblate shapes is predicted to exist in $^{155}\mathrm{Yb}$.

The five-dimensional collective Hamiltonian based on the covariant density functional theory is applied to investigate the observed tidal wave mode in the yrast band of $^{102}\mathrm{Pd}$. The energy spectra, the relations between the spin and the rotational frequency, and the ratios of $B(E2)/\mathcal{J}(I)$ in the yrast band are well reproduced by introducing the empirical $ab$ formula for the moments of inertia. This $ab$ formula is related to the fourth order effect of collective momentum in the collective Hamiltonian. It is also shown that the shape evolution in the tidal wave is determined microscopically by the competition between the rotational kinetic energy and the collective potential in the framework of the collective Hamiltonian.

The structure of $^{133}\text{La}$ has been investigated using the $^{116}\text{Cd}(^{22}\text{Ne},4pn)$ reaction and the Gammasphere array. Three new bands of quadrupole transitions and one band of dipole transitions are identified and the previously reported level scheme is revised and extended to higher spins. The observed structures are discussed using the cranked Nilsson-Strutinsky formalism, covariant density functional theory, and the particle-rotor model. Triaxial configurations are assigned to all observed bands. For the high-spin bands it is found that rotations around different axes can occur, depending on the configuration. The orientation of the angular momenta of the core and of the active particles is investigated, suggesting chiral rotation for two nearly degenerate dipole bands and magnetic rotation for one dipole band. It is shown that the ${h}_{11/2}$ neutron holes present in the configuration of the nearly degenerate dipole bands have significant angular momentum components not only along the long axis but also along the short axis, contributing to the balance of the angular momentum components along the short and long axes and thus giving rise to a chiral geometry.

Two pairs of positive-and negative-parity doublet bands together with eight strong electric dipole transitions linking their yrast positive- and negative-parity bands have been identified in ^{78}Br. They are interpreted as multiple chiral doublet bands with octupole correlations, which is supported by the microscopic multidimensionally-constrained covariant density functional theory and triaxial particle rotor model calculations. This observation reports the first example of chiral geometry in octupole soft nuclei.

WOS: 000371740600004, Lifetimes of excited states in the neutron-deficient odd-odd nucleus Re-166 have been measured for the first time using the recoil distance Doppler-shift method. The measured lifetime for the (8(-)) state; tau = 480 (80) ps, enabled an assessment of the multipolarities of the gamma rays depopulating this state. Information on electromagnetic transition strengths were deduced for the gamma-ray transitions from the (9(-)), (10(-)), and (11(-)) states, and in the case of the (10(-)) and (11(-)) states limits on the B (M1) and B(E2) strengths were estimated. The results are compared with total Routhian surface predictions and semiclassical calculations. Tilted-axis cranking calculations based on a relativistic mean-field approach (TAC-RMF) have also been performed in order to test the possibility of magnetic rotation in the 166Re nucleus. While the TAC-RMF calculations predict a quadrupole-deformed nuclear shape with similar beta(2) deformation as obtained by using the TRS model, it was found that the experimental electromagnetic transition rates are in better agreement with a collective -rotational description., Swedish Research CouncilSwedish Research Council [621-2010-3694]; Academy of Finland under the Finnish Centre of Excellence ProgrammeAcademy of Finland; UK Science and Technology Facilities CouncilScience & Technology Facilities Council (STFC); European UnionEuropean Union (EU) [262010]; China Scholarship CouncilChina Scholarship Council [201306210205]; Academy of FinlandAcademy of Finland [131665]; Science and Technology Facilities CouncilScience & Technology Facilities Council (STFC) [ST/L005670/1, EP/E004385/1, ST/L005689/1, ST/G008671/1, ST/J000094/1, EP/C015266/1], The authors would like to thank the staff at the Accelerator Laboratory of the University of Jyvaskyla for their excellent technical support. This work was supported by the Swedish Research Council (Project No. 621-2010-3694), the Academy of Finland under the Finnish Centre of Excellence Programme 2012 - 2017, the UK Science and Technology Facilities Council, and the European Union Seventh Framework Programme Integrating Activities-Transnational Access, Project No. 262010 (ENSAR). Li is supported in part by the China Scholarship Council under Grant No. 201306210205. Additionally, we thank the GAMMAPOOL European Spectroscopy Resource for the loan of the detectors for JUROGAM II array. T.G. acknowledges the support from the Academy of Finland (Contract No. 131665).

The spectroscopy of $^{76}\mathrm{Se}$ has been studied using the $^{70}\mathrm{Zn}(^{12}\mathrm{C}, \ensuremath{\alpha}2{\mathrm{n})}^{76}\mathrm{Se}$ fusion evaporation reaction. The yrast band of $^{76}\mathrm{Se}$ has been extended to substantially higher spin, allowing observation of the second band crossing. The much-delayed ${g}_{9/2}$ proton-pair alignment is discussed in terms of the cranked shell model and most likely is caused by a shape transition from prolate to oblate along the yrast line occurring in $^{76}\mathrm{Se}$. Based on the systematic investigation of the band crossings associated with the ${g}_{9/2}$ quasiparticle alignments and their relationships with the shape evolutions in the even-$A$ Se and Kr isotopes, a comprehensive picture of shape evolution along with spin and isospin in these nuclei is obtained.

The spectroscopy properties and angular momentum geometry for the wobbling motion of a simple triaxial rotor are investigated within the triaxial rotor model up to spin $I=40\hbar$. The obtained exact solutions of energy spectra and reduced quadrupole transition probabilities are compared to the approximate analytic solutions by harmonic approximation formula and Holstein-Primakoff formula. It is found that the low lying wobbling bands can be well described by the analytic formulas. The evolution of the angular momentum geometry as well as the $K$-distribution with respect to the rotation and the wobbling phonon excitation are studied in detail. It is demonstrated that with the increasing of wobbling phonon number, the triaxial rotor changes its wobbling motions along the axis with the largest moment of inertia to the axis with the smallest moment of inertia. In this process, a specific evolutionary track that can be used to depict the motion of a triaxial rotating nuclei is proposed., 10 pages, 8 figures, submitted to Chinese Physics C