Two newly observed bands built on a two-quasiparticle configuration in 130Ba have been investigated for the first time with the microscopic projected shell model. The experimental energy spectra and the available electromagnetic transition probabilities are well reproduced. The wobbling character of the higher band is revealed by the angular momentum projected wavefunctions via the K plot and the azimuthal plot. This provides the first strong microscopic evidence for wobbling motion based on a two-quasiparticle configuration in even-even nuclei.
The wobbling motion of a triaxial rotor coupled to a high-j quasiparticle is treated semiclassi- cally. Longitudinal and transverse coupling regimes can be distinguished depending on, respectively, whether the quasiparticle angular momentum is oriented parallel or perpendicular to the rotor axis with the largest moment of inertia. Simple analytical expressions for the wobbling frequency and the electromagnetic E2 and M1 transition probabilities are derived assuming rigid alignment of the quasiparticle with one of the rotor axes and harmonic oscillations (HFA). Transverse wobbling is characteri…
The quasiparticle random phase approximation is used to study the properties of the wobbling bands in $^{163}$Lu. Assuming that the wobbling mode represents pure isoscalar orientation oscillations results in too low wobbling frequencies and too strong M1 transitions between the one- and zero-phonon wobbling bands. The inclusion of an LL interaction, which couples the wobbling mode to the scissors mode, generates the right upshift of the wobbling frequencies and the right suppression of the B(M1)$_{out}$ values toward the experimental values. In analogy to the quenching of low-energy E1 transit…
The three moments of inertia associated with the wobbling mode built on the triaxial superdeformed states in Lu--Hf region are investigated by means of the cranked shell model plus random-phase approximation to the configurations with aligned quasiparticle(s). The result indicates that it is crucial to take into account the direct contribution to the moments of inertia from the aligned quasiparticle(s) so as to realize \mathcal{J}_x > \mathcal{J}_y in positive-γshapes.
The three moments of inertia associated with the wobbling mode built on the superdeformed states in 163Lu are investigated by means of the cranked shell model plus random phase approximation to the configuration with an aligned quasiparticle. The result indicates that it is crucial to take into account the direct contribution to the moments of inertia from the aligned quasiparticle so as to realize J_x > J_y in positive-gamma shapes. Quenching of the pairing gap cooperates with the alignment effect. The peculiarity of the recently observed 163Lu data is discussed by calculating not only the el…
Two new bands built on the two-quasiparticle $π(h_{11/2})^2$ 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-quasipartic…
The existence of one-phonon and possible two-phonon transverse wobbling bands is proposed for the first time in two even-even nuclei, $^{134}$Ce and $^{136}$Nd. The predominant $E2$ character of the $ΔI = 1$ transitions connecting the one-phonon wobbling band in $^{134}$Ce to the two-quasiparticle yrast band supports the wobbling interpretation. The extracted wobbling frequencies decrease with increasing spin, indicating the transverse character of the wobbling motion, with the angular momenta of the two quasiparticles aligned perpendicular to the axis of collective rotation. A candidate for t…
A pair of transverse wobbling bands has been observed in the nucleus $^{135}$Pr. The wobbling is characterized by $ΔI$ =1, E2 transitions between the bands, and a decrease in the wobbling energy confirms its transverse nature. Additionally, a transition from transverse wobbling to a three-quasiparticle band comprised of strong magnetic dipole transitions is observed. These observations conform well to results from calculations with the Tilted Axis Cranking (TAC) model and the Quasiparticle Triaxial Rotor (QTR) Model.
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 rotational band built on the high-K multi-quasiparticle state can be interpreted as a multi-phonon band of the precession mode, which represents the precessional rotation about the axis perpendicular to the direction of the intrinsic angular momentum. By using the axially symmetric limit of the random-phase-approximation (RPA) formalism developed for the nuclear wobbling motion, we study the properties of the precession modes in $^{178}$W; the excitation energies, B(E2) and B(M1) values. We show that the excitations of such a specific type of rotation can be well described by the RPA forma…
Rotation of triaxially deformed nucleus has been an interesting subject in the study of nuclear structure. In the present series of work, we investigate wobbling motion and chiral rotation by employing the microscopic framework of angular-momentum projection from cranked triaxially deformed mean-field states. In this first part the wobbling motion is studied in detail. The consequences of the three dimensional cranking are investigated. It is demonstrated that the multiple wobbling rotational bands naturally appear as a result of fully microscopic calculation. They have the characteristic prop…
Excited states of $^{133}$La have been investigated to search for the wobbling excitation mode in the low-spin regime. Wobbling bands with $n_ω$ = 0 and 1 are identified along with the interconnecting $ΔI$ = 1, $E2$ transitions, which are regarded as one of the characteristic features of the wobbling motion. An increase in wobbling frequency with spin implies longitudinal wobbling for $^{133}$La, in contrast with the case of transverse wobbling observed in $^{135}$Pr. This is the first observation of a longitudinal wobbling band in nuclei. The experimental observations are accounted for by cal…
A particle-triaxial rigid core Hamiltonian is semi-classically treated. The coupling term corresponds to a particle rigidly coupled to the triaxial core, along a direction that does not belong to any principal plane of the inertia ellipsoid.The equations of motion for the angular momentum components provide a sixth-order algebraic equation for one component and subsequently equations for the other two. Linearizing the equations of motion, a dispersion equation for the wobbling frequency is obtained. The equations of motion are also considered in the reduced space of generalized phase space coo…
The wobbling spectrum of $^{163}$Lu is described through a novel approach, starting from a triaxial rotor model within a semi-classical picture, and obtaining a new set of equations for all four rotational bands that have wobbling character. Redefining the band structure in the present model is done by adopting the concepts of Signature Partner Bands and Parity Partner Bands. Indeed, describing a wobbling spectrum in an even-odd nucleus through signature and parity quantum numbers is an inedited interpretation of the triaxial super-deformed bands.
Evolution of chirality from transverse wobbling in $^{135}$Pr
University of Notre Dame（圣母大学）；University of North Carolina Chapel Hill（北卡罗来纳大学教堂山分校）；Triangle Universities Nuclear Laboratory, Duke University（杜克大学三角大学核实验室）；East China Normal University（华东师范大学）；National Nuclear Data Center, Brookhaven National Laboratory（布鲁克海文国家实验室国家核数据中心）；Argonne National Laboratory（阿贡国家实验室）
The rare phenomenon of nuclear wobbling motion has been investigated for the nucleus $^{187}$Au. A longitudinal wobbling-bands pair has been identified and clearly distinguished from the associated signature-partner band on the basis of angular distribution measurements. Theoretical calculations in the framework of the Particle Rotor Model (PRM) are found to agree well with the experimental observations. This is the first experimental evidence for longitudinal wobbling bands where the expected signature partner band has also been identified, and establishes this exotic collective mode as a gen…
Novel chiral-wobbling excitation mode in atomic nuclei
Islamic University of Science and Technology（伊斯兰科学技术大学）；University of Kashmir（克什米尔大学）；Institute of Physics (IOP)（物理研究所（IOP））；Homi Bhabha National Institute（霍米·巴巴国家研究所）；Government Degree College Shopian（肖皮安政府学位学院）；Government Degree College Kulgam（库尔加姆政府学位学院）；Shandong University（山东大学）
The high-spin rotational properties of two-quasiparticle bands in the doubly-odd ${}^{166}$Ta are analyzed using the cranked shell model with pairing correlations treated by a particle-number conserving method, in which the blocking effects are taken into account exactly. The experimental moments of inertia and alignments and their variations with the rotational frequency $\hbarω$ are reproduced very well by the particle-number conserving calculations, which provides a reliable support to the configuration assignments in previous works for these bands. The backbendings in these two-quasipartic…
Predictions of the spectroscopic properties of low-lying states are critical for nuclear structure studies, but are problematic for nuclei with an odd nucleon due to the interplay of the unpaired single particle with nuclear collective degrees of freedom. In this work, a microscopic core-quasiparticle coupling (CQC) model based on the covariant density functional theory is developed that contains the collective excitations of even-mass cores and spherical single-particle states of the odd nucleon as calculated from a quadrupole collective Hamiltonian combined with a constrained triaxial relati…
The Thermal Quasiparticle Random-Phase Approximation is combined with the Skyrme energy density functional method (Skyrme-TQRPA) to study the response of a hot nucleus to an external perturbation. For the sample nuclei, $^{56}$Fe and $^{82}$Ge, the Skyrme-TQRPA is applied to analyze thermal effects on the strength function of charge-neutral Gamow-Teller transitions which dominate neutrino-nucleus reactions at $E_ν\lesssim 20$~MeV. For the relevant supernova temperatures we calculate the cross sections for inelastic neutrino scattering. We also apply the method to examine the rate of neutrino-a…
Inclusive neutrino-nucleus cross sections are calculated using a consistent relativistic mean-field theoretical framework. The weak lepton-hadron interaction is expressed in the standard current-current form, the nuclear ground state is described with the relativistic Hartree-Bogoliubov model, and the relevant transitions to excited nuclear states are calculated in the relativistic quasiparticle random phase approximation. Illustrative test calculations are performed for charged-current neutrino reactions on $^{12}$C, $^{16}$O, $^{56}$Fe, and $^{208}$Pb, and results compared with previous stud…
The odd $A$ proton drip line nucleus $^{17}$F has been studied in a semi-microscopic model which couples proton quasiparticle motion to the vibrational motion of the neighbouring even-even $^{18}$Ne core. The experimentally observed low lying excitation spectrum, electric quadrupole moment, magnetic dipole moment, $B(E1)$ and $B(E2)$ values have been fairly well reproducd. The calculated rms radius of the first excited state is well reproduced and is found to be larger than that of the ground state which agrees with the experimental observation.
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…
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},…
An enhanced model, based on the Extended Boson Approximation, for the lowest-lying states in odd-mass nuclei is presented. Our approach is built on the Quasiparticle Phonon Model, extending it to take into account the ground state correlations due to the action of the Pauli principle more accurately than in the conventional theory. The derived interaction strengths between the quasiparticles and the phonons in this model depend on the quasiparticle occupation numbers explicitly coupling the odd-mass nucleus equations with those of the even-even core. Within this model we calculated the transit…
It has been debated whether the experimentally-identified superdeformed rotational band in $^{40}$Ar [E. Ideguchi, et al., Phys. Lett. B 686 (2010) 18] has an axially or triaxially deformed shape. Projected shell model calculations with angular-momentum-projection using an axially-deformed basis are performed up to high spins. Our calculated energy levels indicate a perfect collective-rotor behavior for the superdeformed yrast band. However, detailed analysis of the wave functions reveals that the high-spin structure is dominated by mixed 0-, 2-, and 4-quasiparticle configurations. The calcula…
A computer code for quasiparticle random phase approximation-QRPA and projected quasiparticle random phase approximation-PQRPA models of nuclear structure is explained in details. An important application of the code consists in evaluating nuclear matrix elements involved in neutrino-nucleus reactions. As an example, cross section for 56Fe and 12C are calculated and the code output is explained. The application to other nuclei and the description of other nuclear and weak decay processes is also discussed.
The microscopic origin of the $γ$-softness (fluctuations in the triaxiality parameter $γ$ of the nuclear shape) observed in atomic nuclei is studied in the framework of the triaxial projected shell model approach, which is based on the deformed mean-field picture with multi-quasiparticle configuration space. It is demonstrated that the coupling to quasiparticle excitations drives the system from a $γ$-rigid to a $γ$-soft pattern. As an illustrative example for a $γ$-soft nucleus, a detailed study has been performed for the $^{104}$Ru nucleus. The experimental energies and a large sample of mea…
Band structure properties of $^{182}$Os are investigated through a particle number and angular momentum constrained generator coordinate(GCM) calculation based on self-consistent three-dimensional cranking solutions. From the analysis of the wave function of the lowest GCM solution, we confirm that this nucleus shows a tilted rotational motion in its yrast states, at least with the present set of force parameters of the pairing-plus-quadrupole interaction Hamiltonian. A close examination of behavior of other GCM solutions reveals a sign of a possible occurrence of multi-band crossing in the nu…
Inclusion of time-odd components into the wave function is important for reliable description of rotational motion by the angular-momentum-projection method; the cranking procedure with infinitesimal rotational frequency is an efficient way to realize it. In the present work we investigate the effect of this infinitesimal cranking for triaxially deformed nucleus, where there are three independent cranking axes. It is found that the effects of cranking about three axes on the triaxial energy spectrum are quite different and inclusion of all of them considerably modify the resultant spectrum fro…
Background: The coupling of the last nucleon with configurations in the ground state of the even-even core is known to augment the single quasiparticle fragmentation pattern. In a recent experimental study by Yordanov \emph{et al.} the values of the magnetic dipole and electric quadrupole moments of the $11/2^-$ state in a long chain of Cd isotopes were found to follow a simple trend which we try to explain by means of incorporating long-range correlations in the ground state. Purpose: Our purpose is to study the influence of the ground-state correlations (GSC) on the magnetic moments and comp…
Probing the two-quasiparticle $K^π=8^+$ isomeric structure and enhanced stability in the proton drip-line nuclei
School of Physics, Zhengzhou University（郑州大学物理学院）；Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所高精度核谱学重点实验室）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）
An outstanding problem in the theory of nuclear fission is to understand the Hamiltonian dynamics at the scission point. In this work the fissioning nucleus is modeled in self-consistent mean-field theory as a set of Generator Coordinate (GCM) configurations passing through the scission point. In contrast to previous methods, the configurations are constructed in the Hartree-Fock approximation with axially symmetric mean fields and using the K-partition numbers as additional constraints. The goal of this work is to find paths through the scission point where the overlaps between neighboring co…
A systematic study of 2-quasiparticle bands of the proton-rich odd-odd nuclei in the mass A ~ 70-80 region is performed using the projected shell model approach. The study includes Br-, Rb-, and Y-isotopes with N = Z+2, and Z+4. We describe the energy spectra and electromagnetic transition strengths in terms of the configuration mixing of the angular-momentum projected multi-quasiparticle states. Signature splitting and signature inversion in the rotational bands are discussed and are shown to be well described. A preliminary study of the odd-odd N = Z nucleus, 74Rb using the concept of sponta…
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…
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 νh11/2^2 , 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 coexist…
Recent experimental data have demonstrated that $^{76}$Ge may be a rare example of a nucleus exhibiting rigid $γ$-deformation in the low-spin regime. In the present work, the experimental analysis is supported by microscopic calculations using the multi-quasiparticle triaxial projected shell model (TPSM) approach. It is shown that to best describe the data of both yrast and $γ$-vibrational bands in $^{76}$Ge, a rigid-triaxial deformation parameter $γ\approx 30^\circ$ is required. TPSM calculations are discussed in conjunction with the experimental observations and also with the published resul…
High-spin states in the doubly-odd $^{198}$Bi nucleus have been studied by using the $^{185,187}$Re($^{16}$O, xn) reactions at the beam energy of 112.5 MeV. $γ-γ$ coincidence were measured by using the INGA array with 15 Compton suppressed clover HPGe detectors. The observed levels have been assigned definite spin-parity. The high spin structure is grouped into three bands (B1, B2 and B3), of which two (B1 and B2) exhibit the properties of magnetic rotation (MR). Tilted axis cranking calculations were carried out to explain the MR bands having large multi-quasiparticle configurations. The calc…
Background: Heavy-ion induced two-nucleon transfer reactions are powerful tools to reveal peculiar aspects of the atomic nucleus, such as pairing correlations, single-particle and collective degrees of freedom, and more. Also, these processes are in competition with the direct meson exchange in the double charge exchange reactions, which have recently attracted great interest due to their possible connection to neutrinoless double-beta decay. In this framework, the exploration of two-nucleon transfer reactions in the 20Ne+116Cd collision at energies above the Coulomb barrier is particularly re…
