The anomalous low-energy $E2$-related behavior of a triaxially-deformed nucleus bas been identified and analyzed based on the SU(3) algebraic theory within the framework of the interacting boson model. The results show striking features that include a $B(E2;4_1^+\rightarrow2_1^+)/B(2_1^+\rightarrow0_1^+)<1.0$ transition rate ratio and a $E(4_1^+)/E(2_1^+)>2.0$ excitation energy ratio that can be tracked back to a finite-$N$ effect, which in a large-$N$ limit of the theory yields normal results for a stable $γ$-deformation. This description is shown to be able to explain observed $E2$ anomalous phenomenon in neutron-deficient nuclei such as $^{172}$Pt and $^{168}$Os, and in so doing yields a deeper understanding of the physical features of a soft triaxially-deformed nucleus.
Macroscopic manifestations of rotating triaxial superfluid nuclei
最近，Allmond和Wood [Phys. Lett. B 767，226（2017）]能够从实验数据中提取十几个超流三轴核的三个转动惯量$I_k$。观察到的$I_k$对变形参数的依赖性是相当平滑的。在这里，我们表明，这些转动惯量可以令人惊讶地很好地解释了半经典曲柄哈特里-福克-Bogoliubov（HFB）计算中的速度场是一个简单的叠加刚性和无旋流。
The influence of triaxial deformation $γ$ on the purely collective form of wobbling motion in even-even nuclei are discussed based on the triaxial rotor model. It is found that the harmonic approximation is realized well when $γ=30^{\circ}$ for the properties of energy spectra and electric quadrupole transition probabilities, while this approximation gets bad when $γ$ deviates from $30^{\circ}$. A recent data from Coulomb excitation experiment, namely $3_1^+$ and $2_2^+$ for the $^{110}$Ru are studied and might be suggested as the bandhead of the wobbling bands. In addition, two types of angul…
Triaxial shapes in even-even nuclei: A theoretical overview
National Centre for Scientific Research “Demokritos”（德谟克利特国家科学研究中心）；Czech Academy of Sciences（捷克科学院）；National and Kapodistrian University of Athens（雅典国立卡波蒂斯坦大学）；Bulgarian Academy of Sciences（保加利亚科学院）
Three-dimensional rotation of even-even triaxial nuclei
利用自洽的三维曲柄Hartree-Fock-Bogoliubov（3d-cranked HFB）方法，研究了$A\simeq 130$质量区偶偶核（$^{134}_{58}$ Ce $_{76}$）在Yrast线附近的各种转动运动.手征旋转的可能性，倾斜旋转，和这些旋转的动力学方面进行了讨论，通过分析的3D曲柄HFB解决方案。虽然手征旋转的稳定的平面解被获得，一个非平面的手征配置被发现是不稳定的三轴变形时，处理自洽。
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…
Coupling shape and pairing vibrations in a collective Hamiltonian based on nuclear energy density functionals (II): low-energy excitation spectra of triaxial nuclei
In this work, we present a new version of the Bohr collective Hamiltonian for triaxial nuclei within Deformation-Dependent Mass formalism (DDM) using the Hulthén potential. We shall call the developed model Z(5)-HD. Analytical expressions for energy spectra are derived by means of the recent version of the Asymptotic Iteration Method. The calculated numerical results of energies and B(E2) transition rates are compared with the experimental data, and several theoretical results from Z(5) model, the model Z(5)-H using the Hulthén potential without DDM formalism as well as theoretical predictions…
The nuclear matrix elements of neutrinoless double-$β$ decay for nuclei $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd are studied within the triaxial projected shell model, which incorporates simultaneously the triaxial deformation and quasiparticle configuration mixing. The low-lying spectra and the $B(E2:0^+\rightarrow2^+)$ values are reproduced well. The effects of the quasiparticles configuration mixing, the triaxial deformation, and the closure approximation on the nuclear matrix elements are studied in detail. For nuclei $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^…
Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei: Systematic investigation of the triaxiality effect on fission barrier
In an effort to elucidate the rich band structures observed in odd-neutron systems, triaxial projected shell model approach is extended to include three-quasineutron and five-quasiparticle configurations. This extension makes it possible to investigate the high-spin states up to and including the second band crossing. Detailed investigation has been performed for odd-mass Xe isotopes with the extended basis, and it is shown that character of the band crossing along the yrast line changes with shell filling of the 1h11/2 orbital. Further, it is observed that the three-quasiparticle state that c…
It is known that nuclear deformation plays an important role in inducing the halo structure in neutron-rich nuclei by mixing several angular momentum components. While previous theoretical studies on this problem in the literature assume axially symmetric deformation, we here consider non-axially symmetric deformations. With triaxial deformation, the $Ω$ quantum number is admixed in a single-particle wave function, where $Ω$ is the projection of the single-particle angular momentum on the symmetric axis, and the halo structure may arise even when it is absent with the axially symmetric deforma…
Collective motion in triaxial nuclei within minimal length concept
受海森堡代数的启发，将最小长度概念应用于原子核的几何集体玻尔-莫特森模型（BMM）。利用变形正则对易关系和Pauli-Podolsky公式，我们导出了三轴核的量子化哈密顿算符，正如我们以前对轴长$γ$ -刚性核所做的那样（M. Chabab等人，Phys. Lett. B 758（2016）212-218）。通过考虑$β$集体形状变量中的无限方势阱，得到了哈密顿量的本征值与最小长度参数的显式依赖关系.此外，与我们所建立的模型相关联的对称性可以看作是原子核结构中一种新的准动力学临界点对称性。理论结果表明，对于较低的角动量值，最小长度对能级有显着的贡献（低效应），而对于较高的角动量值，最小长度对能级有规则的贡献（显着效应）。事实上，这些特征表明，最小长度的情况下，这是有用的，在识别具有高自旋或强旋转的真实变形核的性质。最后，对${}^{124,128,130}$和${}^{114}$ Pd等核进行了数值计算，结果与实验数据定性一致.
The conventional cranking model for uniaxial rotation is frequently used to study rotational features in deformed nuclei. However, the model uses a constant angular velocity. To investigate the effect of a dynamic angular velocity, a quantal microscopic time-reversal and D2 invariant cranking model for triaxial rotation (MSCRM3) including residual correction terms is derived from a unitary transformation of the nuclear Schrodinger equation and using Hartree-Fock approach. Except for the angular velocity and residual terms, MSCRM3 and the conventional cranking model for triaxial rotation (CCRM3…
The effect of coupling between pairing and quadrupole triaxial shape vibrations on the low-energy collective states of $γ$-soft nuclei is investigated using a model based on the framework of nuclear energy density functionals (EDFs). Employing a constrained self-consistent mean-field (SCMF) method that uses universal EDFs and pairing interactions, potential energy surfaces of characteristic $γ$-soft Os and Pt nuclei with $A\approx190$ are calculated as functions of the pairing and triaxial quadrupole deformations. Collective spectroscopic properties are computed using a number-nonconserving in…
