The configuration-fixed constrained triaxial relativistic mean-field approach is extended by including time-odd fields and applied to study the candidate multiple chiral doublets (MKiD) nucleus 106Rh. The energy contribution from time-odd fields and microscopical evaluation of center-of-mass correction as well as the modification of triaxial deformation parameters beta, gamma due to the time-odd fields are investigated. The contributions of the time-odd fields to the total energy are 0.1-0.3 MeV and they modify slightly the gamma values. However, the previously predicted multiple chiral doublets still exist.
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.
Adiabatic and configuration-fixed constraint triaxial relativistic mean field (RMF) approaches are developed for the first time and a new phenomenon, the existence of multi chiral-doublets (M$χ$D), i.e., more than one pairs of chiral doublets bands in one single nucleus, is suggested for nuclei in A~100 region, typically for $^{106}$Rh, based on the triaxial deformations together with their corresponding proton and neutron configurations.
Following the reports of two pairs of chiral doublet bands observed in $^{105}$Rh, the adiabatic and configuration-fixed constrained triaxial relativistic mean-field (RMF) calculations are performed to investigate their triaxial deformations with the corresponding configuration and the possible multiple chiral doublet (M$χ$D) phenomenon. The existence of M$χ$D phenomenon in $^{105}$Rh is highly expected.
A rotating system, such as a star, liquid drop, or atomic nucleus, may rotate as an oblate spheroid about its symmetry axis or, if the angular velocity is greater than a critical value, as a triaxial ellipsoid about a principal axis. The oblate and triaxial equilibrium configurations minimize the total energy, a sum of the rotational kinetic energy plus the potential energy. For a star or galaxy the potential is the self-gravitating potential, for a liquid drop, the surface tension energy, and for a nucleus, the potential is the sum of the repulsive Coulomb energy plus the attractive surface e…
A microscopic self-consistent triaxial relativistic Hartree-Bogoliubov theory in continuum (TRHBc), which simultaneously takes into account the triaxiality and pairing correlations as well as continuum effects, is established and applied to explore the novel halo phenomenon in aluminum isotopes. The experimental proton drip line and the available data of neutron separation energies and charge radii are reproduced well without any free parameters. The neutron-richest odd-odd aluminum isotope observed so far, 42Al, is predicted to be triaxially deformed with beta=0.35 and gamma=42. Its one-neutr…
Transition probabilities of the ground-state bands in $γ$-soft nuclei are studied for the first time using the triaxial projected shell model approach. It is observed that the angular-momentum dependence of the transition quadrupole moment $Q_t$ is related to the triaxial deformation of the nuclear mean-field potential. The introduction of the $γ$-degree of freedom in the shell model basis is shown to have a little influence on the {\it constant} behavior of the low-spin $Q_t$ in a well-deformed nucleus. However, the {\it increasing} collectivity with spin for the low-spin states in a $γ$-soft…
The positive-parity states of even-even Xe nuclei are investigated within the framework of modified O(6) limit of the interacting boson model (IBM1). The effective three-body interaction [QQQ] where Q is the IBM O(6) quadrupole operator is introduced to exhibit the triaxiality nature. The shape of nuclear surface is described by the deformation parameters beta, gamma by using the intrinsic coherent state. The potential energy surfaces (PES) of the transition U(5)-Triaxiality-O(6) are calculated and analyzed and the critical phase transition points are identified. For each nucleus a fitting pro…
With the self-consistent three-dimensional cranked Hartree-Fock-Bogoliubov (3d-cranked HFB) method, various types of rotational motion near the yrast line are investigated in an even-even nucleus in the $A\simeq 130$ mass region ($^{134}_{58}$Ce$_{76}$). The possibilities of chiral rotations, tilted-rotations, and dynamical aspects of these rotations are discussed through the analysis of the 3d-cranked HFB solutions. Although a stable planar solution of the chiral rotation is obtained, an aplanar chiral configuration is found to be unstable when triaxial deformation is treated self-consistentl…
The nearly degenerate triplet bands with the $πg_{9/2}^{-1}\otimes νh_{11/2} (g_{7/2},d_{5/2})$ configuration in $^{105}$Ag are studied via the relativistic mean-field (RMF) theory and the multiparticle plus rotor model (MPRM), which indicates that these bands are associated with chiral symmetry and pseudospin symmetry. The configuration-fixed constrained triaxial RMF calculations exhibit the pseudospin symmetry in single particle spectra and the triaxial shape coexistence. The experimental excitation energies and the electromagnetic transition probabilities for the triplet bands are reproduce…
The evolution of structure property along the fission path in the superheavy nucleus $^{256}$Sg is predicted through the multi-dimensional potential-energy(or Routhian)-surface calculations,in which the phenomenological deformed Woods-Saxon potential is adopted. Calculated nuclear deformations and fission barriers for $^{256}_{106}$Sg$_{150}$ and its neighbors, e.g., $^{258,260}$Sg, $^{254}$Rf and $^{252}$No are presented and compared with other theoretical results. A series of energy maps and curves are provided and used to evaluate the corresponding shape-instability properties, especially i…
Distribution of the two phonon $γ$ vibrational collectivity in the rotating triaxial odd-$A$ nucleus, $^{103}$Nb, that is one of the three nuclides for which experimental data were reported recently, is calculated in the framework of the particle vibration coupling model based on the cranked shell model plus random phase approximation. This framework was previously utilized for analyses of the zero and one phonon bands in other mass region and is applied to the two phonon band for the first time. In the present calculation, three sequences of two phonon bands share collectivity almost equally …
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 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…
A new dynamical symmetry limit of the two-fluid Interacting Vector Boson Model (IVBM), defined through the chain $Sp(12,R) \supset U(3,3) \supset U^{\ast}(3) \otimes SU(1,1) \supset SU^{\ast}(3) \supset SO(3)$, is introduced. The $SU^{\ast}(3)$ algebra considered in the present paper closely resembles many properties of the $SU^{\ast}(3)$ limit of IBM-2, which have been shown by many authors geometrically to correspond to the rigid triaxial model. The influence of different types of perturbations on the $SU^{\ast}(3)$ energy surface, in particular the addition of a Majorana interaction and an …
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},…
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）
We study the low-lying energy spectrum of the rp-process waiting point nucleus 80Zr with state-of-the-art beyond mean field methods with the Gogny D1S interaction. Symmetry restoration and configuration mixing of axial and triaxial shapes are included in the calculations. Five 0+ states corresponding to different nuclear shapes are obtained below 2.25 MeV and several rotational and γ- bands built upon them are identified. Nevertheless, these states do not modify the β-decay half-life having a negligible effect in the rp-process. A good agreement with the available experimental data is obtained…
Recently, values for the Kumar quadrupole deformation parameters of the nucleus $^{130}$Xe have been computed from the results of a Coulomb excitation experiment, indicating that this xenon isotope has a prominent triaxial ground state. Within a different context, it was recently argued that the analysis of particle correlations in the final states of ultra-relativistic heavy-ion collisions performed at the Large Hadron Collider (LHC) points to a similar structure for the adjacent isotope, $^{129}$Xe. In the present work, we report on state-of-the-art multi-reference energy density functional …
The rotational behaviour of T=0 and T=1 bands in the odd-odd N=Z nucleus 62Ga is studied theoretically using the spherical shell model (laboratory frame) and the cranked Nilsson-Strutinsky model (intrinsic frame). Both models give a good description of available experimental data. The role of isoscalar and isovector pairing in the T=0 and T=1 bands as functions of angular momentum is studied in the shell model. The observed backbending in the T=0 band is interpreted as an unpaired band-crossing between two configurations with different deformation. The two configurations differ by 2p-2h and ar…
We study the ground state properties, potential energy curves and potential energy surfaces of the superheavy nucleus $^{270}$Hs by using the multidimensionally-constrained relativistic mean-field model with the effective interaction PC-PK1. The binding energy, size and shape as well as single particle shell structure corresponding to the ground state of this nucleus are obtained. $^{270}$Hs is well deformed and exhibits deformed doubly magic feature in the single neutron and proton level schemes. One-dimensional potential energy curves and two-dimensional potential energy surfaces are calcula…
A particle rotor model is developed which couples several valence protons and neutrons to a rigid triaxial rotor core. It is applied to investigating the chirality in odd-$A$ nucleus $^{135}$Nd with $πh_{11/2}^2\otimesνh^{-1}_{11/2}$ configuration for the first time in a fully quantal approach. For the two chiral sister bands, the observed energies and the $B(M1)$ and $B(E2)$ values for the in-band as well as interband transitions are reproduced excellently. Root mean square values of the angular momentum components and their probability distributions are used for discussing in detail the chir…
Spectroscopic properties that characterize shape phase transitions in neutron-rich odd-A Zr isotopes are investigated using the framework of nuclear density functional theory and particle-core coupling. The interacting-boson Hamiltonian of the even-even core nuclei, and the single-particle energies and occupation probabilities of the unpaired neutron are completely determined by deformation constrained self-consistent mean-field calculations based on the relativistic Hartree-Bogoliubov model with a choice of a universal energy density functional and pairing interaction. The triaxial $(β,γ)$ de…
The beyond mean field approximation combined with the Gogny interaction is used to analyze the spherical to prolate deformed shape transition in the Neodymium isotopic chain. The vibrator as well as the rotor limits are nicely reproduced while the transitional region is only qualitatively described probably due to the lack of triaxial correlations in the calculations. Our results do not support the interpretation of $^{150}$Nd as a critical point nucleus and question the interpretation of shape changes as nuclear shape phase transitions.
Spectroscopic properties that characterize the shape phase transitions in krypton isotopes with the mass $A\approx80$ region are investigated within the framework of the nuclear density functional theory. Triaxial quadrupole constrained self-consistent mean-field calculations that employ relativistic energy density functionals and a pairing interaction are carried out for the even-even nuclei $^{76-86}$Kr. The spectroscopic properties are computed by solving the triaxial quadrupole collective Hamiltonian, with the ingredients, i.e., the deformation-dependent moments of inertia and mass paramet…
A particle rotor model, which couples nucleons in four single-$j$ shells to a triaxial rotor core, is developed to investigate the five pairs of nearly degenerate doublet bands recently reported in the even-even nucleus $^{136}$Nd. The experimental energy spectra and available $B(M1)/B(E2)$ values are successfully reproduced. The angular momentum geometries of the valence nucleons and the core support the chiral rotation interpretations not only for the previously reported chiral doublet, but also for the other four candidates. Hence, $^{136}$Nd is the first even-even candidate nucleus in whic…
The open problem on whether or not the chirality exists in doublet bands M1 and M4 in light-mass even-even nucleus $^{60}$Ni is studied by adopting the recently developed fully quantal four-$j$ shells triaxial particle rotor model. The corresponding experimental energy spectra, energy differences between doublet bands, and the available $B(M1)/B(E2)$ values are successfully reproduced. The analyses on the basis of the angular momentum components, the azimuthal plots, and the $K$-plots suggest that the chiral modes exist at $I\geq 12\hbar$ in doublet bands M1 and M4.
A triaxial rotor Hamiltonian with a rigidly aligned high-$j$ quasiparticle is treated by a time-dependent variational principle, using angular momentum coherent states. The resulting classical energy function have three unique critical points in a space of generalized conjugate coordinates, which can minimize the energy for specific ordering of the inertial parameters and a fixed angular momentum state. Due to the symmetry of the problem, there are only two unique solutions, corresponding to wobbling motion around a principal axis and respectively a tilted-axis. The wobbling frequencies are ob…
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…
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）
A shape change of the self-consistent mean-field induced by a configuration change is discussed within the conventional constrained Hartree-Fock (CHF) theory. It is stressed that a single-particle level crossing dynamics should be treated carefully, because the shape of the mean-field in such a finite many-body system as the nucleus strongly changes depending on its configuration. This situation is clearly shown by applying an adiabatic assumption, where the most energetically favorable single-particle states are assumed to be occupied. The excited HF states and the continuously-connected pote…
First observation of multi-phonon $γ$-vibrations in an odd-odd nuclear system
Shandong University（山东大学）；Vanderbilt University（范德堡大学）；Université Claude Bernard Lyon 1（里昂第一大学）；GANIL（法国国家大科学装置重离子加速器联合实验室）；Variable Energy Cyclotron Centre（可变能量回旋加速器中心）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Government Degree College Shopian（肖皮安政府学位学院）；Islamic University of Science and Technology（伊斯兰科学与技术大学）；University of Kashmir（克什米尔大学）
Two distinct sets of chiral-partner bands have been identified in the nucleus $^{133}$Ce. They constitute a multiple chiral doublet (M$χ$D), a phenomenon predicted by relativistic mean field (RMF) calculations and observed experimentally here for the first time. The properties of these chiral bands are in good agreement with results of calculations based on a combination of the constrained triaxial RMF theory and the particle-rotor model.
To describe the yrast states in weakly bound nuclei, I directly solve the coordinate-space cranked Skyrme-Hartree-Fock-Bogoliubov equation on a three-dimensional lattice with the continuum states discretized in a box. After the numerical demonstration for the ground-state band in a medium-mass nucleus, I apply the newly-developed method to neutron-rich even-$N$ Mg isotopes. I find that the appearance of the significantly low $I^π=2^+$ state in $^{40}$Mg is mainly due to the suppression of pairing. The calculation predicts that the $2^+$ state in $^{42}$Mg appears as high in energy as in $^{34\…
The nucleus $^{44}$Ti has low-lying levels of various kinds of mutually very different nuclear structure displaying the richness of the nuclear many-body dynamics. It is shown that the deformed-basis antisymmetrized molecular dynamics by the use of the Gogny D1S force reproduces successfully and unifiedly two types of coexistence phenomena in $^{44}$Ti. Namely, on one hand, the coexistence of the mean field structure and the cluster structure is confirmed by verifying the normally deformed structure of the $K^π$=$3^-_1$ band with a 1-particle-jump intrinsic configuration and the $α+ ^{40}$Ca c…
A new theoretical framework named as deformed base antisymmetrized molecular dynamics that uses the localized triaxially deformed Gaussian as the single particle wave packet is presented. The model space enables us to describe sufficiently well the deformed mean-field structure as well as the cluster structure and their mixed structure within the same framework. The improvement over the original version of the antisymmetrized molecular dynamics which uses the spherical Gaussian is verified by the application to $^{20}{\rm Ne}$ nucleus. The almost pure $α+ ^{16}{\rm O_{g.s}}$ cluster structure …
\item[Background] For cranked mean-field calculations with arbitrarily oriented rotational frequency vector $\boldsymbolω$ in the intrinsic frame, one has to employ constraints on average values of the quadrupole-moment tensor, so as to keep the nucleus in the principal-axis reference frame. Kerman and Onishi [Nucl. Phys. A {\bf 361}, 179 (1981)] have shown that the Lagrangian multipliers that correspond to the required constraints are proportional to $\boldsymbolω \times \boldsymbol{J}$, where $\boldsymbol{J}$ is the average angular momentum vector. \item[Purpose] We study the validity and co…
Nuclear lattice effective field theory as a testing ground for $α$-cluster structures in ${}^{24}\mathrm{Mg}$
IJCLab, In2p3, CNRS（法国国家科学研究中心）；Université Paris-Saclay（巴黎萨克雷大学）；King-Fahd University of Petroleum and Minerals（法赫德国王石油与矿产大学）；Gaziantep Islam Science and Technology University（加济安泰普伊斯兰科学与技术大学）
