The low-energy structure and $β$ decay properties of neutron-rich even- and odd-mass Pd and Rh nuclei are studied using a mapping framework based on the nuclear density functional theory and the particle-boson coupling scheme. Constrained Hartree-Fock-Bogoliubov calculations using the Gogny-D1M energy density functional are performed to obtain microscopic inputs to determine the interacting-boson Hamiltonian employed to describe the even-even core Pd nuclei. The mean-field calculations also provide single-particle energies for the odd systems, which are used to determine essential ingredients of the particle-boson interactions for the odd-nucleon systems, and of the Gamow-Teller and Fermi transition operators. The potential energy surfaces obtained for even-even Pd isotopes as well as the spectroscopic properties for the even- and odd-mass systems suggest a transition from prolate deformed to $γ$-unstable and to nearly-spherical shapes. The predicted $β$ decay $\log{ft}$ values are shown to be sensitive to the details of the wave functions for the parent and daughter nuclei, and therefore serve as a stringent test of the employed theoretical approach.
Microscopic study of low-lying states in odd-mass nuclei for atomic electric dipole moment searches
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, Sun Yat-Sen University（中山大学广东省量子计量与传感重点实验室）
Variable Energy Cyclotron Centre（变能回旋加速器中心）；Homi Bhabha National Institute（霍米·巴哈国家研究所）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Department of Physics, University of Kashmir（克什米尔大学物理系）；Department of Higher Education (GDC Shopian)（高等教育部（Shopian政府学院））；Department of Higher Education (GDC Kulgam)（高等教育部（Kulgam政府学院））；Department of Physics, ICFAI University Tripura（特里普拉ICFAI大学物理系）；Government General Degree College（政府综合学位学院）
A simultaneous calculation for the shape evolution and the related spectroscopic properties of the low-lying states, and the $β$-decay properties in the even- and odd-mass Ge and As nuclei in the mass $A\approx70-80$ region, within the framework of the nuclear density functional theory and the particle-core coupling scheme, is presented. The constrained self-consistent mean-field calculations using a universal energy density functional (EDF) and a pairing interaction determines the interacting-boson Hamiltonian for the even-even core nuclei, and the essential ingredients of the particle-boson …
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 low-lying structure of neutron-rich odd-mass Kr isotopes is studied within the interacting boson-fermion model (IBFM) based on the Gogny-D1M energy density functional (EDF). The $(β,γ)$-deformation energy surfaces, spherical single-particle energies and occupation probabilities of the odd-mass systems are obtained using the constrained Hartree-Fock-Bogoliubov (HFB) approximation. Those quantities are used as a microscopic input to determine most of the parameters of the IBFM Hamiltonian. The remaining parameters are specifically tailored to the experimental spectrum for each of the studied…
The spectroscopic properties of the odd-odd isotopes $^{124-132}$Cs have been studied within the interacting boson-fermion-fermion model based on the Gogny-D1M energy density functional framework. Major ingredients to build the interacting boson-fermion-fermion Hamiltonian, such as the ($β,γ$)-deformation energy surfaces for the even-even core nuclei $^{124-132}$Xe as well as single-particle energies and occupation probabilities of the odd nucleons, have been computed microscopically with the constrained Hartree-Fock-Bogoliubov method. A few coupling constants of the boson-fermion and residual…
The low-energy excitations and $β$ decays of odd-A nuclei are studied within the interacting boson-fermion model (IBFM), based on the Gogny-D1M nuclear energy density functional (EDF). The constrained Hartree-Fock-Bogoliubov (HFB) approximation is employed to compute potential energy surfaces in terms of triaxial quadrupole degrees of freedom for even-even Xe and Ba nuclei in the mass $A\approx 130$ region. The mean field approximation also provides spherical single-particle energies and occupation probabilities for the neighboring odd-A nuclei. Those quantities represent a microscopic input f…
We develop an effective field theory (EFT) for deformed odd-mass nuclei. These are described as an axially symmetric core to which a nucleon is coupled. In the coordinate system fixed to the core the nucleon is subject to an axially symmetric potential. Power counting is based on the separation of scales between low-lying rotations and higher-lying states of the core. In leading order, core and nucleon are coupled by universal derivative terms. These comprise a covariant derivative and gauge potentials which account for Coriolis forces and relate to Berry-phase phenomena. At leading order, the…
The interacting boson-fermion model (IBFM), with parameters determined from the microscopic Hartree-Fock-Bogoliubov (HFB) approximation, based on the parametrization D1M of the Gogny energy density functional (EDF), is employed to study the structural evolution in odd-mass $γ$-soft nuclei. The deformation energy surfaces of even-even nuclei, single-particle energies and occupation probabilities of the corresponding odd-mass systems have been obtained within the constrained HFB approach. Those building blocks are then used as a microscopic input to build the IBFM Hamiltonian. The coupling const…
Electromagnetic properties of the deformed neutron-odd nucleus $^{229}$Th are investigated in the framework of the unified model, with primary emphasis upon the properties of the low-lying isomeric state.
$α$ decay is usually associated with both ground and low-lying isomeric states of heavy and superheavy nuclei, and the unpaired nucleon plays a key role on $α$ decay. In this work, we systematically studied the $α$ decay half-lives of odd-$A$ nuclei, including both favored and unfavored $α$ decay within the two-potential approach based on the isospin dependent nuclear potential. The $α$ preformation probabilities are estimated by using an analytic formula taking into account the shell structure and proton-neutron correlation, and the parameters are obtained through the $α$ decay half-lives dat…
The newly observed isomer and ground-state band in the odd-Z neutron-rich rare-earth nucleus $^{163}$Eu are investigated by using the cranked shell model (CSM) with pairing treated by the particle-number conserving (PNC) method. This is the first time detailed theoretical investigations are performed of the observed $964(1)$ keV isomer and ground-state rotational band in $^{163}$Eu. The experimental data are reproduced very well by the theoretical results. The configuration of the $964(1)$ keV isomer is assigned as the three-particle state $\frac{13}{2}^{-}(ν\frac{7}{2}^{+}[633]\otimesν\frac{1…
One-particle properties of deformed N $\approx$ 28 odd-N nuclei with weakly-bound or resonant neutrons
利用基于变形Woods-Saxon势的Nilsson图研究了含N $\approx$ 28的奇N核向中子滴线方向的可能变形.在正确的边界条件下，直接求解空间坐标网格中的薛定谔方程，得到了弱束缚和共振单粒子能级。如果我们使用与$β$稳定核相同的扩散势，中子2 p $_{3/2}$和1f $_{7/2}$能级之间的能量差变得非常小，或者N=28的能隙几乎消失，因为这些能级的结合能接近于零。这表明，这些中子滴线核的基态可能会变形。特别地，研究了奇N核$^{43}_{16}$ S $_{27}$和$^{45}_{16}$ S $_{29}$基态的自旋宇称和磁矩.此外，还提出了在位于滴线外的$^{39}_{12}$ Mg $_{27}$中，如果N=28能隙几乎为零，则最低共振态可能具有5/2 $^{-}$。
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…
[Background] Predictions of spectroscopic properties of low-lying states are critical for nuclear structure studies. Theoretical methods can be particularly involved for odd-mass nuclei because of the interplay between the unpaired nucleon and collective degrees of freedom. Only a few models have been developed for systems in which octupole collective degrees of freedom play a role. [Purpose] We aim to predict spectroscopic properties of odd-mass nuclei characterized by octupole shape deformation, employing a model that describes single-particle and collective degrees of freedom within the sam…
Multireference covariant density functional theory for shape coexistence and isomerism in $^{43}$S
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；College of Physics and Communication Electronics, Jiangxi Normal University（江西师范大学物理与通信电子学院）；Jiangxi Provincial Key Laboratory of Advanced Electronic Materials and Devices（江西省先进电子材料与器件重点实验室）；College of Physics and Electronic Engineering, Chongqing Normal University（重庆师范大学物理与电子工程学院）；Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, Sun Yat-Sen University（中山大学广东省量子计量与传感重点实验室）；Physik Department, Technische Universität München（慕尼黑工业大学物理系）
Experimental data indicate that the mass tensor of collective Bohr Hamiltonian cannot be considered as a constant but should be considered as a function of the collective coordinates. In this work our purpose is to investigate the properties of low-lying collective states of the odd nuclei $^{173}$Yb and $^{163}$Dy by using a new generalized version of the collective quadrupole Bohr Hamiltonian with deformation-dependent mass coefficients. The proposed new version of the Bohr Hamiltonian is solved for Davidson potential in $β$ shape variable, while the $γ$ potential is taken to be equal to the…
A detailed feasibility study on deducing the high-lying single-particle components (HLSPCs), which are important but used to be ignored, in the ground and low-lying excited states of even-even light nuclei is performed by analyses of $(p,d)$ reactions with \nuc{12}{C}, \nuc{24}{Mg}, \nuc{28}{Si}, and \nuc{40}{Ca} targets at 51.93 MeV. Coupled reaction channels (CRC) analyses have been made for $(p,d)$ transitions to the $j$-forbidden excited states in \nuc{11}{C} (${\tfrac{5}{2}}^-$, 4.32 MeV), \nuc{23}{Mg} (${\tfrac{7}{2}}^+$, 2.05 MeV), \nuc{27}{Si} (${\tfrac{7}{2}}^+$, 2.16 MeV) and \nuc{39…
Effective interactions and shell model studies of heavy tin isotopes
本文给出了在1f ~（7/2），2 p ~（3/2），0 h ~（9/2），2 p ~（1/2），1f ~（5/2），0 i ~（13/2）单粒子轨道定义的壳模型空间下，对134 ~ 142}Sn的偶、奇锡同位素的大尺度壳模型计算结果.采用基于现代核子-核子相互作用的有效两体相互作用。壳模型的结果反过来分析其配对的内容，使用广义的资历方法。我们的研究结果表明，一个配对模型的图片捕捉了大量的结构和最低躺态的偶，奇同位素的相关性。
We calculate for the first time the electric dipole moment (EDM) of $^{13}$C generated by the isovector CP-odd pion exchange nuclear force in the $α$-cluster model, which describes well the structures of low lying states of the $^{13}$C nucleus. The linear dependence of the EDM of $^{13}$C on the neutron EDM and the isovector CP-odd nuclear coupling is found to be $d_{^{13}{\rm C}} = -0.33 d_n - 0.0020 \bar G_π^{(1)}$. The linear enhancement factor of the CP-odd nuclear coupling is smaller than that of the deuteron, due to the difference of the structure between the $1/2^-_1$ state and the opp…
