The relevance of the pseudospin symmetry in nuclei is considered. New insight is obtained from looking at the continuous transition from a model satisfying the spin symmetry to another one satisfying the pseudospin symmetry. This study suggests that there are models allowing no missing single-particle states in this transition, contrary to what is usually advocated. It rather points out to an association of pseudospin partners different from the one usually assumed, together with a strong violation of the corresponding symmetry. A comparison with results obtained from some relativistic approaches is made.
We investigate the spin and pseudospin symmetry in the single-particle resonant states by solving the Dirac equation containing a Woods-Saxon potential with Green's function method. Taking double-magic nucleus $^{208}$Pb as an example, three spin doublets $3d$, $2h$, and $1j$ and three pseudospin doublets $3\tilde{p}$, $1\tilde{i}$, and $1\tilde{j}$ are obtained for the single-neutron resonant states. By analyzing the energy splittings, we find that the threshold effect plays an important role in resonant pseudospin doubles. Besides, there is a reversed level structure of pseudospin doublets i…
A reflection-asymmetric triaxial particle rotor model with three quasiparticles and a reflection-asymmetric triaxial rotor is developed, and applied to investigate the observed multiple chiral doublets (M\c{hi}D) candidates with octupole correlations in 131Ba, i.e., two pairs of positive-parity bands D3-D4 and D5-D6, as well as one pair of negative-parity bands D7-D8. The energy spectra, the energy staggering parameters, the B(M1)/B(E2) ratios, and the B(E1)/B(E2) ratios are reproduced well. The chiral geometries for these M\c{hi}D candidates are examined by the azimuthal plots, and the evolut…
Pseudospin symmetry has been useful in understanding atomic nuclei. We review the arguments that this symmetry is a relativistic symmetry. The condition for this symmetry is that the sum of the vector and scalar potentials in the Dirac Hamiltonian is a constant. We give the generators of pseudospin symmetry. We review some of the predictions that follow from this insight into the relativistic origins of pseudospin symmetry. Since in nuclei the sum of the scalar and vector potentials is not zero but is small, we discuss preliminary investigations into the conditions on the potentials to produce…
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…
Symmetry plays a fundamental role in physics. The quasi-degeneracy between single-particle orbitals $(n, l, j = l + 1/2)$ and $(n-1, l + 2, j = l + 3/2)$ indicates a hidden symmetry in atomic nuclei, the so-called pseudospin symmetry (PSS). Since the introduction of the concept of PSS in atomic nuclei, there have been comprehensive efforts to understand its origin. Both splittings of spin doublets and pseudospin doublets play critical roles in the evolution of magic numbers in exotic nuclei discovered by modern spectroscopic studies with radioactive ion beam facilities. Since the PSS was recog…
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…
The quasi-degeneracy between the single-particle states $(n,\,l,\,j=l+1/2)$ and $(n-1,\,l+2,\,j=l+3/2)$ indicates a special and hidden symmetry in atomic nuclei---the so-called pseudospin symmetry (PSS)---which is an important concept in both spherical and deformed nuclei. A number of phenomena in nuclear structure have been successfully interpreted directly or implicitly by this symmetry, including nuclear superdeformed configurations, identical bands, quantized alignment, pseudospin partner bands, and so on. Since the PSS was recognized as a relativistic symmetry in 1990s, there have been co…
We present finite temperature Dirac-Hartree-Bogoliubov (FTDHB) calculations for the tin isotope chain to study the dependence of pseudospin on the nuclear temperature. In the FTDHB calculation, the density dependence of the self-consistent relativistic mean fields, the pairing, and the vapor phase that takes into account the unbound nucleon states are considered self-consistently. The mean field potentials obtained in the FTDHB calculations are fit by Woods-Saxon (WS) potentials to examine how the WS parameters are related to the energy splitting of the pseudospin pairs as the temperature incr…
As the experimental data from kaonic atoms and $K^{-}N$ scatterings imply that the $K^{-}$-nucleon interaction is strongly attractive at saturation density, there is a possibility to form $K^{-}$-nuclear bound states or kaonic nuclei. In this work, we investigate the ground-state properties of the light kaonic nuclei with the relativistic mean field theory. It is found that the strong attraction between $K^{-}$ and nucleons reshapes the scalar and vector meson fields, leading to the remarkable enhancement of the nuclear density in the interior of light kaonic nuclei and the manifest shift of t…
From spin to pseudospin symmetry: The origin of magic numbers in nuclear structure
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）；Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）；Facility for Rare Isotope Beams, Michigan State University（密歇根州立大学稀有同位素束设施）；Department of Physics & Astronomy, Michigan State University（密歇根州立大学物理与天文学系）；Department of Physics, Graduate School of Science, The University of Tokyo（东京大学理学研究科物理学专业）
A new way to study the spin-isospin dependence of the $ΞN$ interaction is explored through the energy levels of $ΞNα$ and $ΞNαα$ systems with $α$ being a spectator to attract the $ ΞN$ pair without changing its spin-isospin structure. By using the Gaussian expansion method (GEM) with the state-of-the-art $ΞN$ potential obtained from lattice QCD calculations, it is found that $ΞNαα$ has spin-doublet bound states with $J^π={1^-}$ and $2^-$ in both isospin triplet and singlet channels. The inversion of the $1^-$-$2^-$ spin-doublet between the iso-triplet and the iso-singlet is found to be strongl…
Since the prediction of nuclear chirality in 1997, tremendous progresses both theoretically and experimentally have been achieved. Experimentally, 59 chiral doublet bands in 47 chiral nuclei (including 8 nuclei with multiple chiral doublets) have been reported in $A\sim80,~100,~130$,~and~190 mass regions. The spins, parities, energies, ratios of the magnetic dipole transition strengths to the electric quadrupole transition strengths, and related references for these nuclei are compiled and listed in Table 1. For these nuclei with the magnetic dipole transition strengths and the electric quadru…
The longitudinal form factors of the weak vector current of particles with spin $ J = 1/2 $ and isospin $ I = 1/2 $ are determined by the mass difference and the charge radii of members of the isotopic doublets. The most promising reactions to measure these form factors are the reactions with large momentum transfers involving the spin-1/2 isotopic doublets with a maximum mass splitting. Numerical estimates of longitudinal form factors are given for nucleons and eight nuclear spin-1/2 isotopic doublets.
The basis space in the triaxial projected shell model (TPSM) approach is generalized for odd-odd nuclei to include two-neutron and two-proton configurations on the basic one-neutron coupled to one-proton quasiparticle state. The generalization allows to investigate odd-odd nuclei beyond the band crossing region and as a first application of this development, high-spin band structures recently observed in odd-odd $^{194-200}$Tl isotopes are investigated. In some of these isotopes, the doublet band structures observed after the band crossing have been conjectured to arise from the spontaneous br…
Exact conservation and breaking of pseudospin symmetry in single particle resonant states
本文介绍了单粒子共振态赝自旋对称性的研究结果。PSS是与核子狄拉克波函数的小分量相联系的相对论动力学对称性。人们做了许多努力来研究束缚态中的这种对称性。最近，我们通过检查对应于径向狄拉克波函数的小分量的Jost函数的零点和连续态的相移[1，Phys. Rev. Lett. 109（2012）072501]。我们证明了当吸引标量势和排斥矢量势大小相同但符号相反时，核中单粒子共振态的PSS是守恒的。在单粒子共振的精确守恒和这种对称性的破坏的例子给出了球形方井和伍兹-撒克逊潜力。
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 $γ$-$γ$-$γ$ and $γ$-$γ$-$γ$-$γ$ 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 $K^π=4^+$ new band decaying to an 1s isomeric state is assigned to be the high-$K$ Gallagher-Moszkowski (GM) partner of the kn…
Global systematics and theoretical interpretation of $l$-forbidden $M1$ transitions in odd-$A$ nuclei
Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University（中山大学中法核工程与技术学院）；Department of Physics, KTH Royal Institute of Technology（皇家理工学院物理系）
