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 recognized as a relativistic symmetry in 1990s, many special features, including the spin symmetry (SS) for anti-nucleon, and many new concepts have been introduced. In the present Review, we focus on the recent progress on the PSS and SS in various systems and potentials, including extensions of the PSS study from stable to exotic nuclei, from non-confining to confining potentials, from local to non-local potentials, from central to tensor potentials, from bound to resonant states, from nucleon to anti-nucleon spectra, from nucleon to hyperon spectra, and from spherical to deformed nuclei. Open issues in this field are also discussed in detail, including the perturbative nature, the supersymmetric representation with similarity renormalization group, and the puzzle of intruder states.Comment: Review Article, 242 pages, 58 figures, 10 table

The self-consistent tilted axis cranking relativistic mean-field theory based on a point-coupling interaction has been established and applied to investigate systematically the newly observed shears bands in 60Ni. The tilted angles, deformation parameters, energy spectra, and reduced M1 and $E2$ transition probabilities have been studied in a fully microscopic and self-consistent way for various configurations and rotational frequencies. It is found the competition between the configurations and the transitions from the magnetic to the electric rotations have to be considered in order to reproduce the energy spectra as well as the band crossing phenomena. The tendency of the experimental electromagnetic transition ratios B(M1)/B(E2) is in a good agreement with the data, in particular, the B(M1) values decrease with increasing spin as expected for the shears mechanism, whose characteristics are discussed in detail by investigating the various contributions to the total angular momentum as well.Comment: 17 pages, 5 figure

For the first time a fully self-consistent charge-exchange relativistic RPA based on the relativistic Hartree-Fock (RHF) approach is established. The self-consistency is verified by the so-called isobaric analog state (IAS) check. The excitation properties and the non-energy weighted sum rules of two important charge-exchange excitation modes, the Gamow-Teller resonance (GTR) and the spindipole resonance (SDR), are well reproduced in the doubly magic nuclei 48 Ca, 90 Zr and 208 Pb without readjustment of the particle-hole residual interaction. The dominant contribution of the exchange diagrams is demonstrated.PACS numbers: 24.30. Cz, 21.60.Jz, 24.10.Jv, 25.40.Kv At present, spin-isospin resonances become one of the central topics in nuclear physics and astrophysics. Basically, a systematic pattern of the energy and collectivity of these resonances could provide direct information on the spin and isospin properties of the in-medium nuclear interaction, and the equation of state of asymmetric nuclear matter. Furthermore, a basic and critical quantity in nuclear structure, neutron skin thickness, can be determined indirectly by the sum rule of spin-dipole resonances (SDR) [1,2] or the excitation energy spacing between isobaric analog states (IAS) and Gamow-Teller resonances (GTR) [3]. More generally, spin-isospin resonances allow one to attack other kinds of problems outside the realm of nuclear structure, like the description of neutron star and supernova evolutions, the β-decay of nuclei which lie on the r-process path of stellar nucleosynthesis [4,5], even the existence of exotic odd-odd nuclei [6] and the efficiency of a solar neutrino detector [7].It was realized long ago that the Random Phase Approximation (RPA) is an appropriate microscopic approach for charge-exchange giant resonances [8,9]. The importance of full self-consistency was stressed [9], and Skyrme-RPA calculations of charge-exchange modes exist for about 30 years [10]. Recently, a fully self-consistent charge-exchange Skyrme-QRPA model has been developed [11]. Self-consistency is an extremely important requirement for the analysis of long isotopic chains extending towards the drip lines. On the relativistic side, so far the charge-exchange (Q)RPA model based on the relativistic mean field (RMF) theory has been developed [3,12,13,14].However, the self-consistency of the RMF+RPA is not completely fulfilled for the following reasons. First, the isovector pion plays an important role in the relativistic description of spin-isospin resonances. Because of the parity conservation this degree of freedom is absent in the ground-state description under the Hartree approximation. Therefore, the pion is out of control in this bestfitting effective field theory. Second, to cancel the contact interaction coming from the pseudovector pion-nucleon coupling, a zero-range counter-term is needed with the strength g ′ = 1/3 exactly [15]. However, in order to reproduce the excitation energies of the GTR, g ′ must be treated as an adjustable parameter in RMF+RPA m...

The β-decay half-lives of neutron-rich nuclei with 20 Z 50 are systematically investigated using the newly developed fully self-consistent proton-neutron quasiparticle random phase approximation (QRPA), based on the spherical relativistic Hartree-Fock-Bogoliubov (RHFB) framework. Available data are reproduced by including an isospin-dependent proton-neutron pairing interaction in the isoscalar channel of the RHFB+QRPA model. With the calculated β-decay half-lives of neutron-rich nuclei a remarkable speeding up of r-matter flow is predicted. This leads to enhanced r-process abundances of elements with A 140, an important result for the understanding of the origin of heavy elements in the universe.

Self-consistent random phase approximation (RPA) approaches in the relativistic framework are applied to calculate the isospin symmetry-breaking corrections δc for the 0 + → 0 + superallowed transitions. It is found that the corrections δc are sensitive to the proper treatments of the Coulomb mean field, but not so much to specific effective interactions. With these corrections δc, the nucleusindependent Ft values are obtained in combination with the experimental f t values in the most recent survey and the improved radiative corrections. It is found that the constancy of the Ft values is satisfied for all effective interactions employed. Furthermore, the element V ud and unitarity of the Cabibbo-Kobayashi-Maskawa matrix are discussed.

Covariant density functional theory and the tilted axis cranking method are used to investigate antimagnetic rotation (AMR) in nuclei for the first time in a fully self-consistent and microscopic way. The experimental spectrum as well as the B(E2) values of the recently observed AMR band in (105)Cd are reproduced very well. This gives a further strong hint that AMR is realized in specific bands in nuclei.

The origin of pseudospin symmetry (PSS) and its breaking mechanism are explored by combining supersymmetry (SUSY) quantum mechanics, perturbation theory, and the similarity renormalization group (SRG) method. The Schrödinger equation is taken as an example, corresponding to the lowest-order approximation in transforming a Dirac equation into a diagonal form by using the SRG. It is shown that while the spin-symmetry-conserving term appears in the single-particle Hamiltonian H, the PSS-conserving term appears naturally in its SUSY partner HamiltonianH.The eigenstates of Hamiltonians H andH are exactly one-to-one identical except for the so-called intruder states. In such a way, the origin of PSS deeply hidden in H can be traced in its SUSY partner HamiltonianH. The perturbative nature of PSS in the present potential without spin-orbit term is demonstrated by the perturbation calculations, and the PSS-breaking term can be regarded as a very small perturbation on the exact PSS limits. A general tendency that the pseudospinorbit splittings become smaller with increasing single-particle energies can also be interpreted in an explicit way.

Bayesian neural network (BNN) approach is employed to improve the nuclear mass predictions of various models. It is found that the noise error in the likelihood function plays an important role in the predictive performance of the BNN approach. By including a distribution for the noise error, an appropriate value can be found automatically in the sampling process, which optimizes the nuclear mass predictions. Furthermore, two quantities related to nuclear pairing and shell effects are added to the input layer in addition to the proton and mass numbers. As a result, the theoretical accuracies are significantly improved not only for nuclear masses but also for singlenucleon separation energies. Due to the inclusion of the shell effect, in the unknown region, the BNN approach predicts a similar shell-correction structure to that in the known region, e.g., the predictions of underestimation of nuclear mass around the magic numbers in the relativistic meanfield model. This manifests that better predictive performance can be achieved if more physical features are included in the BNN approach.1 Mass is a fundamental property of atomic nuclei. It can be employed to extract various nuclear structure information, such as nuclear pairing correlation, shell effect, deformation transition, and so on [1]. Nowadays it has been also widely used to determine nuclear effective interactions [2]. Moreover, nuclear mass is essential to determine the nuclear reaction energy in astrophysics and hence plays a crucial role in understanding the origin of elements in Universe [3]. In addition, the accurate mass determination is very important to test the unitarity of Cabibbo-Kobayashi-Maskawa matrix [4,5].Measurements of nuclear mass have achieved great progress in recent years [6,7] and about 3000 nuclear masses have been measured up to now [8]. However, the accurate predictions of nuclear mass are still a great challenge for theoretical models, due to the difficulties in the exact theory of nuclear interaction and in the quantum many-body calculations. Nowadays three types of nuclear models are mainly used in global mass predictions: macroscopic, macroscopic-microscopic, and microscopic mass models. The Bethe-Weizsäcker (BW) mass formula is the first model used to estimate nuclear masses [9,10], which belongs to the macroscopic type. It assumes the nucleus is similar to a charged liquid drop, so the microscopic effects, such as shell effect, cannot be well described. By taking into account the important corrections related to the microscopic effects, the macroscopic-microscopic models are developed, such as the finite-range droplet model (FRDM) [11] and the Weizsäcker-Skyrme (WS) model [12]. The microscopic mass models are mainly rooted in the density functional theory, which are more complicated but potentially have a better ability of extrapolation. In the non-relativistic framework, a series of Hartree-Fock-Bogoliubov (HFB) mass models have been constructed with the Skyrme [13,14] or Gogny [15] effective interactions. In recent years,...