Bing-Nan Lu

Pseudospin Symmetry in Single Particle Resonant States

The pseudospin symmetry (PSS) is a relativistic dynamical symmetry connected with the small component of the Dirac spinor. The origin of PSS in single particle bound states in atomic nuclei has been revealed and studied extensively. By examining the zeros of Jost functions corresponding to the small components of Dirac wave functions and phase shifts of continuum states, we show that the PSS in single particle resonant states in nuclei is conserved when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. The exact conservation and the breaking of the PSS are illustrated for single particle resonances in spherical square-well and Woods-Saxon potentials.

Potential energy surfaces of actinide nuclei from a multidimensional constrained covariant density functional theory: Barrier heights and saddle point shapes

The potential energy surfaces of actinide nuclei in the (beta(20), beta(22), beta(30)) deformation space are obtained from a multidimensional constrained covariant density functional theory. With this newly developed theory, we are able to explore the importance of the triaxial and octupole shapes simultaneously along the whole fission path. It is found that aside from the octupole deformation, the triaxiality also plays an important role upon the second fission barriers. Both the outer and the inner barriers are lowered by the triaxial deformation compared with axially symmetric results. This lowering effect for the reflection-asymmetric outer barrier is 0.5 similar to 1 MeV, accounting for 10%similar to 20% of the barrier height. With the inclusion of the triaxial deformation, a good agreement with the data for the outer barriers of actinide nuclei is achieved.

Quadrupole deformation

The shapes of light normal nuclei and Lambda hypernuclei are investigated in the (beta,gamma) deformation plane by using a newly developed constrained relativistic mean field (RMF) model. As examples, the results of some C, Mg, and Si nuclei are presented and discussed in details. We found that for normal nuclei the present RMF calculations and previous Skyrme-Hartree-Fock models predict similar trends of the shape evolution with the neutron number increasing. But some quantitative aspects from these two approaches, such as the depth of the minimum and the softness in the. direction, differ a lot for several nuclei. For Lambda hypernuclei, in most cases, the addition of a Lambda hyperon alters slightly the location of the ground state minimum toward the direction of smaller beta and softer gamma in the potential energy surface E similar to (beta,gamma). There are three exceptions, namely, (13)(Lambda)C, (23)(Lambda)C, and (31)(Lambda)Si in which the polarization effect of the additional Lambda is so strong that the shapes of these three hypernuclei are drastically different from their corresponding core nuclei.

(\beta,\gamma)

A systematic analysis of low-lying quadrupole and octupole collective states is presented based on the microscopic energy density functional framework. By mapping the deformation constrained self-consistent axially symmetric mean-field energy surfaces onto the equivalent Hamiltonian of the sdf interacting boson model (IBM), that is, onto the energy expectation value in the boson condensate state, the Hamiltonian parameters are determined. The study is based on the global relativistic energy density functional DD-PC1. The resulting IBM Hamiltonian is used to calculate excitation spectra and transition rates for the positive- and negative-parity collective states in four isotopic chains characteristic for two regions of octupole deformation and collectivity: Th, Ra, Sm, and Ba. Consistent with the empirical trend, the microscopic calculation based on the systematics of β_2-β_3 energy maps, the resulting low-lying negative-parity bands and transition rates show evidence of a shape transition between stable octupole deformation and octupole vibrations characteristic for β3-soft potentials.

of light

Background: Many different shape degrees of freedom play crucial roles in determining the nuclear ground state and saddle point properties and the fission path. For the study of nuclear potential energy surfaces, it is desirable to have microscopic and self-consistent models in which all known important shape degrees of freedom are included. Purpose: By breaking both the axial and the spatial reflection symmetries simultaneously, we develop multidimensionally-constrained relativistic mean field (MDC-RMF) models. Methods: The nuclear shape is assumed to be invariant under the reversion of x and y axes, i.e., the intrinsic symmetry group is V-4 and all shape degrees of freedom beta(lambda mu) with even mu, such as beta(20), beta(22), beta(30), beta(32), beta(40), ..., are included self-consistently. The single-particle wave functions are expanded in an axially deformed harmonic oscillator (ADHO) basis. The RMF functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the nonlinear or density- dependent couplings. The pairing effects are taken into account with the BCS approach. Results: The one-, two, and three-dimensional potential energy surfaces of Pu-240 are illustrated for numerical checks and for the study of the effect of the triaxiality on the fission barriers. Potential energy curves of even-even actinide nuclei around the first and second fission barriers are studied systematically. Besides the first ones, the second fission barriers in these nuclei are also lowered considerably by the triaxial deformation. This lowering effect is independent of the effective interactions used in the RMF functionals. Further discussions are made about different predictions on the effect of the triaxiality between the macroscopic-microscopic and MDC-RMF models, possible discontinuities on PESs from self-consistent approaches, and the restoration of broken symmetries. Conclusions: MDC-RMF models give a reasonably good description of fission barriers of even-even actinide nuclei. It is important to include both the nonaxial and the reflection asymmetric shapes simultaneously for the study of potential energy surfaces and fission barriers of actinide nuclei and of those in unknown mass regions such as, e.g., superheavy nuclei.

\Lambda

Background: The pseudospin symmetry (PSS) has been studied extensively for bound states. Recently, we justified rigorously that the PSS in single-particle resonant states is exactly conserved when the attractive scalar and repulsive vector potentials of the Dirac Hamiltonian have the same magnitude but opposite sign [Phys. Rev. Lett. 109, 072501 (2012)]. Purpose: To understand more deeply the PSS in single-particle resonant states, we focus on several issues related to the exact conservation and breaking mechanism of the PSS in single-particle resonances. In particular, we are interested in how the energy and width splittings of PS partners depend on the depth of the scalar and vector potentials. Methods: We investigate the asymptotic behaviors of radial Dirac wave functions. Spherical square-well potentials are employed in which the PSS breaking part in the Jost function can be well isolated. By examining the zeros of Jost functions corresponding to small components of the radial Dirac wave functions, general properties of the PSS are analyzed. Results: By examining the Jost function, the occurrence of intruder orbitals is explained and it is possible to trace continuously the PS partners from the PSS limit to the case with a finite potential depth. The dependence of the PSS in resonances as well as in bound states on the potential depth is investigated systematically. We find a threshold effect in the energy splitting and an anomaly in the width splitting of pseudospin partners when the depth of the single-particle potential varies from zero to a finite value. Conclusions: The conservation and the breaking of the PSS in resonant states and bound states share some similar properties. The appearance of intruder states can be explained by examining the zeros of Jost functions. Origins of the threshold effect in the energy splitting and the anomaly in the width splitting of PS partners, together with many other problems, are still open and should be further investigated.

hypernuclei in constrained relativistic mean field model: shape evolution and shape polarization effect of

Background: Potential energy surfaces (PESs) of actinide nuclei are characterized by a two-humped barrier structure. At large deformations beyond the

\Lambda

Background: Studies of fission dynamics, based on nuclear energy density functionals, have shown that the coupling between shape and pairing degrees of freedom has a pronounced effect on the nonperturbative collective inertia and, therefore, on dynamic (least-action) spontaneous fission paths and half-lives. Purpose: The aim is to analyze the effects of particle-number fluctuation degrees of freedom on symmetric and asymmetric spontaneous fission (SF) dynamics, and to compare the findings with the results of recent studies based on the self-consistent Hartree-Fock-Bogoliubov (HFB) method.

hyperon

The nonaxial reflection-asymmetric beta(32) shape in some transfermium nuclei with N = 150, namely, Cm-246, Cf-248, Fm-250, and No-252, are investigated with multidimensional constrained covariant density functional theories. By using the density-dependent point-coupling covariant density functional theory with the parameter set DD-PC1 in the particle-hole channel, it is found that, for the ground states of Cf-248 and Fm-250, the nonaxial octupole deformation parameter beta(32) > 0.03 and the energy gain due to the beta(32) distortion is larger than 300 keV. In Cm-246 and No-252, shallow beta(32) minima are found. The occurrence of the nonaxial octupole beta(32) correlations is mainly from a pair of neutron orbitals, [734]9/2 (nu j(15/2)) and [622]5/2 (nu g(9/2)), which are close to the neutron Fermi surface, and a pair of proton orbitals, [521]3/2 (pi f(7/2)) and [633]7/2 (pi i(13/2)), which are close to the proton Fermi surface. The dependence of the nonaxial octupole effects on the form of the energy density functional and on the parameter set is also studied.

Microscopic description of octupole shape-phase transitions in light actinide and rare-earth nuclei

Multi-dimensional constrained covariant density functional theories were developed recently. In these theories, all shape degrees of freedom \beta_{\lambda\mu} deformations with even \mu are allowed, e.g., \beta_{20}, \beta_{22}, \beta_{30}, \beta_{32}, \beta_{40}, \beta_{42}, \beta_{44}, and so on and the CDFT functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent couplings. In this contribution, some applications of these theories are presented. The potential energy surfaces of actinide nuclei in the (\beta_{20}, \beta_{22}, \beta_{30}) deformation space are investigated. It is found that besides the octupole deformation, the triaxiality also plays an important role upon the second fission barriers. The non-axial reflection-asymmetric \beta_{32} shape in some transfermium nuclei with N = 150, namely 246Cm, 248Cf, 250Fm, and 252No are studied.