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Real stabilization method for nuclear single particle resonances

Li Zhang; Shan-Gui Zhou; Jie Meng; En-Guang ZhaoSubjects: Physics >> Nuclear Physics

We develop the real stabilization method within the framework of the relativistic mean field (RMF) model. With the self-consistent nuclear potentials from the RMF model, the real stabilization method is used to study single-particle resonant states in spherical nuclei. As examples, the energies, widths and wave functions of low-lying neutron resonant states in 120Sn are obtained. These results are compared with those from the scattering phase shift method and the analytic continuation in the coupling constant approach and satisfactory agreements are found. |

A new barrier penetration formula and its application to α-decay half-lives

Lu-Lu Li; Shan-Gui Zhou; En-Guang Zhao; Werner ScheidSubjects: Physics >> Nuclear Physics

Starting from the WKB approximation, a new barrier penetration formula is proposed for poten- tial barriers containing a long-range Coulomb interaction. This formula is especially proper for the barrier penetration with penetration energy much lower than the Coulomb barrier. The penetra- bilities calculated from the new formula agree well with the results from the WKB method. As a first attempt, this new formula is used to evaluate α decay half-lives of atomic nuclei and a good agreement with the experiment is obtained. |

Spherical-box approach for resonances in presence of Coulomb interaction

Shan-Gui Zhou; Jie Meng; En-Guang ZhaoSubjects: Physics >> Nuclear Physics

The spherical-box approach is extended to calculate the resonance parameters and the real part of the wave function for single particle resonances in a potential containing the long-range Coulomb interaction. A model potential is taken to demonstrate the ability and accuracy of this approach. The calculated resonance parameters are compared with available results from other methods. It is shown that in the presence of the Coulomb interaction, the spherical-box approach works well for not so broad resonances. In particular, for very narrow resonances, the present method gives resonance parameters in a very high precision. |

Particle-number conserving analysis of rotational bands in 247,249Cm and 249Cf

Zhen-Hua Zhang; Jin-Yan Zeng; En-Guang Zhao; Shan-Gui ZhouSubjects: Physics >> Nuclear Physics

The recently observed high-spin rotational bands in odd-A nuclei 247,249Cm and 249Cf [Tandel et al., Phys. Rev. C 82 (2010) 041301R] are investigated by using the cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method in which the blocking effects are taken into account exactly. The experimental moments of inertia and alignments and their variations with the rotational frequency ω are reproduced very well by the PNC-CSM calculations. By examining the ω-dependence of the occupation probability of each cranked Nilsson orbital near the Fermi surface and the contributions of valence orbitals to the angular momentum alignment in each major shell, the level crossing and upbending mechanism in each nucleus is understood clearly. |

Subjects: Physics >> Nuclear Physics

The shapes of light normal nuclei and Λ hypernuclei are investigated in the (β,γ) 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 γ direction, differ a lot for several nuclei. For Λ hypernuclei, in most cases, the addition of a Λ hyperon alters slightly the location of the ground state minimum towards the direction of smaller β and softer γ in the potential energy surface E ∼ (β,γ). There are three exceptions, namely, 13C, 23C, and ΛΛ 31Si in which the polarization effect of the additional Λ is so strong that the shapes of these three Λ hypernuclei are drastically different from their corresponding core nuclei. |

Subjects: Physics >> Nuclear Physics

For the first time the potential energy surfaces of actinide nuclei in the (β20, β22, β30) deformation space are obtained from a multi-dimensional 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 besides the octupole deformation, the triaxiality also plays an important role upon the second fission barriers. The outer barrier as well as the inner barrier are lowered by the triaxial deformation compared with axially symmetric results. This lowering effect for the reflection asymmetric outer barrier is 0.5 ∼ 1 MeV, accounting for 10 ∼ 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. |

Subjects: Physics >> Nuclear Physics

The rotational bands in nuclei with Z ≈ 100 are investigated systematically by using a cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method, in which the blocking effects are taken into account exactly. By fitting the experimental single-particle spectra in these nuclei, a new set of Nilsson parameters (κ and μ) and deformation parameters (ε2 and ε4) are proposed. The experimental kinematic moments of inertia for the rotational bands in even-even, odd-A and odd-odd nuclei, and the bandhead energies of the 1- quasiparticle bands in odd-A nuclei, are reproduced quite well by the PNC-CSM calculations. By analyzing the ω-dependence of the occupation probability of each cranked Nilsson orbital near the Fermi surface and the contributions of valence orbitals in each major shell to the angular momentum alignment, the upbending mechanism in this region is understood clearly. |

Subjects: Physics >> Nuclear Physics

By using a newly developed di-nuclear system model with a dynamical potential energy surface— the DNS-DyPES model, hot fusion reactions for synthesizing superheavy nuclei (SHN) with the charge number Z = 112–120 are studied. The calculated evaporation residue cross sections are in good agreement with available data. In the reaction 50Ti+249Bk → 299−x119 + xn, the maximal evaporation residue (ER) cross section is found to be about 0.11 pb for the 4n-emission channel. For projectile-target combinations producing SHN with Z = 120, the ER cross section increases with the mass asymmetry in the incident channel increasing. The maximal ER cross sections for 58Fe+244Pu and 54Cr+248Cm are relatively small (less than 0.01 pb) and those for 50Ti+249Cf and 50Ti+251Cf are about 0.05 and 0.25 pb, respectively. |

Pseudospin symmetry in single particle resonant states

Bing-Nan Lu; En-Guang Zhao; Shan-Gui ZhouSubjects: Physics >> Nuclear Physics

The pseudospin symmetry is a relativistic dynamical symmetry connected with the small com- ponent of the Dirac spinor. The origin of pseudospin symmetry 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 pseudospin symmetry 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 pseudospin symmetry are illustrated for single particle resonances in spherical square-well and Woods-Saxon potentials. |

Subjects: Physics >> Nuclear Physics

The non-axial reflection-asymmetric β32 shape in some transfermium nuclei with N = 150, namely 246Cm, 248Cf, 250Fm, and 252No are investigated with multidimensional constrained covariant den- sity 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 248Cf and 250Fm, the non-axial octupole deformation parameter β32 > 0.03 and the energy gain due to the β32 distortion is larger than 300 keV. In 246Cm and 252No, shallow β32 minima are found. The occurrence of the non-axial octupole β32 correlations is mainly from a pair of neutron orbitals [734]9/2 (νj15/2) and [622]5/2 (νg9/2) which are close to the neutron Fermi surface and a pair of proton orbitals [521]3/2 (πf7/2) and [633]7/2 (πi13/2) which are close to the proton Fermi surface. The dependence of the non-axial octupole effects on the form of energy density functional and on the parameter set is also studied. |