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

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

Bing-Nan Lu (吕炳楠), En-Guang Zhao (赵恩广), and Shan-Gui Zhou (周善贵)

Phys. Rev. C 85, 011301(R) – Published 11 January 2012

Abstract

The potential energy surfaces of actinide nuclei in the $(β_{20}, β_{22}, β_{30})$ 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 $\sim$ 1 MeV, accounting for $10 % \sim 20 %$ 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.

Received 31 October 2011

DOI:https://doi.org/10.1103/PhysRevC.85.011301

Authors & Affiliations

Bing-Nan Lu (吕炳楠)¹, En-Guang Zhao (赵恩广)^1,2,3, and Shan-Gui Zhou (周善贵)^1,2,*

¹State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
²Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000, China
³School of Physics, Peking University, Beijing 100871, China

^*sgzhou@itp.ac.cn

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Vol. 85, Iss. 1 — January 2012

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Images

Figure 1
Potential energy curves of $^{240}$ Pu with various self-consistent symmetries imposed. The solid black curve represents the calculated fission path with $V_{4}$ symmetry imposed, the red dashed curve represents that with axial symmetry (AS) imposed, the green dotted curve represents that with reflection symmetry (RS) imposed, the violet dotted-dashed line represents that with both symmetries (AS and RS) imposed. The empirical inner (outer) barrier height $B_{emp}$ is denoted by the gray square (circle). The energy is normalized with respect to the binding energy of the ground state. The parameter set used is PC-PK1.Reuse & Permissions
Figure 2
Potential energy surfaces of $^{240}$ Pu in the $(β_{20}, β_{30})$ plane from calculations (a) without and (b) with the triaxial deformation included. The energy is normalized with respect to the binding energy of the ground state. The numbers in (b) show the values of $β_{22}$ at these points. The fission path is represented by a dashed-dotted line. The ground state and fission isomer are denoted by full and open circles. The first and second saddle points are denoted by full and open triangles. The contour interval is 1 MeV.Reuse & Permissions
Figure 3
Sections of the three-dimensional PES of $^{240}$ Pu in the $(β_{22}, β_{30})$ plane calculated at $β_{20}$ = 0.3 (around the ground state), 0.6 (around the first saddle point), 0.9 (around the fission isomer), 1.3 (around the second saddle point), and 1.6 (beyond the outer barrier), respectively. The energy is normalized with respect to the binding energy of the ground state. The contour interval is 0.5 MeV. Local minima are denoted by crosses.Reuse & Permissions
Figure 4
The inner ( $B_{f}^{i}$ ) and outer ( $B_{f}^{o}$ ) barrier heights of even-even actinide nuclei. The axial (triaxial) results are denoted by open (full) symbols. The empirical values are taken from Ref. [45] and represented by gray squares.Reuse & Permissions
Figure 5
(a) One-dimensional potential energy curve $E \sim β_{20}$ and (b) two-dimensional potential energy surface $E \sim (β_{20}, β_{30})$ of $^{248}$ Cm, in the outer barrier region with the axial symmetry imposed in the calculation. In both figures, the energy is normalized with respect to the binding energy of the ground state. The fission path I (II) is represented by solid (dashed-dotted) lines and the corresponding saddle point is denoted by up (down) triangles. The fission isomer is denoted by an open circle. In (a), the empirical outer barrier height is depicted by the dashed-dotted line. In (b), the contour interval is 0.5 MeV.Reuse & Permissions

Physical Review C

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