Research on the static fission properties of ${}^{240}\mathrm{Pu}$ within the reflection asymmetric relativistic mean-field theory

The reflection asymmetric relativistic mean-field (RASRMF) theory was applied to investigate the static fission properties of ${}^{240}\mathrm{Pu}$. The potential energy curves with different spatial symmetries were obtained, and the calculated fission barrier heights are in good agreement with available experimental data. Compared with other theoretical calculations, better consistency with experiments is achieved. The matter density distributions clearly show the shape evolution along the fission path. Notably, the outer barrier is significantly reduced due to the reflection asymmetric deformations, making mass-asymmetric fission more favorable. These results indicate that the reflection asymmetric degree of freedom plays an important role in regulating the fission barrier and fission path of ${}^{240}\mathrm{Pu}$. Furthermore, the sensitivity of fission barriers to pairing correlations was examined. The use of the BCS approximation with a constant pairing gap led to unphysical results; therefore, a variable pairing strength was used to evaluate its influence on the fission barriers. It was found that a slight increase in pairing strength enhanced ground state stability but reduced fission barrier heights, promoting fission through more effective state repopulation during nuclear elongation. This conclusion remains consistent across RASRMF calculations employing both the NL3 and PK1 parameters.

Figure 1

Potential energy curves of ${}^{240}\mathrm{Pu}$ as a function of the quadrupole deformation ${\beta }_2$. The black solid line corresponds to the result obtained in the RSRMF calculations, and the red solid line corresponds to that obtained in the RASRMF calculations. The energy is normalized with respect to the binding energy of the ground state. The parameter set used is NL3*.

Figure 2

Matter density distributions of ${}^{240}\mathrm{Pu}$ at the ground state, first saddle point, isomeric state, and second saddle point on the plane $x=0$. Panel (a) is for reflection symmetry imposed, and panel (b) is for reflection asymmetry imposed with ${\beta }_3=-0.029$. The parameter set used is NL3*.

Figure 3

The pairing gaps of neutrons and protons for ${}^{240}\mathrm{Pu}$ as a function of the quadrupole deformation ${\beta }_2$. These results are obtained in the RASRMF calculations with the parameter set NL3*.

Figure 4

The potential energy curves for ${}^{240}\mathrm{Pu}$ in the RASRMF calculations with the parameter sets NL1 [93] and NLSH [94]. The labels “constant $\mathrm{\Delta }$” and “constant $G$” represent the BCS approximation with a constant pairing gap $\mathrm{\Delta }$ and a constant strength $G$, respectively. The results with NL1 and NLSH are respectively displayed in the upper and lower panels.

Figure 5

The potential energy curves of ${}^{240}\mathrm{Pu}$ with different pairing strengths obtained in the RASRMF calculations. The parameter set used is NL3*.

Figure 6

The potential energy curves of ${}^{240}\mathrm{Pu}$ obtained in the RASRMF calculation with the three parameter sets NL3 [98], NL3* [85], and PK1 [99].