Probing the delicate balance of the spontaneous fission instability in sub-μs superheavy nucleus 252Rf

TL;DR

The paper investigates spontaneous fission stability in the superheavy nucleus 252Rf by analyzing high-K and shape isomer contributions within a configuration-constrained potential-energy-surface framework. It uses a multidimensional deformation space and blocking schemes to map energy landscapes along fission paths, revealing how triaxial, octupole, and higher-order deformations influence barriers. A key finding is that multipath decay routes to intermediate states can undermine stability, partially offsetting the high-K isomer’s stabilizing effect and explaining the observed lifetimes. The work emphasizes the critical role of including multiple deformation channels and diabatic vs adiabatic blocking in predicting fission probabilities for superheavy nuclei.

Abstract

Stimulated by the recent experimental discovery of the sub-$μ$s fission nucleus $^{252}$Rf [Phys. Rev. Lett. 134 (2025) 022501], we perform an improved configuration-constrained potential-energy-surface calculation, revealing the mechanism of intricate balance for the enhanced stability due to the high-$K$ (e.g., $K^π= 6^+$) isomer, possibly building on a shape isomeric state. The different deformation and coupling effects, such as triaxial $γ$, reflection-asymmetric $β_{3}$ and high-order $β_{6}$ deformations, are discussed for both ground state and isomeric state based on the corresponding potential-energy curves along the fission valley. In particular, it is pointed out for the first time that possible multipath decay, e.g., from the high-$K$ isomeric state to those states formed between potential energy surfaces of this isomeric state and the ground state during the fission process, may reduce the nuclear lifetime and balance the fission stability. These results elucidate not only the enhanced stability of the high-$K$ isomeric state, including the inversion of stability between it and the ground state, but also the limitation of the stability increase of such an isomeric state.

Figures (3)

• Figure 1: Neutron single-particle energies as a function of quadrupole deformation $\beta_{2}$ for $^{252}_{104}$Rf$_{148}$, focusing on the domain near the Fermi surface. Solid and dotted curves refer to the levels with positive and negative parity, respectively. The diagonalisations of the Hamiltonian matrices for positive and negative parities are independently performed and the curves with the same parity connect energies according to non-crossing rule, except for the two interested orbitals $5/2^{+}[622]$ and $7/2^{+}[624]$. More details, see the text.
• Figure 3: Calculated potential-energy curves against the quadrupole deformation $\beta_{2}$ for the ground state and the $K^\pi = 6^+ \{\nu5/2^{+}[622]$$\otimes$$\nu7/2^{+}[624]\}$ isomeric state (including the adiabatic- and diabatic-blocking results) of $^{252}$Rf. For simplicity, other deformation degrees of freedom are ignored.
• Figure 4: Four types of potential-energy curves as functions of deformation $\beta_2$ for the ground state (a) and the $K^\pi = 6^+ \{\nu5/2^{+}[622]$$\otimes$$\nu7/2^{+}[624]\}$ isomeric state (b) of $^{252}$Rf. Calculations are performed in the deformation space ($\beta_{2},\gamma,\beta_{3},\beta_{4},\beta_{6}$). At each $\beta_2$ point, the energy minimization is performed over {$\beta_{3},\beta_{4},\beta_{6}$} (I; solid red curve), {$\gamma,\beta_{4},\beta_{6}$} (II; solid green curve), {$\gamma,\beta_{3},\beta_{4}$} (III; solid blue curve) and {$\gamma,\beta_{3},\beta_{4},\beta_{6}$} (IV; solid black curve). For comparison, the ground-state curve IV in (a) is also plotted in (b) as a dash black curve. See text for further explanations.