Microscopic description of complex nuclear decay: Multimodal fission

Our understanding of nuclear fission, a fundamental nuclear decay, is still incomplete due to the complexity of the process. In this paper, we describe a study of spontaneous fission using the symmetry-unrestricted nuclear density functional theory. Our results show that the observed bimodal fission can be explained in terms of pathways in multidimensional collective space corresponding to different geometries of fission products. We also predict a new phenomenon of trimodal spontaneous fission for some rutherfordium, seaborgium, and hassium isotopes.

Figure 1

Two-dimensional total energy surfaces for ${}^{258}\mathrm{Fm}$ in the plane of collective coordinates: $Q_{20}\text{−}{Q}_{30}$ (a) and $Q_{20}\text{−}{Q}_{40}$ (b). The fission pathways are marked: symmetric compact fragments (sCF), symmetric elongated fragment (sEF), and asymmetric elongated fragments (aEF) pathways. The difference between contour lines is 5 MeV in (a) and 10 MeV in (b). The asymmetric trajectory aEF bifurcates away near $Q_{20}\approx 150$ b from $Q_{30}=0$ while the bifurcation between sEF and sCF occurs near $Q_{20}\approx 225$ b. The inset shows the multipole moments $Q_{\lambda 0}$ along sCF and sEF.

Figure 2

Calculated 1D fission pathways for ${}^{252,258,264}\mathrm{Fm}$ as functions of the driving quadrupole moment, $Q_{20}$. Open circles, light diamonds, and dark diamonds denote the symmetric compact fragment (sCF), symmetric elongated fragment (sEF), and asymmetric elongated fragment (aEF) valleys, respectively. The effect of triaxiality is important in the region of the first barrier; the corresponding energy gain is marked by gray shading.

Figure 3

Potential energy curves of ${}^{252}\mathrm{Fm}$, ${}^{256}\mathrm{Fm}$, ${}^{258}\mathrm{Fm}$, and ${}^{260}\mathrm{Fm}$ along optimum 1D paths containing the quantum zero-point energy correction, drawn in the common scale relative to values calculated at the ground-state minima.

Figure 4

Fission half lives of even-even fermium isotopes with $242⩽A⩽260$, calculated in this study compared with experimental data [52, 53] for the two values of the zero-point energy $E_0=0.3$ MeV and 0.5 MeV.

Figure 5

Similar to Fig. 2 except for fission pathways in ${}^{254}\mathrm{Cf}$ (asymmetric fission), ${}^{260}\mathrm{Fm}$ (symmetric compact fission), ${}^{258}\mathrm{No}$ (bimodal fission), and ${}^{262}\mathrm{Hs}$ (trimodal fission).

Figure 6

Summary of fission pathway results obtained in the present study. Nuclei around ${}^{252}{\mathrm{Cf}}_{154}$ are predicted to fission along the asymmetric path aEF; those around ${}^{262}{\mathrm{No}}_{160}$ along the symmetric pathway sCF. These two regions are separated by the bimodal symmetric fission (sCF + sEF) around ${}^{258}{\mathrm{Fm}}_{158}$. In a number of the Rf, Sg, and Hs nuclei, all three fission modes are likely (aEF + sCF + sEF; trimodal fission). In some cases, labeled by two-tone shading with one tone dominant, calculations predict coexistence of two decay scenarios with a preference for one. Typical nuclear shapes corresponding to the calculated nucleon densities are marked.