Fission properties for $r$-process nuclei

We present a systematics of fission barriers and fission lifetimes for the whole landscape of superheavy elements (SHE), i.e., nuclei with $Z\ge 100$. The fission lifetimes are also compared with the $\alpha$-decay half-lives. The survey is based on a self-consistent description in terms of the Skyrme-Hartree-Fock (SHF) approach. Results for various different SHF parametrizations are compared to explore the robustness of the predictions. The fission path is computed by quadrupole constrained SHF. The computation of fission lifetimes takes care of the crucial ingredients of the large-amplitude collective dynamics along the fission path, as self-consistent collective mass and proper quantum corrections. We discuss the different topologies of fission landscapes which occur in the realm of SHE (symmetric versus asymmetric fission, regions of triaxial fission, bimodal fission, and the impact of asymmetric ground states). The explored region is extended deep into the regime of very neutron-rich isotopes as they are expected to be produced in the astrophysical $r$ process.

Figure 1

Upper panel: Raw potential energy surface (PES) $\mathcal{V}\left({\alpha }_{20}\right)$ and ZPE corrected PES $V\left({\alpha }_{20}\right)$ for ${}^{290}$Sg. The energy $E_0$ of the collective ground state is indicated by a heavy horizontal line. The points $a$, $b$, and $c$ indicate the three crossing points of the $E_0$ line with the collective potential $V\left({\alpha }_{20}\right)$. Tunneling and repetition rates $W$ and $T$ are also indicated. Lower: Inverse collective mass $B_{{\alpha }_{20}}$ calculated by a self-consistent cranking scheme (ATDHF cranking). Schematic nuclear shapes are sketched.

Figure 2

Fission lifetimes of the isotopes No, Rf, Sg, and Hs computed with three different Skyrme parametrizations, as indicated, and compared with data from [3, 6, 7, 50, 51, 52, 53, 54].

Figure 3

Fission barriers (lower) and lifetimes (upper) for two groups of experimental known superheavy elements. Compared are results from a variety of Skyrme parametrizations with experimental data [5, 50, 55, 56, 57, 58]. The error bars on the barriers for SV-min are the uncertainties in the extrapolation as implied in the least-squares fits of the parametrization [41].

Figure 4

Schematic survey of fission modes for the various SHE. The two panels on the left and right show examples for the different regions as indicated: a) triaxial fission, b) asymmetrical ground-state energy, c) bi- or multimodal fission, d) asymmetric calculation removes completely the outer barrier.

Figure 5

Systematics of fission barriers of even-even nuclei for four different Skyrme parametrizations SLy6 [40], SkI3 [33], SV-min [41], and SV-bas [41]. Grey indicates a possible triaxial fission, as already seen in Fig. 4.

Figure 6

Results for fission barriers of four theoretical mass models HFB-14 [42], ETFSI [65], FRDM [63], TF [66] in the same region of nuclei. The shown data are reduced to even-even nuclei to enable a better comparison.

Figure 7

Systematics of fission lifetimes calculated in the range of proton numbers $100\le Z\le 120$ and neutron numbers $140\le N\le 260$ for even-even nuclei using the Skyrme parametrizations SkI3, SLy6, SV-min, and SV-bas.

Figure 8

$\alpha$-decay half-lives computed by using the $Q_{\alpha }$ values and the semi empirical Viola-Seaborg formula.

Figure 9

Minimal lifetime plots for the competing decay channels $\alpha$ decay and spontaneous fission. Experimental known decay channels [50] are compared to results using the parametrization SV-min and SLy6.

Figure 10

PES of the isotopes ${}^{294}$Rf and ${}^{294}$Rf for symmetric and asymmetric shapes calculated with the Skyrme parametrization SLy6. The fission path is indicated by a faint horizontal line.

Figure 11

Difference of ground state energies $\Delta E_0$ and fission barriers $\delta B_f$ between reflection symmetric and asymmetric calculations for the isotopes as indicated. The upper panels show results computed with the Skyrme parametrization SLy6 and the lower panels with SV-min.

Figure 12

Comparison of symmetric and asymmetric fission barriers and half-lives in region b) of the schematic survey Fig. 4 where asymmetric ground states can play a role. The upper panels show barriers and the lower panels lifetimes. The left panels show results from reflection symmetric calculations and the right panels from calculations where asymmetric shapes were allowed. The results are calculated with the parametrization SV-min.