Fission Barrier of Superheavy Nuclei and Persistence of Shell Effects at High Spin: Cases of ${}^{254}\mathrm{No}$ and ${}^{220}\mathrm{Th}$

We report on the first measurement of the fission barrier height in a heavy shell-stabilized nucleus. The fission barrier height of ${}^{254}\mathrm{No}$ is measured to be $B_{\mathrm{f}}=6.0\pm 0.5\mathrm{MeV}$ at spin $15\hslash$ and, by extrapolation, $B_{\mathrm{f}}=6.6\pm 0.9\mathrm{MeV}$ at spin $0\hslash$. This information is deduced from the measured distribution of entry points in the excitation energy versus spin plane. The same measurement is performed for ${}^{220}\mathrm{Th}$ and only a lower limit of the fission barrier height can be determined: $B_{\mathrm{f}}(I)>8\mathrm{MeV}$. Comparisons with theoretical fission barriers test theories that predict properties of superheavy elements.

Figure 1

Entry distributions for $E_{\text{beam}}=219$ (a) and 223 MeV (b) obtained from one unfolding procedure. Each contour line corresponds to a decrement of 10% of the maximum population. The yrast line and neutron separation energy are represented by the solid red and dotted black lines, respectively. The neutron separation energy at spin $I$ is defined as $S_n(I)=S_n+E_{\text{yrast}}^{A-1}(I+1/2)-E_{\text{yrast}}^A(I)$, where $S_n$ is the ground-state mass difference, for $I>I_{\mathrm{g}.\mathrm{s}}^{A-1}$, and linearly extrapolated to the energy of the first $I=1/2\hslash$ state for $I<I_{\mathrm{g}.\mathrm{s}}^{A-1}$. The maximum possible excitation-energy range is represented by the blue dotted lines, with the higher (lower) value corresponding to a reaction at the front (back) of the target. The half-maximum point for each spin slice is marked in purple with error bars. The solid and dashed green lines between 10 and $22\hslash$ represent the $E_{1/2}$ values predicted with our deduced value for $B_f$ and with $B_f$ 2 MeV higher. Panels (c) and (d) show the corresponding spin projections of the distributions. The points where the spin distributions fall to 10% of their maximum are marked with a red arrow.

Figure 2

Plot of the $E_{\text{saddle}}$ points extracted from the entry distributions of ${}^{254}\mathrm{No}$ (a) and ${}^{220}\mathrm{Th}$ (b). For ${}^{254}\mathrm{No}$, points are given for the two beam energies: 219 (red squares) and 223 MeV (blue triangles). For ${}^{220}\mathrm{Th}$, the blue squares are the lower limits for $E_{\text{saddle}}$—see the text. The red line is the yrast energy; the dashed black line is the neutron separation energy. Theoretical saddle energies are shown for comparison: the triangles are from DFT [17]; the circles are from a macroscopic-microscopic model [4]. Based on the latter, the dotted brown line shows our estimate of saddle energies at high spin—see the text.

Figure 3

Entry distribution for ${}^{220}\mathrm{Th}$, with its spin projection. See Fig. 1 for a description.