Microscopic description of cluster radioactivity fission valleys along isotopic and isotonic chains

Abstract

Cluster radioactivity has been successfully described as a super-asymmetric fission mode within the microscopic self-consistent Gogny Hartree-Fock-Bogoliubov approximation [Phys. Rev. C 84, 044608 (2011)]. For nuclei preserving the neutron-to-proton $N/Z$ ratio of the doubly magic $^{208}$Pb, a cluster radioactivity fission valley has been identified. Such a valley can also be found both in actinides and super-heavy nuclei. In this paper, chains of isotopes and isotones are examined to determine the limits of existence of the cluster radioactivity fission mode. It is shown that the super-asymmetric valley can be found in a wide range of the nuclear chart. Nevertheless, the valley flattens more and more when diverging from the isospin asymmetry of $^{208}$Pb. For neutron-deficient nuclei with $N/Z <$ 1.41, it is found that the valley diminishes before reaching the scission point, and cluster radioactivity can not be observed.

Figures (13)

• Figure 1: Fragment of the nuclear chart. Black squares represent known even-even isotopes. Isotopes and isotones considered in this paper are marked in green. The blue line corresponds to the characteristic $N/Z =$126/82 ratio for $^{208}$Pb. The red lines correspond to the ratios 130/92 and 160/92 for $^{222}$U and $^{252}$U.
• Figure 2: PESs for the isotopes $^{222,232,242,252}$U. The asymmetric fission path is depicted with a yellow line. The super-asymmetric fission path is plotted with a white line before scission, and with a blue line after scission. The ground state is marked by a red dot, and the saddle by a black circle.
• Figure 3: The same as in Fig. \ref{['U1']}, but for the $N=140$ isotones $^{224}$Po, $^{230}$Th, $^{236}$Cm and $^{242}$No.
• Figure 4: Cluster fission paths, in the $(Q_{20}, Q_{30})$-coordinates, obtained for U isotopes (top panel) and $N=140$ isotones (bottom panel). The path corresponding to $^{232}$U is highlighted by dots. Open squares mark the saddle points.
• Figure 5: The nuclear matter distribution of $^{232}$U at the super-asymmetric fission path $Q_{20}=23 \mathrm{b}$, $Q_{30}= 20 \mathrm{b}^{3/2}$ (left) and at the ridge $Q_{20}=37 \mathrm{b}$, $Q_{30}= 20 \mathrm{b}^{3/2}$ (right). A circle of radius 6 fm is added to emphasize the sphericity of the heavy fragment on the path.