Multidimensionally constrained relativistic mean-field study of triple-humped barriers in actinides

Background: Potential energy surfaces (PES's) of actinide nuclei are characterized by a two-humped barrier structure. At large deformations beyond the second barrier, the occurrence of a third barrier was predicted by macroscopic-microscopic model calculations in the 1970s, but contradictory results were later reported by a number of studies that used different methods. Purpose: Triple-humped barriers in actinide nuclei are investigated in the framework of covariant density functional theory (CDFT). Methods: Calculations are performed using the multidimensionally constrained relativistic mean field (MDC-RMF) model, with the nonlinear point-coupling functional PC-PK1 and the density-dependent meson exchange functional DD-ME2 in the particle-hole channel. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. Results: Two-dimensional PES's of Th-226,Th-228,Th-230,Th-232 and U-232,U-234,U-236,U-238 are mapped and the third minima on these surfaces are located. Then one-dimensional potential energy curves along the fission path are analyzed in detail and the energies of the second barrier, the third minimum, and the third barrier are determined. The functional DD-ME2 predicts the occurrence of a third barrier in all Th nuclei and U-238. The third minima in Th-230,Th-232 are very shallow, whereas those in Th-226,Th-228 and U-238 are quite prominent. With the functional PC-PK1 a third barrier is found only in Th-226,Th-228,Th-230. Single-nucleon levels around the Fermi surface are analyzed in Th-226, and it is found that the formation of the third minimum is mainly due to the Z = 90 proton energy gap at beta(20) approximate to 1.5 and beta(30) approximate to 0.7. Conclusions: The possible occurrence of a third barrier on the PES's of actinide nuclei depends on the effective interaction used in multidimensional CDFT calculations. More pronounced minima are predicted by the DD-ME2 functional, as compared to the functional PC-PK1. The depth of the third well in Th isotopes decreases with increasing neutron number. The origin of the third minimum is due to the proton Z = 90 shell gap at relevant deformations.