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

Abstract

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 one was predicted by Mic-Mac model calculations in the 1970s, but contradictory results were later reported. In this paper, triple-humped barriers in actinide nuclei are investigated with covariant density functional theory (CDFT). Calculations are performed using the multidimensionally-constrained relativistic mean field (MDC-RMF) model, with functionals PC-PK1 and DD-ME2. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. Two-dimensional PES's of ${}^{226,228,230,232}$Th and ${}^{232,234,236,238}$U 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. DD-ME2 predicts the occurrence of a third barrier in all Th nuclei and ${}^{238}$U. The third minima in ${}^{230,232}$Th are very shallow, whereas those in ${}^{226,228}$Th and ${}^{238}$U are quite prominent. With PC-PK1 a third barrier is found only in ${}^{226,228,230}$Th. Single-nucleon levels around the Fermi surface are analyzed in ${}^{226}$Th, and it is found that the formation of the third minimum is mainly due to the $Z=90$ proton energy gap at ${\beta }_{20}\approx 1.5$ and ${\beta }_{30}\approx 0.7$. The possible occurrence of a third barrier in 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.

arXiv comment10 pages, 7 figures; Phys. Rev. C, in press; due to the limitation "The abstract field cannot be longer than 1,920 characters", the abstract appearing here is slightly shorter than that in the PDF file

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