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

TL;DR

This study investigates the existence of triple-humped fission barriers in actinide nuclei using advanced covariant density functional theory, revealing that the occurrence and depth of third minima depend on the nuclear functional and specific shell effects.

Contribution

It provides the first systematic analysis of triple-humped barriers in actinides with multidimensional CDFT, highlighting the influence of different energy functionals on barrier predictions.

Findings

DD-ME2 predicts third barriers in all Th nuclei and $^{238}$U.

Third minima are shallow in $^{230,232}$Th but prominent in $^{226,228}$Th and $^{238}$U.

The formation of the third minimum is mainly due to the $Z=90$ proton shell gap.

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.