Potential energy surfaces of actinide and transfermium nuclei from multi-dimensional constraint covariant density functional theories

Multi-dimensional constrained covariant density functional theories were developed recently. In these theories, all shape degrees of freedom \beta_{\lambda\mu} deformations with even \mu are allowed, e.g., \beta_{20}, \beta_{22}, \beta_{30}, \beta_{32}, \beta_{40}, \beta_{42}, \beta_{44}, and so on and the CDFT functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent couplings. In this contribution, some applications of these theories are presented. The potential energy surfaces of actinide nuclei in the (\beta_{20}, \beta_{22}, \beta_{30}) deformation space are investigated. It is found that besides the octupole deformation, the triaxiality also plays an important role upon the second fission barriers. The non-axial reflection-asymmetric \beta_{32} shape in some transfermium nuclei with N = 150, namely 246Cm, 248Cf, 250Fm, and 252No are studied.Comment: 7 pages, 6 figures; invited talk at the International Conference on Nuclear Structure and Related Topics, Jul 02-July 7, 2012, Dubn

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

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.Comment: 10 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 fil