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

To what extent does the self-consistent mean-field exist?

A non-convergent difficulty near level-repulsive region is discussed within the self-consistent mean-field theory. It is shown by numerical and analytic studies that the mean-field is not realized in the many-fermion system when quantum fluctuations coming from two-body residual interaction and quadrupole deformation are larger than an energy difference between two avoided crossing orbits. An analytic condition indicating a limitation of the mean-field concept is derived for the first time

Relativistic mean-field approximation with density-dependent screening meson masses in nuclear matter

The Debye screening masses of the $\sigma$, $\omega$ and neutral $\rho$ mesons and the photon are calculated in the relativistic mean-field approximation. As the density of the nucleon increases, all the screening masses of mesons increase. It shows a different result with Brown-Rho scaling, which implies a reduction in the mass of all the mesons in the nuclear matter except the pion. Replacing the masses of the mesons with their corresponding screening masses in Walecka-1 model, five saturation properties of the nuclear matter are fixed reasonably, and then a density-dependent relativistic mean-field model is proposed without introducing the non-linear self-coupling terms of mesons.Comment: 14 pages, 3 figures, REVTEX4, Accepted for publication in Int. J. Mod. Phys.