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Register a new userThe fission barriers in Actinides and superheavy nuclei in covariant density functional theory
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The impact of pairing correlations on the fission barriers is investigated in Relativistic Hartree Bogoliubov (RHB) theory and Relativistic Mean Field (RMF)+BCS calculations. It is concluded that the constant gap approximation in the usual RMF+BCS calculations does not provide an adequate description of the barriers. The RHB calculations show that there is a substantial difference in the predicted barrier heights between zero-range and finite range pairing forces even in the case when the pairing strengths of these two forces are adjusted to the same value of the pairing gap at the ground state.
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The cranked relativistic Hartree-Bogoliubov (CRHB) theory has been applied for a systematic study of pairing and rotational properties of actinides and light superheavy nuclei. Pairing correlations are taken into account by the Brink-Booker part of finite range Gogny D1S force. For the first time in the covariant density functional theory (CDFT) framework the pairing properties are studied via the quantities (such as three-point $Delta^{(3)}$ indicators) related to odd-even mass staggerings. The investigation of the moments of inertia at low spin and the $Delta^{(3)}$ indicators shows the need for an attenuation of the strength of the Brink-Booker part of the Gogny D1S force in pairing channel. The investigation of rotational properties of even-even and odd-mass nuclei at normal deformation, performed in the density functional theory framework in such a systematic way for the first time, reveals that in the majority of the cases the experimental data are well described. These include the evolution of the moments of inertia with spin, band crossings in the $Ageq 242$ nuclei, the impact of the particle in specific orbital on the moments of inertia in odd-mass nuclei. The analysis of the discrepancies between theory and experiment in the band crossing region of $Aleq 240$ nuclei suggests the stabilization of octupole deformation at high spin, not included in the present calculations. The evolution of pairing with deformation, which is important for the fission barriers, has been investigated via the analysis of the moments of inertia in the superdeformed minimum. The dependence of the results on the CDFT parametrization has been studied by comparing the results of the calculations obtained with the NL1 and NL3* parametrizations.
The systematic investigation of the ground state and fission properties of even-even actinides and superheavy nuclei with $Z=90-120$ from the two-proton up to two-neutron drip lines with proper assessment of systematic theoretical uncertainties has been performed for the first time in the framework of covariant density functional theory (CDFT). These results provide a necessary theoretical input for the r-process modeling in heavy nuclei and, in particular, for the study of fission recycling. Four state-of-the-art globally tested covariant energy density functionals (CEDFs), namely, DD-PC1, DD-ME2, NL3* and PC-PK1, representing the major classes of the CDFT models are employed in the present study. Ground state deformations, binding energies, two neutron separation energies, $alpha$-decay $Q_{alpha}$ values and half-lives and the heights of fission barriers have been calculated for all these nuclei. Theoretical uncertainties in these physical observables and their evolution as a function of proton and neutron numbers have been quantified and their major sources have been identified. Spherical shell closures at $Z=120$, $N=184$ and $N=258$ and the structure of the single-particle (especially, high-$j$) states in their vicinities as well as nuclear matter properties of employed CEDFs are two major factors contributing into theoretical uncertainties. However, different physical observables are affected in a different way by these two factors. For example, theoretical uncertainties in calculated ground state deformations are affected mostly by former factor, while theoretical uncertainties in fission barriers depend on both of these factors.
Using the microscopic-macroscopic model based on the deformed Woods-Saxon single-particle potential and the Yukawa-plus-exponential macroscopic energy we calculated static fission barriers $B_{f}$ for 1305 heavy and superheavy nuclei $98leq Z leq 126$, including even - even, odd - even, even - odd and odd - odd systems. For odd and odd-odd nuclei, adiabatic potential energy surfaces were calculated by a minimization over configurations with one blocked neutron or/and proton on a level from the 10-th below to the 10-th above the Fermi level. The parameters of the model that have been fixed previously by a fit to masses of even-even heavy nuclei were kept unchanged. A search for saddle points has been performed by the Imaginary Water Flow method on a basic five-dimensional deformation grid, including triaxiality. Two auxiliary grids were used for checking the effects of the mass asymmetry and hexadecapole non-axiallity. The ground states were found by energy minimization over configurations and deformations. We find that the non-axiallity significantly changes first and second fission barrier in many nuclei. The effect of the mass - asymmetry, known to lower the second, very deformed barriers in actinides, in the heaviest nuclei appears at the less deformed saddles in more than 100 nuclei. It happens for those saddles in which the triaxiallity does not play any role, what suggests a decoupling between effects of the mass-asymmetry and triaxiality. We studied also the influence of the pairing interaction strength on the staggering of $B_f$ for odd- and even-particle numbers. Finally, we provide a comparison of our results with other theoretical fission barrier evaluations and with available experimental estimates.
Using the ETFSI (extended Thomas-Fermi plus Strutinsky integral) method, we have calculated the fission barriers of nearly 2000 exotic nuclei, including all the neutron-rich nuclei up to A=318 that are expected to be relevant to the r-process, and all the superheavy nuclei in the vicinity of N=184, with Z<=120. Our calculations were performed with the Skyrme force SkSC4, which was determined in the ETFSI-1 mass fit. For proton-deficient nuclei in the region of N=184 we find the barriers to be much higher than previously believed, which suggests that the r-process path might continue to mass numbers well beyond 300. For the superheavy nuclei we typically find barrier heights of 6-7 MeV.
The neutron and proton drip lines represent the limits of the nuclear landscape. While the proton drip line is measured experimentally up to rather high $Z$-values, the location of the neutron drip line for absolute majority of elements is based on theoretical predictions which involve extreme extrapolations. The first ever systematic investigation of the location of the proton and neutron drip lines in the covariant density functional theory has been performed by employing a set of the state-of-the-art parametrizations. Calculated theoretical uncertainties in the position of two-neutron drip line are compared with those obtained in non-relativistic DFT calculations. Shell effects drastically affect the shape of two-neutron drip line. In particular, model uncertainties in the definition of two-neutron drip line at $Zsim 54, N=126$ and $Zsim 82, N=184$ are very small due to the impact of spherical shell closures at N=126 and 184.
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