Nuclear landscape in covariant density functional theory

Abstract

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 Z ∼ 54, N = 126 and Z ∼ 82, N = 184 are very small due to the impact of spherical shell closures at N = 126 and 184.Keywords: Proton and neutron drip lines, covariant density functional theory, two-particle separation energies At present, the nuclear masses of approximately 3000 out of roughly 7000 nuclei expected between nuclear drip lines are known [1]. Nuclear existence ends at the drip lines. While the proton drip line has been delineated in experiment up to protactinium (Z = 91), the position of the neutron drip line beyond Z = 8 is determined only in model calculations. Different models and different parameterizations show rather large variations in predictions of the neutron drip line. Moreover, because of experimental limitations even in foreseeable future it will be possible to define the location of neutron-drip line for the majority of elements only in model calculations. In such a situation it is important to estimate the errors in the location of the predicted neutron drip line introduced by the use of the various calculations. In this context we have to distinguish the results and related theoretical uncertainties obtained within the same model, but with different parameterizations and the results and uncertainties obtained with different models.Theoretical uncertainties(errors) in the prediction of physical observables have several sources of origin. Within one class of models they are the consequences of specific assumptions and the optimization protocols. The differences in the basic assumptions of different model classes is another source. They lead to theoretical uncertainties which can be revealed only by a systematic comparison of a variety of models.The first attempt to estimate theoretical uncertainties in the definition of two-neutron drip line within one class of models has been performed within the Skyrme density functional theory (SDFT) in Ref. The question of theoretical errors in the definition of the neutron drip line is still not resolved since the important class of nuclear structure models known under name covariant density functional theory (CDFT) [7,8,9,10,11] has not been applied so far in a reliable way to the study of this quantity. Typically, non-relativisti...

The limits of the nuclear landscape explored by the relativistic continuum Hartree–Bogoliubov theory

“…Comparing to the drip line of RHB calculations in harmonic oscillator (HO) basis with NL3* [24,25], the present RCHB calculations show considerable difference from it. The considerable difference of the drip line between RHB in HO calculations and present RCHB calculations are due to different functionals (PC-PK1 or NL3*), different pairing forces used, and the treatment of continuum in coordinate or HO space.…”

“…3, the deformed RHB calculations with NL3* in harmonic oscillator basis [24] predicted less neutron-rich dripline nuclei than the RCHB calculations for most of the isotopic chains. Although quite time-consuming and numerically challenging, considering the deformation and continuum effects simultaneously is essential to determine the drip line and should be investigated in the future.…”

“…In addition to the neutron separation energies S 2n and S n , the two-proton S 2p and one-proton separation energies the nucleon drip lines predicted by mass table TMA [23] , HFB-21 [18], FRDM [7], WS3 [11], UNEDF [20], NL3* [24,25], and also PC-PK1…”

“…By employing the state-dependent BCS method with a zero-range pairing force, the first systematic study of the ground-state properties for over 7000 nuclei ranging from the proton drip line to the neutron drip line was performed [23]. To explore the location of the proton and neutron drip lines, a systematic investigation has been performed for even-even nuclei by employing relativistic Hartree-Bogoliubov (RHB) theory with four sets of parametrizations [24][25][26]. Very recently, the binding energies for even-even nuclei with proton number ranging from Z = 8 to Z = 108 were calculated and the dynamical correlation energies which include the rotational correction energies and quadrupole vibrational correction energies were investigated [27,28].…”

Neutron drip line: Single-particle degrees of freedom and pairing properties as sources of theoretical uncertainties

“…The analysis of theoretical uncertainties in the prediction of the position of the two-neutron and two-proton drip-lines has recently attracted great interest [1][2][3] because of the possibility to estimate the number of nuclei which may exist in nature. Fig.…”