Charge radii in covariant density functional theory: a global view

Abstract

A systematic global investigation of differential charge radii has been performed within the CDFT framework for the first time. Theoretical results obtained with conventional covariant energy density functionals and separable pairing interaction of Ref.[1] are compared with experimental differential charge radii in the regions of the nuclear chart in which available experimental data crosses neutron shell closures at N = 28, 50, 82 and 126. The analysis of absolute differential radii of different isotopic chains and their relative properties indicate clearly that such properties are reasonably well described in model calculations in the cases when the mean-field approximation is justified. However, while the observed clusterization of differential charge radii of different isotopic chains is well described above the N = 50 and N = 126 shell closures, it is more difficult to reproduce it above the N = 28 and N = 82 shell closures because of possible deficiencies in underlying single-particle structure. The impact of the latter has been evaluated for spherical shapes and it was shown that the relative energies of the single-particle states and the patterns of their occupation with increasing neutron number have an appreciable impact on the evolution of the δ r 2 N,N values. These factors also limit the predictive power of model calculations in the regions of high densities of the single-particle states of different origin. It is shown that the kinks in the charge radii at neutron shell closures are due to the underlying single-particle structure and due to weakening or collapse of pairing at these closures. The regions of the nuclear chart in which the correlations beyond mean-field are expected to have an impact on charge radii are indicated; the analysis shows that the assignment of a calculated excited prolate minimum to the experimental ground state allows to understand the trends of the evolution of differential charge radii with neutron number in many cases of shape coexistence even at the mean-field level. It is usually assumed that pairing is a dominant contributor to odd-even staggering (OES) in charge radii. Our analysis paints a more complicated picture. It suggests a new mechanism in which the fragmentation of the single-particle content of the ground state in odd-mass nuclei due to particle-vibration coupling provides a significant contribution to OES in charge radii.

Local variations of charge radii for nuclei with even $Z$ from 84 to 120

“…The source of OES behavior is demonstrated by various possible mechanisms [70], such as the staggering oscillation in occupation of single-particle levels between odd and even isotopes [20] and the pairing contributions [23]. Besides, OES in the charge radii might be related to the evolution of nuclear deformation [71], etc.…”

“…Ref. [70], this modified formula can improve the description of nuclear charge radii well, but the accepted truth is that this term cannot be included self-consistently in conventional density functional theories (DFTs). Although the underlying physical meaning of this ansatz is not clear, its predictive power is non-negligible.…”

Global performance of covariant density functional theory in description of charge radii and related indicators

“…The detailed analysis of the nuclei in the regions (i) and (ii) performed in Refs. [15][16][17][18][19] clearly indicates that shape coexistence and the correlations beyond mean-field are the sources of these discrepancies. Note that the latter are neglected in our studies.…”

“…( 2)) is an indicator which is very sensitive to the shell closures, underlying single-particle structure, pairing interaction, and occupation pattern of the single-particle states and their evolution with neutron number (see Refs. [15,24] and references quoted therein). Their systematic global investigation has been performed within the CDFT framework in Ref.…”

“…Their systematic global investigation has been performed within the CDFT framework in Ref. [15] and theoretical results were compared with experimental data which crosses the neutron shell closures at N = 28, 50, 82, and 126. An example of such a comparison is presented in Fig.…”