On the relativistic origin of the kink effect in the chain of Pb isotopes

Abstract

We investigate the origin of the kink effect (KE) in the relativistic mean field theory by transforming the single-particle Dirac equation into a Schrödinger-like equation. It is found that relativistic self-consistent effects as well as contributions coming from the ρ meson determine the actual structure of the KE. However, the spin-orbit force generated by the ρ meson has no significant influence on the KE. On the other hand, in Refs. [3,4] the anomalous behavior of the charge radii of these isotopes has been studied in the relativistic mean field approach (RMFA). The Pb data are well described by this type of theory. In Ref.[4] it is supposed that the success of the RMFA in reproducing the KE is achieved due to the weak isovector dependence of the spin-orbit force generated by the RMFA.In Ref.[5] the problem of isotopic shifts has been investigated with exhaustive detail, both in the SHF and RMFA. The authors of Ref.[5] have proposed a new Skyrme functional SkI4 with a more general structure of the spin-orbit force than that of the standard Skyrme functional. They have also succeeded to reproduce the KE, but at the price of introducing an extra parameter for the two body spin-orbit potential.As the authors of Refs. [3,4] state, the standard RMFA provides an excellent description of the anomalous kink in the isotopic shifts about 208 P b without using extra fitting parameters. In the present paper we shall focus our interest into the problem of the origin of the KE in the RMFA paying special attention to the role of the isovector ρ meson in the kink structure.In the RMFA [6], the relativistic single-nucleon wave function ψ( r), for a nucleon with the rest mass M, satisfies the Dirac equationwhere E = M + ε and ε is the binding energy eigenvalue while S( r) and V ( r) are the scalar and vector potentials, respectively, defined as follows: where the central potential V cent and the spin-orbit potential V SO are given by: For simplicity, we shall mainly concentrate our discussion in the three Pb isotopes 206 P b, 208 P b and 210 P b. The most stable configuration of the 210 P b isotope in the two nonlinear models considered contains two neutrons in the 1i 11/2 states. In the L model, the two configurations in which two neutrons fill up the 1i 11/2 or 2g 9/2 single-particle states are almost degenerate (we shall refer to these two configurations as IC and GC, respectively).We approach the 210 P b ground state by the IC in both linear and nonlinear models, although the BCS formalism would be more appropriate in the first case. Nevertheless, we expect that our conclusions are also valid for the L model, at least, at a qualitative level.The self-consistent results for the charge radii corresponding to the exact models are summarized in Table I, case a, and in Fig. 1 (the r c are normalized in this figure to the 3

Isotopic dependence of the nuclear charge radii and binding energies in the relativistic Hartree-Fock formalism

“…It is worth noting that a decrease of K by means of a mechanism different from the one we have found here, which is based on the m * σ dependence on the density, will not necessarily produce the same increase of the KE 6) . In particular, one can expect that the KE will depend also on the specific form of the E(ρ B )/A for ρ B < ρ 0 , since this region has a strong influence on the value of r c .…”

“…The RHA may provide a good description of the isotopic shift of the charge radii in the above-mentioned chain [5]. In a previous paper [6], we also addressed this question in the RHA. It was found that relativistic self-consistent effects as well as contributions coming from the ρ vector meson are important in determining the actual structure of the anomalous KE, both in linear and nonlinear models.…”

“…The understanding of the evolution of these observables, for different elements, in their isotopic chains, is still an open question that has attracted the attention of nuclear physicists in recent years [1][2][3][4][5][6][7][8][9][10]. Its elucidation will help also to improve our knowledge in some other related topics like superheavy elements, halo nuclei or neutron stars which are fundamental research topics in nuclear physics nowadays.…”

Interactions effectives, théories de champ moyen, masses et rayons nucléaires

“…Cette analyse confirme d'une part l'aptitude des modèles non relativistes à décrire des effets fins sur les rayons qui ne sont pas le seul fait des modèles relativistes [281] et d'autre part l'importance des corrélations tels que celles dues au mouvement du centre de masse qu'il faut désormais prendre en compte de manière systématique.…”

The kink effect of the nuclear charge radii in some isotopic chains and the nucleon-nucleon tensor force within nonlinear relativistic models in the Hartree-Fock approximation

“…This is a consequence of the shell structure of nuclei. The fact that the density-dependent Hartree-Fock model with standard Skyrme functionals [1] or Gogny forces [2] were not able to reproduce this effect for the Pb isotopic chain, for example, whereas the relativistic models in the simple mean-field approach did reasonably well [3,4], has increased the interest in understanding the mechanism responsible for the KE [5][6][7][8]. However, it seems that the full theoretical understanding has not been reached yet.…”