Kink of the nuclear charge radius isotope shift and overlaps of the neutron and proton orbitals in lead

Abstract

Within the relativistic mean field approximation, we analyse the kink effect (KE) in the evolution of the charge radius isotope shift of lead isotopes as a function of the neutron number N. We show that if the interactions between neutron and proton states responsible for the KE are assumed to be proportional either to the overlaps of their corresponding wave functions or to those of their corresponding probability density distributions, it is not possible, by themselves, to explain the KE. However, we find that the small component of the single-particle Dirac spinors plays a relevant role in the kink formation. By considering the contribution of the $N-126$ valence neutrons to the proton central potential, we can explain the generation of the KE and why neutrons in the $1i_{11/2}$ orbital are more kinky than when they are in the $2g_{9/2}$ orbital.