Relativistic effects on the kink of nuclear charge radii in lead

Abstract

The kink in the nuclear charge radii of lead isotopes is studied in the relativistic mean field approximation framework, using the parameter set NL3∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^*$$\\end{document}. Within this approach, it is shown that the small component of the single-particle Dirac spinors plays an essential role in the kink formation through its effects on the single-particle central potential. This is because the structure of this potential in terms of the σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document}-scalar and ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}-vector fields and the contributions of the small component to the scalar and nucleon densities have opposite signs. The impact of the spin-orbit interaction of the valence neutrons on the kink, through its effects on their wave functions, is very small for 1i states but significant for 2g states. Due to relativistic contributions, the effects on the kink of neutrons in the valence levels of a spin-orbit doublet with j=l+1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$j=l+1/2$$\\end{document} and j=l-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$j=l-1/2$$\\end{document} are rather different from each other, even in the limit case of neglecting their spin-orbit interaction.