Isospin dependence of nuclear charge radii and its microscopic demonstration

The analysis of experimental nuclear charge radii Rc indicates that Rc deviates systematically from the A1/3 law, i.e., Rc/A1/3 gradually decreases with increasing A, whereas Rc/Z1/3 remains almost a constant. This statement is also supported by the analysis of a large amount of experimental nuclear giant monopole resonance energy data Ex∝R-1. The deviation of nuclear charge radii from the A1/3 law is basically caused by the isospin independence of A1/3 law, and the isospin dependence has been partly included in Z1/3 law. In the frame of nuclear shell model, a microscopic demonstration of the Z1/3 law is given. The difference in the harmonic oscillator potential strength between proton and neutron (ωp and ωn) can be accounted for by the Z1/3 law. Similar to Wigner's nuclear isobaric multiplet mass equation (IMME), a modified Z1/3 law for nuclear charge radii is proposed. (authors)