The recent laser spectroscopic measurements of nuclear root-mean-square charge radii on a chain of Zr isotopes exhibit a rich structure. A prominent kink is observed at ${}^{90}\mathrm{Zr}$ and a sharp change is noticed between ${}^{98}\mathrm{Zr}$ and ${}^{100}\mathrm{Zr}$, in the neutron rich region. In the present work, the ground state properties of these nuclei are calculated in the relativistic mean field (RMF) framework. The calculations are in good accord with the experiment. The RMF densities are folded with the extended Jeukenne, Lejeune, and Mahaux energy and density dependent nucleon-nucleon interaction to yield the semimicroscopic optical potential which in turn is used to calculate the elastic scattering cross sections for 50 MeV proton scattering from a chain of Zr isotopes. The differential cross sections obtained from the calculations agree remarkably well with the experiment. The calculation reveals a correlation between the mean-square charge radii and the corresponding reaction cross sections for $A⩾88$. There is a monotonic increase in ${\sigma }_R$ from $A=84$ to 106 with the hint of a slight jump from $A=98$ to $A=100$.

• Received 2 April 2004

DOI:https://doi.org/10.1103/PhysRevC.70.044320