Abstract
We systematically investigate the elastic electron scattering on both stable and unstable nuclei with the relativistic eikonal approximation, where the charge density distributions of nuclei are from the self-consistent relativistic mean field model. Calculations show that the relativistic eikonal approximation can reproduce the experimental data of electron scattering on nuclei ranging from the light region, such as $^{12}\mathrm{C}$, to the heavy region, such as $^{208}\mathrm{Pb}$. This is the systematic test of the relativistic eikonal approximation for elastic electron scattering for both light and heavy nuclei. With this method, further studies are made of the variation of charge form factors along isotopic chains and the sensitivity of charge form factors to the changes of charge distribution. For isotopic chains with Z = 20 and 28, we find that the charge form factors vary significantly with neutron number. The charge form factors shift outward and downward when the target nucleus moves from the neutron-rich region to the proton-rich region along the isotopic chain. The significant shift shows that the charge form factor is very sensitive to a change of neutron number. If the isotopic shifts of the charge form factor are measured on the next-generation electron-nucleus collider (at RIKEN and GSI), the charge size and charge distribution can be determined for unstable nuclei. The calculations will provide a reference for future experiments.
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