Extraction of the second and fourth radial moments of nuclear charge density from the elastic electron-nucleus scattering

The expression for the radial moments $\left\langle r^{n}\right\rangle_{c}$ of nuclear charge density has been discussed under plane wave Born approximation (PWBA) method recently, which is significant to investigate surface thickness and neutron distribution radius. In this paper, we extend studies extracting second-order moment r^{2}\right\rangle_{c}$ fourth-order r^{4}\right\rangle_{c}$ from Coulomb form factors $|F_{C}(q)|^2$ by distorted (DWBA) at small momentum transfer $ q region. Based on relativistic mean-field (RMF) calculations, DWBA $F_{C}^{DW}(q)$ are expanded into q^4 $, where corresponding distributions corrected contributions spin-orbit densities. region, it found that experimental can be well reproduced considering Through further analyzing expansion coefficients $F_{C}^{DW}(q)$, relationship between proton number Z obtained. By relationship, extract limited data Within permissible range error, extracted consistent with in paper.