Journal of Al-Nahrain University Vol.20 (3), September, 2017, pp.83-90 Science 83 Study of Charge Density Distributions and Elastic Charge Form Factors for 40 Ca and 48 Ca Arkan R. Ridha Department of Physics, College of Science, University of Baghdad, Baghdad-Iraq. Corresponding Author: arkan_rifaah@yahoo.com. Abstract The ground charge density distributions (CDD), elastic charge form factors and proton, charge, neutron, and matter root mean square () radii for stable 40 Ca and 48 Ca have been calculated using single-particle radial wave functions of Woods-Saxon (WS) and harmonic-oscillator (HO) potentials. Different central potential depths are used for each subshell which is adjusted so as to reproduce the experimental single-nucleon binding energies. An excellent agreement between the calculated  charge radii and experimental data are found for both nuclei using WS and HO potentials. The calculated proton  radii for 40 Ca are found to be in good agreement with experiment data using both WS and HO potentials while the results for 48 Ca showed an overestimation in WS potential and slight overestimation in HO potential. The calculated neutron  radii are found to be well predicted in HO potential for both 40 Ca and 48 Ca, while there is overestimation in WS results for both isotopes. The calculated  matter radii showed good agreement with experimental data for 40 Ca using WS potential while the result is underestimated in HO potential. For 48 Ca, the results obtained with HO potential is underestimated and slightly underestimated with WS potential. For both nuclei, the calculated ground charge density distributions evaluated with WS are in better agreement with the data than those of HO potential. Finally, the results of the calculated elastic charge form factors demonstrate excellent agreement with experimental data for both nuclei under study in WS potential on contrary to the results of HO potential which are completely failed to predict the existence of third diffraction minimum. [DOI: 10.22401/JNUS.20.3.13] PACS number(s): 21.60.Cs, 25.30.Bf Keywords: stable nuclei, ground density distribution, elastic form factor, root-mean-square radii, Woods-Saxon potential. 1. Introduction The spatial extent of atomic nuclei and the radial distribution of nuclear charge and matter have received great attention [1]. They are important to explore sizes and shapes of nuclei, besides to test the validity of the nuclear single-particle wave functions used especially in density folding models [2]. Because of the Gaussian fall-off behavior at large r of the harmonic-oscillator (HO) radial wave functions which does not reproduce the correct exponential tail. The HO potential is not accurate to describe the nuclear central confining potential because the potential continues to give a contribution even for much larger r and does not become or approaches zero. Elton and Swift [3] generated wave functions in a parameterized single-particle local potential and adjusted the parameters so as to fit the shape of the wave functions to elastic electron scattering data and the eigenenergies to the proton separation energies in the 1p and 2s-1d shell nuclei. Gibson et. al. [4] studied the ground state of the 4 He nucleus using the single-particle phenomenological model. Wave functions were generated from a potential (WS form) whose parameters are chosen to reproduce the correct neutron separation energy. The proton separation energy, electron scattering form factors were then calculated. Gamba et. al. [5] determined the parameters of a WS potential well for ten p-shell nuclei by fitting the electron scattering form factors and single-particle binding energies. Brown et. al. [6] described a new method of calculating nuclear charge and matter distributions. The method was applied to the core nuclei 16 O and 40 Ca. Brown et. al. [7] calculated the rms radii of valence orbits in the tin isotopes using the single-particle potential model. Streets et. al. [8] extracted the nuclear matter distributions from high-energy proton scattering data for many nuclei and compared with calculations using the single-