The ground state proton, neutron, and matter density distributions and corresponding root-mean-square radii (rms) of the unstable neutron-rich
22C exotic nucleus are investigated by two-frequency shell model (TFSM) approach. The single-particle wave functions of harmonic-oscillator (HO)
potential are used with two oscillator parameters bcore and bhalo. According to this model, the core nucleons of 20C are assumed to move in the model
space of spsdpf. Shell model calculations are performed with (0+2)hw truncations using Warburton-Brown psd-shell (WBP) interaction. The outer (halo) two neutrons in 22C are assumed to move in HASP (H. Hasper) model space (2s1/2, 1d3/2, 2p3/2, and 1f7/2 orbits) using the HASP interaction. The halo structure of 22C is confirmed with 2s1/2-dominant
configuration. Elastic electron scattering form factors of 22C nucleus are also investigated using the plane wave Born approximation. The effect of the long tail behavior (found in the calculated matter density distribution) on the elastic form factor of 22C is studied. The calculated matter densities and form factors of stable 14C and unstable 22C are compared. It
is found that the difference between the nucleon form factors of 22C and 14C nuclei is attributed to the difference presented in the matter densities of these nuclei. Hence the difference in the matter densities of 22C and 14C nuclei mainly comes from the neutron skin of the core 20C and from the difference in the neutron density distribution of the last two neutrons in
both 14C and 22C nuclei. It is concluded that elastic electron scattering from exotic nuclei can provide predictions for the near future experiments on the electron-radioactive beam colliders, where the effect of the neutron halo or skin on the charge distributions is planned to be studied.