Nuclear longitudinal form factors for axially deformed charge distributions expanded by nonorthogonal basis functions

In this paper, the nuclear longitudinal form factors are systematically studied from the intrinsic charge multipoles. For axially deformed nuclei, two different types of density profiles are used to describe their charge distributions. For the same charge distributions expanded with different basis functions, the corresponding longitudinal form factors are derived and compared with each other. Results show the multipoles C_λ of longitudinal form factors are independent of the basis functions of charge distributions. Further numerical calculations of longitudinal form factors of ¹²C indicates that the C₀ multipole reflects the contributions of spherical components of all nonorthogonal basis functions. For deformed nuclei, their charge RMS radii can also be determined accurately by the C₀ measurement. The studies in this paper examine the model-independent properties of electron scattering, which are useful for interpreting electron scattering experiments on exotic deformed nuclei.