Comparison between shell model and self-consistent mean field calculations for ground charge density distributions and elastic form factors of ¹²C and ¹⁶O nuclei

The ground charge density distributions, elastic form factors and root mean square radii for ¹²C and ¹⁶O nuclei in 1p-shell nuclei are calculated in shell model using core plus valence and no-core–shell model calculations. The single-particle wave functions of harmonic-oscillators potential are used. For such potential, two harmonic-oscillators size parameters are used: one for neutron and the other for proton. Calculations are compared with the results of self-consistent mean field using SKX Skyrme parameterization and experimental data. The calculated charge density distributions in shell model for ¹²C and ¹⁶O nuclei show good agreement with experimental data. The calculated charge form factors at low q in shell model for ¹²C and ¹⁶O show good agreement with experimental data. At high q, the result for ¹⁶O shows no prediction for the position of second diffraction minimum. In general, it is found that enlarging the model space in shell model leads to suppress slightly the behavior of density distribution around central region and also the behavior of form factor at high q, which is good to approach experimental data. On the other side, such increase in model space leads to increase the calculated root mean square radii, which is the same behaviour of the results of Hartree–Fock calculations. The calculated charge form factors in Hartree–Fock calculations show the existence of many diffraction minima, which do not agree with experimental data in contrary to shell model, which predicts less diffraction minima. (author)