Charge density distributions for odd-A of 2s-1d shell nuclei

An analytical expression for the charge density distributions is derived based on the use of occupation numbers of the states and the single particle wave functions of the harmonic oscillator potential with size parameters chosen to reproduce the observed root mean square charge radii for all considered nuclei. The derived expression, which is applicable throughout the whole region of 2s -1d shell nuclei, has been employed in the calculations concerning the charge density distributions for odd- A of 2s -1d shell nuclei, such as Mg Al Si 25 27 29 , , and P 31 nuclei. It is found that introducing an additional parameters, namely 1 a , a1 and , a2 ،which reflect the difference of the occupation numbers of the states from the prediction of the simple shell model leads to obtain a remarkable agreement between the calculated and experimental results of the charge density distributions throughout the whole range of r.