The charge density distributions (CDD) and the elastic electron
scattering form factors F(q) of the ground state for some even mass
nuclei in the 2s 1d shell ( Ne Mg Si 20 24 28 , , and S 32 ) nuclei have
been calculated 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. It is found that
introducing additional parameters, namely 1 , and , 2  which
reflect the difference of the occupation numbers of the states from
the prediction of the simple shell model leads to a remarkable
agreement between the calculated an

The atomic properties have been studied for He-like ions (He atom, Li+, Be2+ and B3+ions). These properties included, the atomic form factor f(S), electron density at the nucleus , nuclear magnetic shielding constant and diamagnetic susceptibility ,which are very important in the study of physical properties of the atoms and ions. For these purpose two types of the wave functions applied are used, the Hartree-Fock (HF) waves function (uncorrelated) and the Configuration interaction (CI) wave function (correlated). All the results and the behaviors obtained in this work have been discussed, interpreted and compared with those previously obtained.

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 shell nuclei, has been employed in the calculations concerning the charge density distributions for odd- of shell nuclei, such as and nuclei. It is found that introducing an additional parameters, namely and which reflect the difference of the occupation numbers of the states from the prediction of the simple shell model leads to obtain a remarkabl

Inelastic longitudinal electron scattering form factors have been calculated for isoscaler transition
T = 0 of the (0+ ®2+ ) and (0+ ®4+ ) transitions for the 20Ne ,24Mg and 28Si nuclei. Model
space wave function defined by the orbits 1d5 2 ,2s1 2 and 1d3 2 can not give reasonable result for
the form factor. The core-polarization effects are evaluated by adopting the shape of the Tassie-
Model, together with the calculated ground Charge Density Distribution CDD for the low mass 2s-1d
shell nuclei using the occupation number of the states where the sub-shell 2s is included with an
occupation number of protons (a ) .

An Expression for the transition charge density is investigated
where the deformation in nuclear collective modes is taken into
consideration besides the shell model transition density. The
inelastic longitudinal C2 and C4 form factors are calculated using
this transition charge density for the Ne Mg 20 24 , , Si 28 and S 32
nuclei. In this work, the core polarization transition density is
evaluated by adopting the shape of Tassie model togther with the
derived form of the ground state two-body charge density
distributions (2BCDD's). It is noticed that the core polarization
effects which represent the collective modes are essential in
obtaining a remarkable agreement between the calculated inelastic
longi

The charge density distributions (CDD) and the elastic electron scattering form
factors F(q) of the ground state for some odd mass nuclei in the 2s 1d shell, such
as K Mg Al Si 19 25 27 29 , , , and P 31
have been calculated 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. It is found that introducing
additional parameters, namely; 1  , and , 2  which reflect the difference of the
occupation numbers of the states from the prediction of the simple shell model leads
to very good agreement between the calculated an

The charge density distributions (CDD) and the elastic electron scattering form
factors F(q) of the ground state for some odd mass nuclei in the 2s 1d shell, such
as K Mg Al Si 19 25 27 29 , , , and P 31
have been calculated 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. It is found that introducing
additional parameters, namely; 1  , and , 2  which reflect the difference of the
occupation numbers of the states from the prediction of the simple shell model leads
to very good agreement between the calculated an

Elastic electron scattering form factors, charge density distributions and charge,
neutron and matter root mean square (rms) radii for P
24
PMg, P
28
PSi and P
32
PS nuclei are
studied using the effect of occupation numbers. Single-particle radial wave functions
of harmonic-oscillators (HO) potential are used. In general, the results of elastic
charge form factors showed good agreement with experimental data. The occupation
numbers are taken to reproduce the quantities mentioned above. The inclusion of
occupation numbers enhances the form factors to become closer to the data. For the
calculated charge density distributions, the results show good agreement with
experimental data except the fail to

the electron correlation effect for inter-shell can be described by evaluating the fermi hole and partial fermi hole for Li atom comparing with Be+ and B+2 ions

The calculations of the shell model, based on the large basis, were carried out for studying the nuclear ^29-34Mg structure. Binding energy, single neutron separation energy, neutron shell gap, two neutron separation energy, and reduced transition probability, are explained with the consideration of the contributions of the high-energy configurations beyond the model space of sd-shell. The wave functions for these nuclei are used from the model of the shell with the use of the USDA 2-body effective interaction. The OBDM elements are computed with the use of NuShellX@MSU shell model code that utilizes the formalism of proton-neutron.