The ground state properties including the density distributions of the neutrons, protons and matter as well as the corresponding root mean square (rms) radii of proton-rich halo candidates 8B, 12N, 23Al and 27P have been studied by the single particle Bear– Hodgson (BH) wave functions with the two-body model of (core+p). It is found that the rms radii of these proton-rich nuclei are reproduced well by this model and the radial wave functions describe the long tail of the proton and matter density distributions. These results indicate that this model achieves a suitable description of the possible halo structure. The plane wave Born approximation (PWBA) has been used to compute the elastic charge form factors.

The neutron, proton, and matter densities of the ground state of the proton-rich ²³Al and ²⁷P exotic nuclei were analyzed using the binary cluster model (BCM). Two density parameterizations were used in BCM calculations namely; Gaussian (GS) and harmonic oscillator (HO) parameterizations. According to the calculated results, it found that the BCM gives a good description of the nuclear structure for above proton-rich exotic nuclei. The elastic form factors of the unstable ²³Al and ²⁷P exotic nuclei and those of their stable isotopes ²⁷Al and ³¹P are studied by the plane-wave Born approximation. The main difference between the elastic form factors of unstable nuclei and the

An analytical form of the ground state charge density distributions
for the low mass fp shell nuclei ( 40  A  56 ) is derived from a
simple method based on the use of the single particle wave functions
of the harmonic oscillator potential and the occupation numbers of
the states, which are determined from the comparison between theory
and experiment.
For investigating the inelastic longitudinal electron scattering form
factors, an expression for the transition charge density is studied
where the deformation in nuclear collective modes is taken into
consideration besides the shell model space transition density. The
core polarization transition density is evaluated by adopting the
shape of Tassie mod

 An analytical form of the ground state charge density distributions
for the low mass fp shell nuclei ( 40  A  56 ) is derived from a
simple method based on the use of the single particle wave functions
of the harmonic oscillator potential and the occupation numbers of
the states, which are determined from the comparison between theory
and experiment.
For investigating the inelastic longitudinal electron scattering form
factors, an expression for the transition charge density is studied
where the deformation in nuclear collective modes is taken into
consideration besides the shell model space transition density. The
core polarization transition density is evaluated by adopting the
shape of Tass

Inelastic longitudinal electron scattering form factors for second
excited state C42 in 42Ti nucleus have been calculated using shell
model theory. Fp shell model space with configuration (1f7/2 2p3/2
1f5/2 2p1/2) has been adopted in order to distribute the valence
particles (protons and neutrons) outside an inert core 40Ca. Modern
model space effective interactions like FPD6 and GXPF1 have been
used to generate model space vectors and harmonic oscillator wave
function as a single particle wave function. Discarder space (core
orbits + higher orbits) has been included in (core polarization effect)
as a first order correction in microscopic theory to measure the
interested multipole form factors via the model

Shell model and Hartree-Fock calculations have been adopted to study the elastic and inelastic electron scattering form factors for 25Mg nucleus. The wave functions for this nucleus have been utilized from the shell model using USDA two-body effective interaction for this nucleus with the sd shell model space. On the other hand, the SkXcsb Skyrme parameterization has been used within the Hartree-Fock method to get the single-particle potential which is used to calculate the single-particle matrix elements. The calculated form factors have been compared with available experimental data.

     In the present study, the properties of the light elements, namely, H, He, Li, and Be, have been reviewed. Specifically, the nuclear decay of these nuclei has been reviewed. The mystery of the nuclear decay and potential is behind this work. The role of neutron has been investigated. The N/Z ratio has also been investigated in the study to relate the nuclear decay with the ratio. A new formula for nuclear potential has been suggested in the present study. This formula can describe the binding energy potential and the decayed particle energy depending on the N/Z ratio.

Inelastic longitudinal electron scattering form factors to 2+ and 4+ states in 65Cu nucleus has been calculated in the (2p3/2 1f 5/2 2p1/2) shell model space with the F5PVH effective interaction. The harmonic oscillator potential has been applied to calculate the wave functions of radial single-particle matrix elements. Two shell model codes, CP and NUSHELL are used to obtain results. The form factor of inelastic electron scattering to 1/21−, 1/22−, 3/22−, 3/23−, 5/21−, 5/22− and 7/2- states and finding the transition probabilities B (C2) (in units of e2 fm4) for these transitions and B (C4) (in units of e2 fm8) for the transition 7/2-, and comparing them with experimental data. Both the form factors and reduced transition pr