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

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

 An edge dominating set    of a graph  is said to be an odd (even) sum degree edge dominating set (osded (esded) - set) of G if the sum of the degree of all edges in X is an odd (even) number. The odd (even) sum degree edge domination number  is the minimum cardinality taken over all odd (even) sum degree edge dominating sets of G and is defined as zero if no such odd (even) sum degree edge dominating set exists in G. In this paper, the odd (even) sum degree domination concept is extended on the co-dominating set E-T of a graph G, where T is an edge dominating set of G.  The corresponding parameters co-odd (even) sum degree edge dominating set, co-odd (even) sum degree edge domination number and co-odd (even) sum degree edge domin

Let G be a graph with p vertices and q edges and  be an injective function, where k is a positive integer. If the induced edge labeling   defined by for each is a bijection, then the labeling f is called an odd Fibonacci edge irregular labeling of G. A graph which admits an odd Fibonacci edge irregular labeling is called an odd Fibonacci edge irregular graph. The odd Fibonacci edge irregularity strength ofes(G) is the minimum k for which G admits an odd Fibonacci edge irregular labeling. In this paper, the odd Fibonacci edge irregularity strength for some subdivision graphs and graphs obtained from vertex identification is determined.

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

The ground state densities of unstable neutron-rich 11Li and 12Be exotic nuclei are studied in the framework of the binary cluster model (BCM). The internal densities of the clusters are described by the single particle harmonic oscillator wave functions. The long tail performance is clearly noticed in the calculated neutron and matter density distributions of these nuclei. The structures of the two valence neutrons in 11Li and 12Be are found to be mixed configurations with dominant (1p1/2)2. Elastic electron scattering proton form factors for 11Li and 12Be are studied using the plane wave Born approximation (PWBA). It is found that the major difference between the calculated form factors of unstable nuclei [11Li, 12Be] and those of stab

The harmonic oscillator (HO) and Gaussian (GS) wave functions within the binary cluster model (BCM) have been employ to investigate the ground state neutron, proton and matter densities as well as the elastic form factors of two- neutron 6He and 16C halo nuclei. The long tail is a property that is clearly revealed in the density of the neutrons since it is found in halo orbits. The existence of a long tail in the neutron density distributions of 6He and 16C indicating that these nuclei have a neutron halo structure. Moreover, the matter rms radii and the reaction cross section (𝜎𝑅 ) of these nuclei have been calculated using the Glauber model.