THEORETICAL STUDY OF PROTON HALO STRUCTURE AND ELASTIC ELECTRON SCATTERING FORM FACTOR FOR 23 Al AND 27 P NUCLEI BY USING FULL CORRELATION FUNCTIONS (TENSOR FORCE AND SHORT RANGE) †

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INTRODUCTION
The nuclear halo is a threshold effect with low separation energy.There are two different kinds of exotic halo nuclei: proton halo [1] and neutron halo [2,3].Neutron halo nuclei have recently undergone extensive experimental and theoretical study [4,5].However, studies on proton halos are very rare.Although the proton separation energy in some light nuclei such as 8 B and 17 F is very low [4,[6][7].
Emil Ryberg and others examined the impact of finite-range corrections for S-wave proton halo nuclei on the halo effective field theory [8].Dellagiacoma et al. [9] provided a straightforward phenomenological technique for creating dynamical short-range and tensor correlations.Da Providencia and Shakin [10] developed a similar correlation operator for explaining short-range correlation effects, as did Malecki and Picchi [11].Luay F. Sultan [12] used the binary cluster model within the single-particle wave functions of Gaussian and harmonic oscillator potentials to investigate the ground state density distributions of proton-rich 23 Al and 27 P halo nuclei.The radial wave functions of the calculated Woods-Saxon potentials for 8 B, 17 F, 17Ne, 23 Al, and 27 P have been used before Rafah I. Noori [13].
Using a coherent density fluctuation model and 2pF to study one-and two-proton halo nuclei for 23 Al, 26 P, and 28 S nuclei is presented by Maha Taha Yassin [14].The two-frequency shell model and the binary cluster model are used to investigate the ground state densities of unstable proton-rich 9 C, 12 N, and 23 Al exotic nuclei [15].
In this study, we will use the two-body charge density distributions (2BCDD's) in the ground state for the protonrich nuclei for ( 23 Al and 27 P) with full correlations (tensor force and short range) with we used two different oscillator size parameters bc and bv and we calculated of rms radii, density distributions for (protons, neutrons, and matter) and form factors for these exotic nuclei.

THEORY
The operator has been used to define the nucleon density of a point-like particle nucleus [16]: This operator can be transformed into a two-body density form ( ( ) ( ) ( ) ( ) ) as [17]: Another relevant transformation is that of the coordinates of the two particles, which may be expressed, ( Subtracting and adding (3-a) and (3-b) can be obtain: Using eqs.(3-c) and (3-d) in Eq (2), we obtain: Using the identity  (for three -dimension), where (a) is a constant.For closed shell nuclei with N=Z, the two ̶ body charge density operator can be deduced from Eq. (4) as: ( The operator from Equation ( 5) can be folded with the two ̶ body correlation functions ij f ~to yield an efficient two ̶ body charge density operator. ( where the from ij f  is given by [18]   It is clear that eq. ( 7) contains two kinds of correlations:  The first term of equation ( 7)'s two ̶ body short range correlations, which is expressed as ƒ(r ij ).Here 1  With the exception of 3 S 1 and 3 D 1 states, is a projection operator onto the space of all two ̶ body wave functions.Shortrange correlations should be observed as important functions of particle separation, which diminish the twobody wave function at short distances where the repulsive core forces the particles apart and heal to unity at a lengthy distance where the interactions are very weak.The two ̶ body short-range correlation is given by [18]: where r c ( fm) is the radius of a suitable hard core and,  = 25 fm -2 [20] correlation parameter.
 The strong tensor component in the nucleon-nucleon force induces the longer range two body tensor correlations that are shown in the second term of equation (7).
This projection operator only affects the 3 S 1 and 3 D 1 states.The typical tensor operator, P ij , is known as [18]: While α (A) can be defined as the strength of tensor correlation and it is non-zero just in the 3 S 1 and 3 D 1 channel.
Where the relative orbital angular momentum    and total spin   S of two particles are coupled to the channel spin   g a projection operator onto triplet coupled states of 3 1 S and 3 1 D .In Eq. ( 7) the radial part is easily included as it only modifies the radial integrals involving 12 r .Acting the operator of Eq. ( 6) into triplet 3   1 and acting the operator 12 f  into triplet 3   1 It makes sense to parameterize the core and halo densities independently in the case of exotic nuclei.Consequently, the following is how the halo nuclei's ground-state matter density distribution can be expressed [19]: The normalization condition of the above ground state densities is given by: g ρ represents one of the following densities: nucleon, charge, core, halo densities.The rms radii of corresponding above densities are given by [20]: where g is (proton, neutron or matter).
The PWBA was used to study the elastic electron scattering form factors from emitted by the nuclei under study.The charge form factor in PWBA is [21]: 0 4 ( ) (r)Sin( r)r r ( ) ( ) where the nucleon finite size correction F fs (q) is defined [22]: 2 0.43 4 ( ) where the free nucleon form factor F fs (q) for protons and neutrons is consider to be the same.According to [23], the center of mass correction F cm (q) is as follows: where b : The harmonic-oscillator size parameter and A : The nuclear mass number.As a result, when the shell model wave function is, removes F cm (q) eliminates the spurious state caused by the center of mass's motion.The form factor F(q) comprising the impact of two-body correlation functions may now be calculated by entering the ground state (r) of equation ( 6) into equation (14).

RESULTS AND DISCUSSION
The density distributions for (protons, neutrons, and matter) of the ground state of ( 23 Al and 27 P) nuclei and rms radii with the form factors F(q) were studied by the two body charge density distributions ( 2BCDD's) with effect shortrange and tensor force by using the two body oscillator model (core +1p) shell model with used parameters (bc), (bv), and by relying on equations 6, 7, and 11.
Table 1, summarizes some of the characteristics of halo nuclei [24,25].The average radius of neutrons and protons was calculated based on equations 6, 7, and 16, where we got the results shown in Table 2, when the full correlation (r c =0.5 fm, α =0.1) and without correlation (r c =0, α=0).It is found that the proton rms radius is larger than the neutron rms radius.   Mg and 26 Si respectively, and exotic nuclei ( 23 Al and 27 P) with oscillator size parameter (b m =1.87, 2.015) for 23 Al and 27 P respectively with effects of the short-range (r c = 0.5 fm) and the tensor force (α= 0.1).The calculated results are in good agreement with the indicated experimental data [26,27].The correlation short range force with root mean square radii . We note an increase in rms values with an increase in short-range force by relying on equations (7, 8), as we showed in Table 4. Table 5, show correlation tensor force with rms radii . It is found to decrease rms values with increased tensor force by relying on equations (7, 9), and 11. Figure 1 shows the relation between the two-body nucleon density distributions (2BNDD's) (in fm -3 ) of the ground state and r (in fm) for 23 Al and 27 P nuclei.The blue curve represents 2BNDD's for the core nuclei 22 Mg and 26 Si (proton + neutron) with oscillator size parameter (bc =2.85, 187) respectively.The green curve represents 2BNDD's for valence (one proton) for 23 Al and 27P nuclei with oscillator size parameter (bv=3.85,3.5) respectively, while the red solid curve represents the total calculation for the core nucleons and the valence one proton, and the shaded curve represents the experimental of nucleon densities of 23 Al and 27 P respectively [25,26]. Figure 1 shows that the computed matter density distributions show a long tail for all of these nuclei and shows that the halo phenomenon and the long tail in 23 Al and 27 P are connected to the outer one proton for nucleon densities but not to the core nucleons, which is consistent with the experimental data.Figure 3: The neutron (blue curves), proton (brown curves), and matter (red curves) show densities of 23 Al and 27 P, respectively.The proton diffuseness is also larger than the neutron diffuseness in these nuclei.There is a large density difference between the proton and neutron in 23 Al and 27 P.The usual performance of the halo nucleus (i.e., the long tail) is apparent in the proton density distributions (brown curves), as indicated by these figures.For 23 Al and 27 P, the difference between the rms radii of the proton and the neutron is (r p -r n = 0.52613, 0.65066 fm).This difference is also supported by the halo structure of these alien cores.
It is seen from the Figure 4 a plotted for the elastic form factor versus q (in fm -1 ) for 23 Al and 27 P calculated with PWBA.The blue solid curve represents the form factor for 2BCDD's with (F fs ≠0, F cm ≠0) and oscillator size parameter (b m =1.87 fm for 23 Al and b m =1.912 fm for 27 P), the red curve represents the form factor for 2BCDD's with correlation and oscillator size parameter (b m =1.87 fm for 23 Al and b m =1.912 fm for 27 P), (F fs = 0, F cm = 0) i.e the finite nucleon size and the center of mass corrections doesn't take into account.The filled circle represents the experimental elastic form factors of 27 Al and 31 P [28].The form factor is determined by the detailed properties of a single proton halo as well as the difference, which is determined by the mass number and the size parameter bm.We obtain good agreement at the momentum for q<3.6, and we note that the behavior of the theoretical results for halo nuclei ( 23

CONCLUSIONS
In this work, halo nuclei are known to have a valence of a proton, the halo of a proton occupies a 2s 1/2 orbital.The measured material density of our halo nuclei showed a long-tailed behavior using the two-body nucleus density distribution framework with two different oscillator size parameters b c and b v with tensor force effects (Increasing its effect, the rms radii increases) and the short range (the increase its effect, the rms radii decreases), which are consistent with the experimental data.The large variation in charge form factors between unstable nuclei ( 23 Al and 27 P) and stable isotopes ( 27 Al and 31 P) is due to the same charge distribution of the protons.

Figure 1 .
Figure 1.Core, halo and matter density distribution of ( 23 Al and 27 P).

Figure 2
Figure2illustrates a comparison of the matter density distributions of halo ( 23 Al and 27 P) (red line) with the matter density distributions of the stable nuclei ( 27 Al and 31 P) (yellow line) by using 2BCDD's with the effect of short-range and tensor force, we shown along tail is clearly in the matter distribution of the halo nuclei.

3 )Figure 2 .
Figure 2. Comparison of matter density distribution of exotic nuclei ( 23 Al and 27 P) with that of stable nuclei ( 27 Al and 31 P).

Table 1 .
Some properties of23Al and 27 P nuclei

Table 2 .
The calculated neutrons and protons rms radii for nuclei ( 23 Al and 27 P)

Table 3 ,
shows the calculated rms radii for core nuclei ( 22 Mg and26Si) with oscillator size parameter (b c =2.85, 187) for

Table 3 .
The calculated core, valance and matter radii rms with experimental data for23Al and 27 P nuclei

Table 4 .
The calculated of the rms radii with different values for the short-range correlations for23Al and 27 P nuclei

Table 5 .
The calculated of the rms radii with different values for the tensor force correlations for23Al and 27 P nuclei Al and 27 P) matches the practical results for stable nuclei (27Al and 31 P).Comparison of proton, neutron and matter densities for23Al and 27 P halo