Elastic Form Factors and Matter Density Distributions of Some Neutron-Rich Nuclei

Abstract


Introduction
Due to their exotic properties, studying exotic (halo) nuclear structures at the proton and neutron drip lines has become a hot subject in modern nuclear physics [1][2][3][4][5]. The halo effect is caused by the last few nucleons' low separation energy and occupation of states with =0,1 which allows the halo nucleon wave functions to extend to large matter radii [6]. Studying the halo structure is very useful for understanding the nuclear structure in both theories and experiments. Because halo nuclei have a short lifetime, they should be investigated by radioactive beam facilities [7]. Few body models can be used to represent the halo nuclei, which are considered to be produced by coupling a compact core with a few weakly bound nucleons. As a result, the halo systems can be divided into two types: the two-body system, in which one valence nucleon surrounds the nucleus core, likely the one neutron halo 19 C; and the three-body halo, in which two valence nucleons surround the nucleus core, likely the two-neutron halo 14 Be [8].
Abdullah [9] investigated the ground state in the ( 6 He, 11 Li, 12 Be, and 14 Be) halo nuclei using a three-body model (Core + 2n). The neutron density and predicted matter density for these nuclei demonstrate the characteristics of the long tail. The computed values for the density of matter were in good agreement with the experiment results. Abdullah [10] has investigated the ground state features such as the proton, neutron, and matter densities and the rms nuclear radii of unstable neutronrich 14 B, 15 C, 19 C, and 22 N nuclei using the cosh potential radial wave functions within the two-body model of (Core + n). The obtained results showed that the cosh potential radial wave functions of the two-body model are capable of reproducing neutron halo in these nuclei.
In this work, the Gaussian (GS) and Woods-Saxon wave functions within the two-body model (TBM) of were used to investigate the properties of the ground state for exotic 18 N and 20 F nuclei, including the neutron, proton and matter densities, and the corresponding rms radii and elastic form factors. The Kox and Glauber models were used to investigate the reaction cross-sections for these nuclei.

Theory
The matter density of halo nuclei can be obtained by adding the core density and the valence density [11]: (1) The GS and WS techniques were employed in this investigation. Both core and valence densities in the GS technique are described by the Gaussian wave functions [11]: where is the Gaussian function; In the WS technique, both core and valence densities are described by the WS radial wave functions obtained from the radial part solution of the Schrödinger equation with WS potential [12]: where: , and are the reduced mass, single-particle binding energy and the core potential, respectively.
can be written as [9]: where , and are the central, spin-orbit and Coulomb (for protons only) potentials, respectively, which take the following forms [9]: for neutrons. in Eq.(1) can be written in terms of neutron and proton densities [13]: where ( ) and ( ) are the core and valence neutron (proton) densities, respectively. The neutron , proton ( ), core matter rms radii are given by [9]: The elastic form factor is given as [14]: The Kox and Glauber models have been used to investigate the reaction cross sections for these nuclei. The in the framework of the Glauber model is given as [15]: w is the transparency function. In the Optical Limit Approximation (OLA), the T(b) is written as [16]: in the framework of the Kox model is given as [17]:

Results and Discussion
The GS and WS wave functions within the TBM of were utilized to investigate the ground-state characteristics of exotic 18 N (S n =2.828 MeV, τ 1/2 =619.2 ms) and 20 F (S n =6.601MeV, τ 1/2 =11.163s [18,19] nuclei, including distributions, related rms radii and elastic form factors. for these nuclei was investigated using the Kox formula and OLA of GM with the singleparticle HO wave functions. The analysis was performed assuming 17 N (J π , T=1/2 -, 3/2) and 19 F (J π , T=1/2 + , 1/2) cores plus one valence proton structure for 18 N (J π , T=1 -, 2) and 20 F (J π , T=2 + ,1), consecutively. The core and valence densities in the GS technique were described by the Gaussian functions. In the WS technique, both core and valence densities were described by the WS radial wave functions. The configurations of the 17 N and 19 F core nuclei are: consecutively. It was assumed that the valence neutron of both 18 N and 20 F occupied the ⁄ orbit.           Theoretical C0 form factors for 18,14 N Fig. 4(a) and 20,19 F Fig. 4(b) calculated by PWBA within proton densities obtained by the WS potential are shown in Fig. 4  The Kox formula and Glauber model with an OLA were used to compute the of 18 N and 20 F on the 12 C-target and the results are reported in Table 5 along with the experimental data [20]. The obtained results of are in good agreement with experimental data, as seen in Table 5.

Conclusions
The GS and WS wave functions within the TBM of were utilized to investigate the ground-state characteristics of halo 18 N and 20 F nuclei, including distributions and related rms radii. According to the calculated results, the TBM provides a good description of the nuclear structure for the above neutron-rich exotic nuclei. The PWBA was used to calculate the elastic form factors of exotic nuclei 18 N and 20 F as well as their stable isotopes 14 N and 19 F.
The variation in the due to the presence of the extra neutrons in 18 N and 20 F leads to a major difference between the elastic form factors of exotic nuclei and their stable isotopes.
for these nuclei was investigated using the Kox formula and OLA of GM with single-particle HO wave functions. Furthermore, the GM was employed to calculate the exotic nucleus matter rms radii. The calculated results for the selected exotic nuclei were in good agreement with the experimental data.