# Master Project: Scattering of halo nuclei

**Project title:** “Scattering of halo nuclei”, Master program.

**Dates and places of research:** Cairo University, Egypt, 2007-2009.

**Sources of funding: **Financial support from Yemeni Ministry of Higher Education and Scientific Research

**Role in the project**: The main researcher.

**Advisors:** Prof. M.Y.M. Hassan, Prof. M. Y. H. Farag, Prof. E.H. Esmael

**Examiners:** Prof. V. K. Lukyanov, JINR, Dubna, Russia; Prof. Angela Bonaccorso, INFN, Pisa, Italy.

**Output of the project:** A thesis, presentation, and two articles in Physical Review C Journal

M.Y.M. Hassan, M.Y.H. Farag, E.H. Esmael, and

**H.M. Maridi**, “Elastic scattering and breakup effect analysis of^{11}Be+^{12}C at 38.4 MeV/nucleon”,**Phys. Rev. C****79**, 064608 (2009).M.Y.M. Hassan, M.Y.H. Farag, E.H. Esmael, and

**H.M. Maridi**,**“***Microscopic model analysis of*^{11}*Li+p elastic scattering at 62, 68.4, and 75 MeV/nucleon*”,**Phys. Rev. C****79**, 014612 (2009).

**Description**

**Description**

Light neutron-rich exotic nuclei at the drip line are characterized by weak binding energies that lead to ”exotic” features as halos. Halo nuclei exhibit a strong cluster structure and anomalously large matter radii. The matter density of the halo nuclei has a long tail due to their weak binding energy where the separation energy of the halo neutrons is very low, so they can easily broken. These nuclei are so short-lived that they cannot be used as targets. Instead, direct reactions can be done in inverse kinematics. To study the structure and reactions of the halo nuclei, it is useful to study the differential and reaction cross sections of the elastic scattering. This work is concerned with the study of elastic scattering of one- and two-neutron halo nuclei. Two reactions have been considered. Proton elastic scattering of ^{11}Li nucleus and ^{11}Be + ^{1}^{2}C elastic scattering taking into consideration breakup effect.

**Microscopic model analysis of **^{11}**Li****+p**** elastic scattering**

^{11}Li+p elastic scattering data at three energies, 62, 68.4, and 75 MeV/nucleon, are analyzed with density-dependent M3Y and KH effective nucleon-nucleon (NN) interactions in the framework of the single folding model. The parameters of density-dependent term are adjusted to fulfill saturation of nuclear matter. The optical potentials (OP’s) and cross sections are calculated using four model densities of ^{11}Li, G (one-parameter Gaussian), GG (Gaussian-Gaussian), GO (Gaussian-Oscillator), and the COSMA (cluster orbital shell model approximation). Comparative studies are performed for real, imaginary, and spin-orbit potentials with the phenomenological and microscopic forms. The microscopic volume and surface imaginary potentials are constructed from both the renormalized folded potentials and their derivatives. The sensitivity of the differential cross section to the four densities is tested. It is found that the ^{11}Li+p elastic scattering cross sections depend strongly upon the behavior of the corresponding potentials. The GG and GO densities obtained from analyzing the data, using Glauber multiple scattering theory at high energies, give good results at energies below 100 MeV/nucleon in the framework of the folding model. The OP’s calculated in the microscopic form using a few parameters give good agreement with the data. Thus, it is not necessary to introduce a large number of arbitrary fitting parameters as done in the phenomenological and semimicroscopic OP’s. The KH effective interaction successfully describes ^{11}Li+p elastic scattering as the popular M3Y interaction. The obtained results of the reaction cross section are in good agreement with previous calculations.

**Elastic scattering and breakup effect analysis of **^{11}**Be + **^{12}**C ****at 38.4 MeV/nucleon**

^{11}Be + ^{12}Celastic scattering data at 38.4 MeV/nucleon has been analyzed using the optical model. The optical potential is calculated in the framework of the double folding model using M3Y effective nucleon-nucleon interaction. The different models of 11Be density are tested and the model which does not include the halo structure gives poor fitting with data. The breakup effect is studied by introducing a complex dynamical polarization potential (DPP) which is added to the ”bare” potential. The DPP is taken in different forms that have been obtained from simple phenomenological, semiclassical approximation, and microscopic methods. The simple phenomenological DPP is approximated and related to the semiclassical approximation method. The sensitivity of the differential and reaction cross sections to these polarization potentials is tested. The microscopic DPP constructed from the derivative of the folding potential succeeded to describe the breakup effect well. It gives an explicit justification for the long range of the polarization potential.