SHERIEF MOHAMED MOHAMED ALI HAMADA

Investigation of the elastic scattering of carbon ions on 1p-shell nuclei at energies near the Coulomb barrier

ABSTRACT

Dissertation submitted in fulfillment of the requirements for the degree Doctor of Philosophy (PhD) in specialty 6D060500 Nuclear Physics

Urgency of the work: Study of elastic scattering of light heavy ion nuclei at energies near the Coulomb barrier is of interest both in terms of establishing reliable values of the parameters of interaction potentials of heavy ions at low energies, and for studying the mechanism of cluster transfer in the scattering. The study of the interaction of light heavy ions elastic scattering is of considerable interest due to the role to be played by these nuclei in nuclear technology, nuclear energy and astrophysics. Nuclear burning process proceed from the transformation of the most abundant element hydrogen to helium, then from helium to carbon and oxygen, and then from these to heavier elements. Some of the key reactions for the carbon and oxygen burning stages of the nucleosynthesis are ¹²C+¹²C, ¹²C+¹⁶O and ¹⁶O+¹⁶O leading to all possible final states. The nucleus ¹²C is one of the most important elements of the fuel cycle due to the different characterization associated with the study of this element, such as Hoyle state and 3α–decomposition. It is commonly known that the study of heavy ion elastic scattering is useful for a better understanding of nuclear structure.

The purpose and the tasks of study: The purpose is to study the peculiarities of the elastic scattering of ¹²C on different 1p-shell nuclei at energies near the Coulomb barrier energy and the elastic and inelastic scattering of ³He and ⁴He on ¹²C.

In accordance with the purpose, it will be studied the following tasks

1. Theoretical analysis of the elastic scattering process ¹⁶O(¹²C,¹²C)¹⁶O and α-transfer reaction ¹⁶O(¹²C,¹⁶O)¹²C within the frame work of the optical model, distorted-wave method and the method of coupled channels;
2. Theoretical analysis of the identical nuclei elastic scattering ¹²C+¹²C using optical model code SPI-GENOA and double folding implemented in code FRESCO;
3. To study the one nucleon transfer reaction between ¹²C and ¹¹B;
4. The elastic scattering of ¹²C+²⁷Al nuclear system through our work showed that, ²⁷Al has no threshold anomaly similar to ²⁸Si due to the transfer reaction or other mechanisms, which result in the increase of the cross section at backward angles;

Research object: Studying the elastic scattering process of ¹²C ions on different 1p-shell nuclei such as ¹¹B, ¹²C and ¹⁶O at energies 1.25, 1.5 and 1.75 MeV/n in the cyclotron DC-60 INP NNC. In addition to the study of α-transfer reaction in ¹⁶O(¹²C,¹⁶O)¹²C and one proton transfer reaction in ¹¹B(¹²C,¹¹B)¹²C. Showing how the dynamics of heavy ion elastic scattering at low energies close to Coulomb barrier energy differ from those at high energies. The study of the elastic and inelastic scattering differential cross sections of ³He and ⁴He on ¹²C at energies 50.5 and 60 MeV in the isochronous cyclotron U-150M INP NNC.

Research subject: The subject of our research work is the experimental measurements of the differential cross sections for the following nuclear systems ¹⁶O(¹²C,¹²C)¹⁶O, ¹²C(¹²C,¹²C)¹²C, ¹¹B(¹²C,¹²C)¹¹B and ²⁷Al(¹²C,¹²C)²⁷Al at low energies close to Coulomb barrier energy. The aforementioned nuclear systems also were analyzed in a wide energy range in order to specify their global potential parameters using different theoretical techniques and codes. Theoretical analysis for elastic and inelastic (first, second, third and fourth excited state) scattering of ¹²C by ³He and ⁴He at energies 50.5 and 60 MeV.

Scientific novelty: There have been rather extensive differential cross section studies at intermediate and high energies up to 500 MeV while data at low energies are scare. From the point of view of applications, nuclear data at intermediate and low energies are steadily becoming of greater interest to such fields as medicine, astrophysics, fusion and accelerator driven systems for the transmutation of nuclear waste and energy conversion. Experimental data are also needed to refine theoretical models by comparing theoretical predictions with new data in extended areas. Differential cross sections at low energies present an example of the data which are necessary for such purposes. In our research work, the differential cross sections for the elastic scattering of ¹²C ions on ¹¹B, ¹²C, ¹⁶O and ²⁷Al were measured at energies E_lab 15, 18 and 21 MeV which are close to the Coulomb barrier energy for these nuclear systems. The theoretical analysis for elastic scattering of ¹²C ions on ¹¹B, ¹²C, ¹⁶O and ²⁷Al were performed in a wide energy range in order to obtain the global potential parameters which could fairly fit the experimental data.

Statement submitted for defense:

1. The experimental angular distribution measurements for ¹²C elastically scattered on ¹¹B, ¹²C, ¹⁶O and ²⁷Al at energies 1.25, 1.5 and 1.75 MeV/n;

2. The optimal potential parameters for the following nuclear systems ¹²C+¹¹B, ¹²C+¹²C, ¹²C+¹⁶O and ¹²C+²⁷Al in a wide energy range;

3. The optimal spectroscopic amplitudes for the configuration ¹⁶O→¹²C+α and for the configuration ¹²C→¹¹B+p.

The structure and scope of the thesis: The thesis consists of an introduction, eight chapters, conclusion and references including 157 resources. The text comprises 125 pages. The manuscript contains 68 figures and 15 tables.

Conclusions:

- This work is devoted to the differential cross section measurements for ¹²C ions elastically scattered on different 1p-shell nuclei such as ¹¹B, ¹²C and ¹⁶O at low energies close to the Coulomb barrier energy, and also for the study of the elastic and inelastic scattering of ³He and ⁴He on ¹²C at energies 50.5 and 60 MeV. These experiments had been performed both in the cyclotron DC-60 located in (Eurasia University) Astana, Kazakhstan, and in the isochronous cyclotron U-150M INP NNC Almaty, Kazakhstan.

- We made a systematic study of the elastic scattering ¹⁶O(¹²C,¹²C)¹⁶O in a wide energy range E_c.m=18−111.4 MeV, and we managed from obtaining the global optical potential parameters which describe the experimental data in that energy range. The process of scattering of ¹²C ions on the nuclei ¹⁶O is quite satisfactorily described in the forward scattering angles within the framework of the optical model. But, at low energies close to Coulomb barrier energy, there is a significant increase in differential cross section at backward angles due to alpha cluster transfer mechanism. To assess the contribution of exchange effect due to clustering phenomena in elastic scattering of carbon on the oxygen nuclei at backward angles, we used Born approximation method of distorted waves. The extracted value of spectroscopic factor SF was close to unity. This transfer reaction was also studied within the framework of code FRESCO, The extracted SF for the configuration ¹⁶O as → ¹²C+α using FRESCO Code is about 0.88.

- Such transfer reaction was also observed during the study of ¹²C+¹¹B nuclear system at low energies close to Coulomb barrier energy. The differential cross section for ¹²C+¹¹B nuclear system also increases at backward angles due to one proton transfer between the projectile (¹²C) and the target nucleus (¹¹B). The extracted SF for the configuration ¹²C as → ¹¹B+p from our present work equals 1.12 using DWUCK5 Code.

- We studied the elastic scattering process in ¹²C+¹²C nuclear system at low energies close to the Coulomb barrier energy (1.25, 1.5 and 1.75 MeV/n), such experiments also were performed in the cyclotron DC-60. In addition to our experimental results, the elastic scattering of ¹²C ion beam on ¹²C nucleus was analyzed in a wide energy range, in order to obtain the global optical potential parameters which gives fairly good fitting to the experimental data using both phenomenological (Code SPI-GENOA) and microscopic double folding (Code FRESCO). The obtained normalization N_r factor at energies 15, 18 and 21 MeV equals 1.2.

- In our present work, a series of experiments had been performed in the cyclotron DC-60 for studying the elastic scattering of ¹²C on the nucleus ²⁷Al at energies 15, 18 and 21 MeV. The experimental data has been analyzed within frame work of the optical potential code SPIVAL. We managed from obtaining the global optical potential parameters which could describe this nuclear system. The elastic scattering showed that ²⁷Al has no threshold anomaly similar to ²⁸Si due to transfer reaction or other mechanisms, which result in the increase of the cross section at backward angles.

- For ³He and ⁴He elastically and inelastically scattering on ¹²C, it is found that a strong refraction of ³He and ⁴He in the 0₂⁺ (7.65 MeV) Hoyle state of ¹²C, which has been suggested to be an α-particle condensate, can be clearly seen in the experimental angular distribution at low incident energy region where there is a pocket in the effective potential as an Airy minimum of the prerainbow oscillations. Because of this strong refraction, the Airy minimum is shifted to a considerably larger angle compared with that of normal ground state. This shift in the angular position of the Airy minimum is an indicator for the radius enlargement. The rms radius for 0₂⁺ state of ¹²C (7.65 MeV) from our calculations is about 4.34 fm.

Publications: The materials of thesis were published in 12 Journals and conferences, 3 publications in the database Scoups with non-zero impact factor, 5 abstracts in international conferences close to our research work of interest.