Beryllium-9 in Cluster Effective Field Theory

The thesis here presented is the result of a PhD research, with the aim to build a program able to solve the non-relativistic eigenvalue problem for the so-called cluster and nuclei (in particular the Beryllium-9 nucleus), in order to study them through the use of Effective Field Theory (EFT) potentials. After a brief introduction, that will show why this type of nuclei are important in the study of stellar nucleosynthesis, I introduce the Hyperspherical Harmonics basis with which the calculations were carried out. The following chapter has the momentum space as the main subject, ending with some results from the program. EFT and cluster nuclei are then introduced in the next chapter, together with the interaction I used for the cluster systems. The second to last chapter shows the results of the code, able to calculate the ground state of Carbon-12 and Beryllium-9 nuclei, two important nuclei in the process of stellar nucleosynthesis. The last chapter contains a brief summary and the future outlook on this research.