${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ nuclei represent essential elements for life on Earth. The study of their formation plays a key role in understanding heavy element nucleosynthesis and stellar evolution. In this paper we present the study of ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ nuclei as systems composed of $\alpha$-particle clusters using a short-range effective field theory–inspired approach. The fundamental and excited states of the studied nuclei are calculated within an ab initio approach using the hyperspherical harmonics method. Thanks to the two-body potential and fine-tuning of the three-body force, we have found the ${}^{12}\mathrm{C}$ system nicely reproduced by theory. However, for the ${}^{16}\mathrm{O}$ case, it is necessary to include a four-body force in order to achieve agreement with the experimental data.

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• Big bang nucleosynthesis
• Effective field theory
• Nuclear astrophysics
• Nuclear reactions
• Nuclear structure & decays
• A ≤ 5
• Ab initio calculations