The 3-$\alpha$ and 4-$\alpha$ particle systems within short-range Effective Field Theory

TL;DR

This paper models the structure of ${}^{12}{\rm C}$ and ${}^{16}{\rm O}$ nuclei as alpha-particle clusters using short-range effective field theory, achieving good agreement with experimental data through ab-initio calculations.

Contribution

It introduces a novel application of short-range effective field theory to alpha-cluster nuclei, including the necessity of a four-body force for ${}^{16}{\rm O}$.

Findings

${}^{12}{\rm C}$ is well reproduced with two- and three-body forces.

${}^{16}{\rm O}$ requires a four-body force for accurate modeling.

The approach advances understanding of alpha-cluster nuclear structures.

Abstract

${}^{12}{\rm C}$ and ${}^{16}{\rm O}$ 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 ${}^{12}{\rm C}$ and ${}^{16}{\rm O}$ nuclei as systems composed of $\alpha$-particle clusters using the short-range effective field theory 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 ${}^{12}{\rm C}$ system nicely reproduced by theory. However, for the ${}^{16}{\rm O}$ case, it is necessary to include a 4-body force in order to achieve agreement with the experimental data.