# The possibility of $^{14}$C cluster as a building block of medium mass nuclei

## TL;DR

This paper explores the potential of $^{14}$C clusters as fundamental building blocks in medium mass nuclei, using advanced models to compare structural properties and predict configurations like linear chains.

## Contribution

It introduces the use of the antisymmetrized quasi-cluster model (AQCM) to analyze $^{14}$C cluster structures and compares results with relativistic mean field calculations, highlighting the role of $^{14}$C in medium nuclei.

## Key findings

- $^{14}$C$+$^{14}$C structures are stable and distinct from $^{12}$C$+$^{12}$C.
- Similar density and rotational properties are found in AQCM and CRMF models.
- Linear chain $^{14}$C cluster structures are predicted in $^{42}$Ar.

## Abstract

The possibility of the $^{14}$C cluster being a basic building block of medium mass nuclei is discussed. Although $\alpha$ cluster structures have been widely discussed in the light $N\approx Z$ mass region, the neutron to proton ratio deviates from unity in the nuclei near $\beta$-stability line and in neutron-rich nuclei. Thus, more neutron-rich objects with $N>Z$ could become the building blocks of cluster structures in such nuclei. The $^{14}$C nucleus is strongly bound and can be regarded as such a candidate. In addition, the path to the lowest shell-model configuration at short relative distances is closed for the $^{14}$C+$^{14}$C structure contrary to the case of the $^{12}$C+$^{12}$C structure; this allows to keep appreciable separation distance between the $^{14}$C clusters. The recent development of antisymmetrized quasi-cluster model (AQCM) allows us to utilize $jj$-coupling shell model wave function for each cluster in a simplified way. The AQCM results for the $^{14}$C+$^{14}$C structure in $^{28}$Mg are compared with the ones of cranked relativistic mean field (CRMF) calculations. Although theoretical frameworks of these two models are quite different, they give similar results for the nucleonic densities and rotational properties of the structure under investigation. The existence of linear chain three $^{14}$C cluster structure in $^{42}$Ar has also been predicted in AQCM. These results confirm the role of the $^{14}$C cluster as a possible building block of cluster structures in medium mass nuclei.