The $\alpha$-particle condensation in diluted $^{16}\text{O}$ at finite temperature

We investigate the effect of temperature on $\alpha$-particle clustering in the diluted nucleus $^{16}\text{O}$ using the multi-constrained finite-temperature relativistic Hartree-Bogoliubov model with the DD-ME2 interaction. At a critical density the nucleus undergoes a Mott-like transition from a homogeneous to a localised configuration characterised by $\alpha$-particle clustering and the emergence of a finite non-axial octupole deformation. We study the interplay between the onset of localisation under nuclear dilution and the suppression of deformation and $\alpha$-particle clustering due to increasing temperature. Investigating the temperature-density plane, our findings indicate that temperature delays the formation of non-axial octupole deformation and $\alpha$-particle clustering in dilute environments. Following the transition from homogeneous to clustered configurations, the non-axial octupole deformation continues to increase with further dilution of the system and becomes nearly independent of temperature. We found that $\alpha$-particle clusters appear at temperatures up to $T = 4.10$ MeV and at a corresponding normalised density $\rho_{\text{Mott}}/\rho_0 \approx 0.09$.