Density-induced suppression of the α-particle condensate in nuclear matter and the structure of α-cluster states in nuclei

Abstract

At low densities, with decreasing temperatures, in symmetric nuclear matter \ensuremath{\alpha} particles are formed, which eventually give raise to a quantum condensate with four-nucleon \ensuremath{\alpha}-like correlations (quartetting). Starting with a model of \ensuremath{\alpha} matter, where undistorted \ensuremath{\alpha} particles interact via an effective interaction such as the Ali-Bodmer potential, the suppression of the condensate fraction at zero temperature with increasing density is considered. Using a Jastrow-Feenberg approach, it is found that the condensate fraction vanishes near saturation density. Additionally, the modification of the internal state of the \ensuremath{\alpha} particle due to medium effects will further reduce the condensate. In finite systems, an enhancement of the $S$-state wave function of the center-of-mass orbital of \ensuremath{\alpha}-particle motion is considered as the correspondence to the condensate. Wave functions have been constructed for self-conjugate $4n$ nuclei that describe the condensate state but are fully antisymmetrized on the nucleonic level. These condensate-like cluster wave functions have been successfully applied to describe properties of low-density states near the $n\ensuremath{\alpha}$ threshold. Comparison with orthogonality condition model calculations in $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ shows strong enhancement of the occupation of the $S$-state center-of-mass orbital of the \ensuremath{\alpha} particles. This enhancement is decreasing if the baryon density increases, similar to the density-induced suppression of the condensate fraction in \ensuremath{\alpha} matter. The ground states of $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ show no enhancement at all, thus a quartetting condensate cannot be formed at saturation densities.