Cluster-liquid transition in finite, saturated fermionic systems

The role of saturation for cluster formation in finite systems such as atomic nuclei is analyzed by considering three length-scale ratios, and performing deformation-constrained self-consistent mean-field calculations. The effect of clusterisation in deformed light systems is related to the saturation property of the inter-nucleon interaction. The formation of clusters at low nucleon density is illustrated by expanding the radius of $^{16}$O. A phase diagram shows that the formation of clusters can be interpreted as a hybrid state between the crystal and the liquid phases. In the hybrid cluster phase the confining potential attenuates the delocalization generated by the effective nuclear interaction