Patterns of the ground states in the presence of random interactions: Nucleon systems

Abstract

We present our results on properties of ground states for nucleonic systems in the presence of random two-body interactions. In particular, we calculate probability distributions for parity, seniority, spectroscopic (i.e., in the laboratory frame) quadrupole moments, and discuss $\ensuremath{\alpha}$ clustering in the ground states. We find that the probability distribution for the parity of the ground states obtained by a two-body random ensemble simulates that of realistic nuclei with $A\ensuremath{\geqslant}70$: positive parity is dominant in the ground states of even-even nuclei, while for odd-odd nuclei and odd-mass nuclei we obtain with almost equal probability ground states with positive and negative parity. In addition, assuming pure random interactions, we find that, for the ground states, low seniority is not favored, no dominance of positive values of spectroscopic quadrupole deformation is observed, and there is no sign of $\ensuremath{\alpha}$-clustering correlation, all in sharp contrast to realistic nuclei. Considering a mixture of a random and a realistic interaction, we observe a second-order phase transition for the $\ensuremath{\alpha}$-clustering correlation probability.