Random interactions with isospin

The explicit inclusion of isospin degrees of freedom in sd-shell shell-model calculations with random two-body interactions produces a richer and more varied pattern of ground-state spins and isospins than has been found with only a single type of valence nucleon. The degree of dominance of 0+ ground states in even-even nuclei is far from uniform in the presence of different numbers of valence neutrons and protons and is mirrored by the prevalence of 1+ ground states in odd-odd nuclei. Random interactions distinguish between the ground-state patterns of even-even and odd-odd nuclei. The natural isospin ordering observed in nuclei (with states of minimum isospin lying lowest in energy and increasing in energy with increasing isospin) is also prominent despite the randomness of the interactions. Universal 0+ even-even ground states and almost universal natural isospin ordering, as observed in nuclei, evidently still require two-body interactions with specific dynamic properties