Regularities in low-lying states of atomic nuclei with random interactions

In this paper we study low-lying states of atomic nuclei with random interactions, within the framework of the nuclear shell model. The distributions of R-6 versus R-4 (where R-I = E-I1(+) / E-21(+)), empirical proton-neutron interaction, and charge radius are investigated by using a two-body random ensemble. The Mallmann plot exhibits statistical correlations between R-6 and R-4. The proton-neutron interaction between the last proton and the last neutron in even-A nuclei is found to be stronger than that in odd-A nuclei, and that in N = Z nuclei is even stronger. Simple relations of nuclear charge radii for neighboring nuclei are found to survive remarkably for the random ensemble.