Monopole pairing correlations with random interactions

In this paper we study the monopole pairing correlation in 0⁺ states of semimagic nuclei under random interactions. We calculate overlaps between S -pair wave functions and exact shell-model wave functions. No dominance of the S -pair components is shown: In a single-j shell 0⁺ states have random overlaps with the S -pair wave function; in a multi-j space the 0₁⁺ state has a small overlap with the S -pair wave function, and this is particularly pronounced if the single-particle splitting is small and/or the spins j of single-particle orbits are large. For the 0₁⁺ state in a multi-j space, the generalized seniority scheme and the seniority truncation of the shell model provide similar results. We study the odd-even staggering of one-neutron separation energies under random interactions. The odd-even staggering phenomenon survives in random samples where all the even members have spin-zero ground states but disappears in random samples where all the even members have spin-nonzero ground states.