A study of randomness, correlations and collectivity in the nuclear shell model

8 pages, 10 figures, 8 tables, submitted to Physical Review CA variable combination of realistic and random two-body interactions allows the study of collective properties, such as the energy spectra and B(E2) transition strengths in 44Ti, 48Cr and 24Mg. It is found that the average energies of the yrast band states maintain the ordering for any degree of randomness, but the B(E2) values lose their quadrupole collectivity when randomness dominates the Hamiltonian. The high probability of the yrast band to be ordered in the presence of pure random forces exhibits the strong correlations between the different members of the band