Towards understanding the probability of 0(+) ground states in even-even many-body systems - art. no. 041301

For single-j shells with j=7/2, 9/2, and 11/2, we relate the large probabil ity of I+ ground states to the largest (smallest) coefficients alpha (J)(I( upsilon beta)) = <n upsilon betaI \A(J+).A(J)\n upsilon betaI >, where n is the particle number, v is the seniority, beta is an additional quantum num ber, and I is the angular momentum of the state. Interesting regularities o f the probabilities of I+ ground states are noticed and discussed for four- particle systems. Several counter examples of the 0(+) ground state (0g.s.) predominance are noticed for the first time.