Simple approach to the angular momentum distribution in the ground states of many-body systems

We propose a simple approach to predict the angular momentum I ground state (I g.s.) probabilities of many-body systems that does not require the diagonalization of Hamiltonians with random interactions. This method is found to be applicable to all cases that have been discussed: even and odd fermion systems (both in single-j and many-j shells), and boson (both sd and sdg) systems. A simple relation for the highest angular momentum g.s. probability is found. Furthermore, it is suggested for the first time that the 0 g.s. dominance in boson systems and in even-fermion systems is given by two-body interactions with specific features.