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In this paper, we discuss the angular momentum distribution in the groundstates of many-body systems interacting via a two-body random ensemble.Beginning with a few simple examples, a simple approach to predict P(I)'s,angular momenta I ground state (g.s.) probabilities, of a few solvable cases,such as fermions in a small single-j shell and d boson systems, is given. Thismethod is generalized to predict P(I)'s of more complicated cases, such as evenor odd number of fermions in a large single-j shell or a many-j shell, d-boson,sd-boson or sdg-boson systems, etc. By this method we are able to tell whichinteractions are essential to produce a sizable P(I) in a many-body system. Theg.s. probability of maximum angular momentum $I_{max}$ is discussed. Anargument on the microscopic foundation of our approach, and certain matrixelements which are useful to understand the observed regularities, are alsogiven or addressed in detail. The low seniority chain of 0 g.s. by using thesame set of two-body interactions is confirmed but it is noted thatcontribution to the total 0 g.s. probability beyond this chain may be moreimportant for even fermions in a single-j shell. Preliminary results by takinga displaced two-body random ensemble are presented for the I g.s.probabilities.Comment: 39 pages and 8 figure

Many-body systems interacting via a two-body random ensemble. I. Angular momentum distribution in the ground states