The following theorem is proved. The spin J g of the ground state of a system of any two particles of spins s 1 , s 2 interacting through rotationally invariant but otherwise arbitrarily spin-dependent potentials fulfils the inequality J g <or=s 1 +s 2 .
We prove that for any nonrelativistic rotationally invariant two-particle quantum system whose interaction is velocity independent the total angular momentum of the ground state is bounded by the sum of the spins; i.e., jmax=s1+s2. .AE
Numerical simulations show that the ground state spin of a finite many-body system with random but rotationally invariant interactions is predominantly zero. This means that it is not sufficient to explain the zero ground state spin of even-even nuclei only by pairing correlations. Simple explanations based on a statistical multiplicity, width of the level density, effective pairing, formation of condensates etc. do not work. We suggest statistical theory based on the effective mean field and geometric chaoticity of angular momentum coupling of individual particles. The results show a significant role of symmetry arguments in finite systems.