0 30 40 38 v 1 1 4 A pr 2 00 3 Number of states with fixed angular momentum for identical fermions and bosons

We present in this paper empirical formulas for the number of angular momentum I states for three and four identical fermions or bosons. In the cases with large I we prove that the number of states with the same M and n but different J is identical if I ≥ (n − 2)J − 1 2 (n − 1)(n − 2) for fermions and I ≥ (n − 2)J for bosons, and that the number of states is also identical for the same M but different n and J if M ≤min(n, 2J + 1 − n) for fermions and for M ≤min(n, 2J) for bosons. Here M = I max − I, n is the particle number, and J refers to the angular momentum of a single-particle orbit for fermions, or the spin L carried by bosons.