Number of states with fixed angular momentum for identical fermions and bosons

الأصل · EN

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 =Imax-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.