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 ${ \cal M}$ and n but different J is identical if $I \ge (n-2)J - { 1/2} (n-1)(n-2)$ for fermions and $I \ge (n-2)J$ for bosons, and that the number of states is also identical for the same ${ \cal M}$ but different n and J if ${ \cal M} \le $min(n, 2J+1 - n) for fermions and for ${ \cal M} \le $min(n, 2J) for bosons. Here ${ \cal M} =I_{ max}-I$, 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.
Categories: nucl-th