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

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

2003-04-14

arxiv.org/abs/nucl-th/0304038v1

Phys.Rev. C68 (2003) 044310

Physics

Nuclear Physics

Nuclear Theory

9 pages, no figures

Scientific paper

10.1103/PhysRevC.68.044310

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.

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