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

Abstract

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 $\mathcal{M}$ 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 $\mathcal{M}$ but different n and J if $\mathcal{M}\le$min(n, 2J+1 - n) for fermions and for $\mathcal{M}\le$min(n, 2J) for bosons. Here $\mathcal{M}=I_{max}-I$, 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.

9 pages, no figures

References in corpus (1)

• Many-body Systems Interacting via a Two-body Random Ensemble (I): Angular Momentum distribution in the ground states

Cited by in corpus (14)

• General pairing interactions and pair truncation approximations for fermions in a single-j shell
• Alternate proof of the Rowe-Rosensteel proposition and seniority conservation
• Alternate Derivation of Ginocchio-Haxton relation [(2j+3)/6]
• Classification of states of single-$j$ fermions with $J$-pairing interaction
• $J$-pairing interaction, number of states, and nine-$j$ sum rules of four identical particles
• Number of Spin $I$ States of Identical Particles
• Number of states for nucleons in a single-$j$ shell
• Isospin relations for four nucleons in a single j shell
• Companion problems in quasispin and isospin
• New Relations for Coefficients of Fractional Parentage--the Redmond Recursion Formula with Seniority
• Total number of $J$ levels for identical particles in a single-$j$ shell using coefficients of fractional parentage
• Exact expressions for the number of levels in single-\textit{j} orbits for three, four and five fermions
• Zeros of 6j Symbols:Atoms:Nuclei and Bosons
• Number of spin-J states and odd-even staggering for identical particles in a single-j shell