Alternate Derivation of Ginocchio-Haxton relation [(2j+3)/6]

Abstract

We address the problem, previously considered by Ginocchio and Haxton (G-H), of the number of states for three identical particles in a single j-shell with angular momentum J=j. G-H solved this problem in the context of the quantum Hall effect. We address it in a more direct way. We also consider the case J=j+1 to show that our method is more general, and we show how to take care of added complications for a system of five identical particles.

7 pages, RevTeX4; submitted to Phys. Rev. C

References in corpus (5)

• General pairing interactions and pair truncation approximations for fermions in a single-j shell
• Number of states with fixed angular momentum for identical fermions and bosons
• Classification of states of single-$j$ fermions with $J$-pairing interaction
• Number of Spin $I$ States of Identical Particles
• Companion problems in quasispin and isospin

Cited by in corpus (10)

• Energy expressions for n=3 and 4 systems in a single-j shell
• Alternate proof of the Rowe-Rosensteel proposition and seniority conservation
• $J$-pairing interaction, number of states, and nine-$j$ sum rules of four identical particles
• Isospin relations for four nucleons in a single j shell
• Number of states for nucleons in a single-$j$ shell
• New Relations for Coefficients of Fractional Parentage--the Redmond Recursion Formula with Seniority
• Special 6j and 9j symbols for a single-j shell
• 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
• Number of spin-J states and odd-even staggering for identical particles in a single-j shell