Number of states for nucleons in a single-$j$ shell
Y. M. Zhao, A. Arima
TL;DR
This paper calculates the number of quantum states with specific spin and isospin values for three and four nucleons in a single-$j$ shell using sum rules of angular momentum coupling symbols.
Contribution
It introduces a method to determine state counts for few-nucleon systems in a single-$j$ shell using sum rules of six-$j$ and nine-$j$ symbols, extending previous theoretical tools.
Findings
Derived formulas for state counts with given $I$ and $T$
Applied sum rules of angular momentum coupling symbols
Enhanced understanding of nucleon configurations in shell models
Abstract
In this paper we obtain number of states with a given spin and a given isospin for systems with three and four nucleons in a single- orbit, by using sum rules of six- and nine- symbols obtained in earlier works.
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