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Isospin relations for four nucleons in a single j shell

L. Zamick·A. Escuderos
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Abstract

We had previously used techniques involving isospin to count the number of states for three identical fermions in a single j shell with total angular momentum I=j. We generalize this to all I, but the main thrust of this work is to consider now a 4-fermion system. As before, one evaluates the eigenvalues of the Hamiltonian \sum_{i<j}[a + bt(i)t(j)] both from an isospin point of view and an angular momentum point of view. In the 4-particle case, we get a more limited result than in the 3-particle case, namely the number of T=0 states minus twice the number of T=2 states, all of a given angular momentum I.

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L. Zamick, A. Escuderos. 2005-08-22. Isospin relations for four nucleons in a single j shell. https://doi.org/10.1103/physrevc.72.044317

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