Solvability of eigenvalues in jn configurations

Details Solvability of eigenvalues in jn configurations Solvability of eigenvalues in jn configurations

2010-05-03

arxiv.org/abs/1005.0232v1

Physics

Nuclear Physics

Nuclear Theory

Scientific paper

Eigenvalues of eigenstates in jn configurations (n identical nucle- ons in the j -orbit) are functions of two-body energies. In some cases they are linear combinations of two-body energies whose coe+/-cients are independent of the interaction and are rational non-negative num- bers. It is shown here that a state which is an eigenstate of any two-body interaction has this solvability property. This includes, in particular, any state with spin J if there are no other states with this J in the jn configuration. It is also shown that eigenstates with solvable eigenvalues have definite seniority v and thus, exhibit partial dynamical symmetry.

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