Degeneracies when [Formula Presented] two body matrix elements are set equal to zero and Regge’s [Formula Presented] symmetry relations

The effects of setting all [Formula Presented] two body interaction matrix elements equal to a constant (or zero) in shell model calculations (designated as [Formula Presented] are investigated. Despite the apparent severity of such a procedure, one gets fairly reasonable spectra. We find that using [Formula Presented] in single-j shell calculations degeneracies appear, e.g., the [Formula Presented] and [Formula Presented] states in [Formula Presented] are at the same excitation energies; likewise the [Formula Presented] and [Formula Presented] states in [Formula Presented] The above degeneracies involve the vanishing of certain [Formula Presented] and [Formula Presented] symbols. The symmetry relations of Regge are used to explain why these vanishings are not accidental. Thus for these states the actual deviation from degeneracy are good indicators of the effects of the [Formula Presented] matrix elements. A further indicator of the effects of the [Formula Presented] interaction in an even-even nucleus is to compare the energies of states with odd angular momentum with those that are even.