1 research outputs found
Degeneracies when T=0 Two Body Matrix Elements are Set Equal to Zero and Regge's 6j Symmetry Relations
The effects of setting all T=0 two body interaction matrix elements equal to
a constant (or zero) in shell model calculations (designated as ) are
investigated. Despite the apparent severity of such a procedure, one gets
fairly reasonable spectra. We find that using in single j shell
calculations degeneracies appear e.g. the and
states in Sc are at the same excitation energies; likewise the
I=,,9 and 10 states in Ti. The
above degeneracies involve the vanishing of certain 6j and 9j 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 T=0 matrix elements. A further indicator of
the effects of the T=0 interaction in an even - even nucleus is to compare the
energies of states with odd angular momentum with those that are even