Shell model test of quadrupole properties predicted by the rotational formula--the degenerate SDI interaction and non-degenerate FPD6
Abstract
In the rotational model for a K=0 band in an even-even nucleus, there is a single parameter--Q0, the intrinsic quadrupole moment. All B(E2)'s in the band and all static quadrupole moments are expressed in terms of this one parameter. In shell-model calculations, this does not have to be the case. In this work, we consider ground-state bands in 44Ti, 46Ti, 48Ti, 48Cr, and 50Cr. We have two models. First, we use a Surface Delta Interaction with degenerate single-particle energies (SDI-deg). We compare this with results of a shell-model calculation using the standard interaction FPD6 and include the single-particle energy splitting. Neither model yields a perfect rotational I(I+1) spectrum, although the SDI-deg model comes somewhat closer. Overall, the simple rotational formula for B(E2)'s and static quadrupole moments hangs together very nicely.
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