Exploratory Calculations of the Effects of Higher Shell Admixtures on Static Electric Quadrupole and Magnetic Dipole Moments of Excited States

Using the interaction Q ·Q + xVS.O. where VS.O. is a twobody spin-orbit interaction, we study the effects of varying x on the static electric quadrupole and magnetic dipole moments of the 2+1 and 2 + 2 states of Be. This is done both in the valence space sp and in a larger space in which 2 h̄ω excitations are allowed. In the former case, for x = 0, we have the Wigner Supermultiplet limit in which the 2+1 and 2 + 2 states are degenerate and correspond to K = 0 and K = 2 rotational states, with equal and opposite static quadrupole moments. Turning on the spin-orbit interaction with sufficient strength in the valence space gives an energy splitting to the two 2 states in accord with experiment. When higher shell admixtures are allowed, we get quite a different behaviour as a function of x than in the valence space. Of particular interest is a value of x for which Q(2+1 ) and Q(2 + 2 ) both nearly vanish, and so does (somewhat coincidentally) μ(2+1 ).