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

Using the interaction $Q \cdot Q ~+~ xV_{S.O.}$ where $V_{S.O.}$ is a two-body 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 $^{10}Be$. This is done both in the valence space $s^4p^6$ and in a larger space in which 2 $\hbar \omega$ 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) $\mu(2^+_1)$.