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