Need for an isovector quadrupole term in the sum rule relating scissors mode excitations toB(E2)values

Abstract

For a $Q\ensuremath{\cdot}Q$ interaction the energy-weighted sum rule for isovector orbital magnetic dipole transitions is proportional to the difference $\ensuremath{\sum}B(E2,\mathrm{isoscalar})\ensuremath{-}\ensuremath{\sum}B(E2,\mathrm{isovector})$, not just to $\ensuremath{\sum}B(E2,\mathrm{physical})$. This fact is important in ensuring that one gets the correct limit as one goes to nuclei, some of which are far from stability, for which one shell (neutron or proton) is closed.