For a $Q cdot Q$ interaction the energy weighted sum rule for isovector orbital magnetic dipole transitions is proportional to the difference $sum B(E2, isoscalar) - sum B(E2, isovector)$, not just to $sum B(E2, physical)$. 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. In $0p$ shell calculations for the even-even Be isotopes it is shown that the Fermion SU(3) model and Boson SU(3) model give different results for the energy weighted scissors mode strengths.
تحميل البحث