but the most outstanding feature in the curve is that the high energy rise is much larger than the low energy rise. The energy weighted sum reaches up to about $8$ $\mu_N^2MeV$. Thus the high energy rise is over three time the low energy rise. For the $Q \cdot Q$ interaction, the first plateau is better defined -it is located at $1$ $\mu_N^2MeV$ and the cumulative sum extends to about $3.8$ $\mu_N^2MeV$.

The Zheng-Zamick Sum Rule
=========================

Energy weighted sum rules for magnetic dipole transitions, be they spin or orbital, are highly model dependent. An energy weighted sum rule for [*isovector orbital*]{} magnetic dipole transitions for the quadrupole-quadrupole interaction $Q \cdot Q$ was developed by Zheng and Zamick [@zz]. This was motivated by the work of the Darmstadt group [@zr] [@rich] showing a linear relationship between summed orbital $B(M1)$ strength and the square of the deformation parameter i.e. $\delta^2$.

The result was

$$\sum_n (E_n-E_0)B(M1)_o=\frac{9\chi}{16\pi}\left\{\sum_i[B(E2,0_1
\rightarrow 2_i)_{isoscalar} - B(E2,0_1 \rightarrow 2_i)_{isovector}]
\right\}~~~~(EWSR)$$

where $B(M1)_o$ is the value for the isovector orbital $M1$ operator ($g_{l\pi}=0.5$ $g_{l\nu}=-0.5$ $g_{s\pi}=0$ $g_{s\nu}=0$) and the operator for the $E2$ transitions is $\sum_{protons}e_pr^2Y_2$ $+$ $\sum_{neutrons}e_nr^2Y_2$ with $e_p=1$, $e_n=1$ for the isoscalar transition, and $e_p=1$, $e_n=-1$ for the isovector 