  Within the unified model of Bohr and Mottelson we derive the following linear
energy weighted sum rule for low energy orbital 1$^+$ excitations in even-even
deformed nuclei $$S_{\rm LE}^{\rm lew} (M_1^{\rm orb}) \cong (6/5) \epsilon
(B(E2; 0^+_1 \rightarrow 2_1^+ K=0)/Z e^2<r^2>^2) \mu^2_N$$ with B(E2) the E2
strength for the transition from the ground state to the first excited state in
the ground state rotational band, $<r^2>$ the charge r.m.s. radius squared and
$\epsilon$ the binding energy per nucleon in the nuclear ground state. It is
shown that this energy weighted sum rule is in good agreement with available
experimental data. The sum rule is derived using a simple ansatz for the
intrinsic ground state wave function that predicts also high energy 1$^+$
strength at 2$\hbar \omega$ carrying 50\% of the total $m_1$ moment of the
orbital M1 operator.

Nuclear Theory