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 ${\mathit{S}}_{\mathrm{LE}}^{\mathrm{lew}}$(${\mathit{M}}_1^{\mathrm{orb}}$) ≃(6/5)ε [B(E2;$0_1^{+}$→$2_1^{+}$K=0)/${\mathit{Ze}}^2$〈${\mathit{r}}^2$${\mathrm{〉}}^2$]${\mathrm{\mu }}_{\mathit{N}}^2$ with B(E2) the E2 strength for the transition from the ground state to the first excited state in the ground-state rotational band, 〈${\mathit{r}}^2$〉 the charge rms radius squared, and ε 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 2ħw carrying 50% of the total ${\mathit{m}}_1$ moment of the orbital M1 operator.

• Received 23 November 1992

DOI:https://doi.org/10.1103/PhysRevC.47.2604