Inelastic alpha scattering studies of the low-energy octupole resonance

Beams of 96 and 115 MeV $\alpha$ particles have been used to study the distribution of isoscalar octupole strength in 18 nuclei from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ to ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. A prominent broad peak ($\Gamma \sim 2.5$ MeV) is observed at $E_x\sim \frac{30}{A^{\frac{1}{3}}}$ MeV in nuclei from ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$ to ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$. No broad peak is observed in this excitation energy range in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ or ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and lighter nuclei. The oscillatory angular distributions of the ($\alpha , {\alpha }^{\prime }$) reaction exciting this peak are in excellent agreement with $l=3\mathrm{}$ distorted-wave Born approximation calculations. Studies of the angular range from ${\sigma }_{\mathrm{lab}}=3.5\mathrm{}° \mathrm{to} 6°$ in ${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$ indicate very little contribution from $l=1\mathrm{}$ strength. Energy- weighted sum rule fractions for this low-energy octupole resonance are generally in the range from 15% to 20%; this corresponds to ½ to $\frac{2}{3}$ of the expected $1\hslash \omega$ octupole strength. The overall distribution of octupole strength in spherical nuclei, including the absence of the low-energy octupole resonance in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, is in very good agreement with random-phase approximation calculations. The low-energy octupole resonance undergoes a pronounced change in structure in soft-vibrational and deformed nuclei. Theoretical calculations for the low-energy octupole resonance in ${}_{}{}^{154}{}_{}{}^{}\mathrm{Sm}$ account qualitatively for the data.