Inelastic alpha scattering studies of the low-energy octupole resonance

Abstract

Beams of 96 and 115 MeV $\ensuremath{\alpha}$ 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 ($\ensuremath{\Gamma}\ensuremath{\sim}2.5$ MeV) is observed at ${E}_{x}\ensuremath{\sim}\frac{30}{{A}^{\frac{1}{3}}}$ 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 ($\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}}$) reaction exciting this peak are in excellent agreement with $l=3$ distorted-wave Born approximation calculations. Studies of the angular range from ${\ensuremath{\sigma}}_{\mathrm{lab}}=3.5\ifmmode^\circ\else\textdegree\fi{} \mathrm{to} 6\ifmmode^\circ\else\textdegree\fi{}$ in $^{116}\mathrm{Sn}$ indicate very little contribution from $l=1$ strength. Energy- weighted sum rule fractions for this low-energy octupole resonance are generally in the range from 15% to 20%; this corresponds to \textonehalf{} to $\frac{2}{3}$ of the expected $1\ensuremath{\hbar}\ensuremath{\omega}$ 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.NUCLEAR REACTIONS $^{40}\mathrm{Ca}$, $^{66}\mathrm{Zn}$, $^{75}\mathrm{As}$, $^{89}\mathrm{Y}$, $^{90}\mathrm{Zr}$, $^{92}\mathrm{Mo}$, $^{100}\mathrm{Mo}$, Ag (nat), $^{116}\mathrm{Sn}$, $^{118}\mathrm{Sn}$, $^{124}\mathrm{Sn}$, $^{142}\mathrm{Nd}$, $^{144}\mathrm{Sm}$, $^{148}\mathrm{Sm}$, $^{154}\mathrm{Sm}$, $^{197}\mathrm{Au}$, $^{208}\mathrm{Pb}(\ensuremath{\alpha}, {\ensuremath{\alpha}}^{\ensuremath{'}})$, ${E}_{\ensuremath{\alpha}}=96, 115$ MeV measured ${E}_{x}$, $\ensuremath{\sigma}(\ensuremath{\theta})$ giant resonances, deduced $l$, $\ensuremath{\beta}$.