Isoscalar multipole strength inMg24through inelastic alpha scattering

Inelastic $\alpha$ scattering was studied on ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ at 70 MeV $\alpha$ energy. With an over-all resolution of 70-100 keV 40 distinct peaks are seen in energy spectra below 16 MeV excitation. The experimental angular distributions for individual peaks were analyzed in terms of the distorted wave Born approximation to extract transition strengths. About 50-70% of the quadrupole energy-weighted sum rule strength is observed up to 19 MeV excitation. Though there is a slight peaking of $l=2\mathrm{}$ strength around 16 MeV excitation it is found to be spread over a broader (∼ 10 MeV) energy range than is the case (typically 5-6 MeV) for heavier ($A>\mathrm{}40\mathrm{}$) nuclei. Up to 16 MeV the observed strength for the octupole vibrations is 10% of the energy-weighted sum rule and it is consistent with that estimated to reside around $1\hslash \omega$ excitation. Only 3% of the $l=4\mathrm{}$ energy-weighted strength is seen below 16 MeV.