Isoscalar giant resonance strength in ${}^{24}\mathrm{Mg}$

The giant resonance region from $9$ MeV $<E_x<60$ MeV in ${}^{24}\mathrm{Mg}$ has been studied with inelastic scattering of $240$-MeV $\alpha$ particles at small angles, including $0^{°}$. Isoscalar $E0$, $E1$, $E2$, and $E3$ strength was identified from $9$ MeV $<E_x<40$ MeV and the effects of differing continua studied.

Figure 1

Inelastic $\alpha$ spectra obtained for average cm angles of ${0.5}^{°}$, ${3.0}^{°}$, and ${5.8}^{°}$. The lines show two continua used for the analysis.

Figure 2

Angular distributions obtained for inelastic $\alpha$ scattering for six excitation energies of the giant resonance peak). The energy bins are approximately 600 keV wide. The line through the data shows the fits. Contributions of each multipole are shown, and the $L$ transfer is indicated.

Figure 3

The multipole strength distributions obtained are shown. The black histogram shows those obtained by analyzing the data for which the out-of-plane angle was measured. The gray histogram shows those obtained in the reanalysis of the data reported in Ref. [3] (in-plane only), and the wide gray histograms show the distributions reported in Ref. [3]. Error bars represent the uncertainty from the fitting of the angular distributions as described in the text and do not include systematic errors.

Figure 4

$K_{\mathrm{nm}}$ obtained by comparing GMR energies in ${}^{24}\mathrm{Mg}$ and ${}^{28}\mathrm{Si}$ with the calculations of Ref. [9] as described in the text, and for ${}^{40}\mathrm{Ca}$, ${}^{90}\mathrm{Zr}$, ${}^{116}\mathrm{Sn}$, ${}^{144}\mathrm{Sm}$, and ${}^{208}\mathrm{Pb}$ as reported in Ref. [13]. The average value reported in Ref. [13] is also shown along with its uncertainty.