Giant resonances in ${}^{24}\mathrm{Mg}$ and ${}^{28}\mathrm{Si}$ from 240 MeV ${}^6\mathrm{Li}$ scattering

Elastic and inelastic scattering of 240 MeV ${}^6\mathrm{Li}$ particles from ${}^{24}\mathrm{Mg}$ and ${}^{28}\mathrm{Si}$ were measured with the MDM spectrometer. Optical potential parameters for ${}^6\mathrm{Li}+{}^{24}\mathrm{Mg}$ and ${}^6\mathrm{Li}+{}^{28}\mathrm{Si}$ scattering systems were obtained by fitting elastic scattering with two different folding model potentials as well as $W\text{−}S$ potentials. $E0\text{−}E3$ giant resonance strength distributions for ${}^{28}\mathrm{Si}$ and ${}^{24}\mathrm{Mg}$ were obtained. $E0$ strength corresponding to ${106}_{-24}^{+34}\%$ of the EWSR was identified in ${}^{24}\mathrm{Mg}$ and ${80}_{-20}^{+35}\%$ was found for ${}^{28}\mathrm{Si}$ between $E_x=8.0$ to 40.0 MeV.

Figure 1

Experimental angular distribution of the cross section (relative to the Rutherford cross section) and fits for ${}^6\mathrm{Li}+{}^{24}\mathrm{Mg}$ elastic scattering using $W\text{−}S$ potential (dash and dot curve), folding potential with CDM3Y6 $\mathit{NN}$ interaction (black curve) and folding potential with JLM $\mathit{NN}$ interaction (dash) are shown. The error bars indicate statistical and systematic errors.

Figure 2

Experimental angular distribution of the cross section (relative to the Rutherford cross section) and fits for ${}^6\mathrm{Li}+{}^{28}\mathrm{Si}$ elastic scattering using $W\text{−}S$ potential (dash and dot curve), folding potential with CDM3Y5 $\mathit{NN}$ interaction (black curve) and folding potential with JLM $\mathit{NN}$ interaction (dash) are shown. The error bars indicate statistical and systematic errors.

Figure 3

The volume integral of the real part of the optical potential for ${}^6\mathrm{Li}$ scattering on ${}^{28}\mathrm{Si}$ and ${}^{24}\mathrm{Mg}$ obtained with $W\text{−}S$ model, folding model with JLM and M3Y effective $\mathit{NN}$ interactions plotted versus incident beam energy. The black curve represents Nadasen et al.'s expression obtained with $W\text{−}S$ potentials [45]. The area between the two dash lines represents the range of volume integral predicted by Nadasen et al. The gray and light gray curves represent Gupta and Murthy's expression for ${}^{24}\mathrm{Mg}$ and ${}^{28}\mathrm{Si}$ obtained with JLM nucleon-nucleus potentials [46]. The bottom gray curve represents Satchler's expression obtained with S1Y effective $\mathit{NN}$ interaction [27]. Volume integrals obtained from Ref. [43] for 210 MeV ${}^6\mathrm{Li}$ scattering on ${}^{28}\mathrm{Si}$ are also plotted in the figure for comparison.

Figure 4

The angular distributions of the differential cross sections for inelastic scattering to the $2^{+}$ state of ${}^{24}\mathrm{Mg}$ calculated with FCI and WS potentials along with the data points are plotted versus average center of mass angle.

Figure 5

The angular distributions of the differential cross sections for inelastic scattering to the low-lying $2^{+}$ state of ${}^{28}\mathrm{Si}$ calculated both with a $W\text{−}S$ potential and with FCI along with the data points are plotted versus average center of mass angle.

Figure 6

The angular distributions of the differential cross sections for inelastic scattering to the low-lying $3^{-}$ state of ${}^{28}\mathrm{Si}$ calculated both with a $W\text{−}S$ potential model and with FCI along with the data points are plotted versus average center of mass angle.

Figure 7

Spectra obtained for ${}^{28}\mathrm{Si}$ at average center of mass angles $1.3^{°}$ and $6.4^{°}$. The gray curves are continuum shapes chosen for the analysis.

Figure 8

Angular distributions of the cross section for ${}^6\mathrm{Li}$ inelastic scattering from ${}^{28}\mathrm{Si}$ for 0.8 MeV wide bins centered at $E_x=10.14,20.46,29.14$ MeV along with DWBA fits. The left column shows those for the giant resonance peak while the right column shows those for the continuum.

Figure 9

Spectra obtained for ${}^{24}\mathrm{Mg}$ at average center of mass angles ${1.3}^{°},{4.7}^{°}$, and ${9.5}^{°}$. The gray curves are different continuum choices for the analysis. The broad structures pointed by the arrow or covered by the bracket are caused by ${}^6\mathrm{Li}$ scattering from hydrogen in the target.

Figure 10

Angular distributions of the cross section for inelastic scattering from ${}^{24}\mathrm{Mg}$ for 0.8 MeV wide bins centered at $E_x=12.94,20.08,28.75$ MeV along with DWBA fits. The left column shows those for the giant resonance peak while the right column shows those for the continuum.

Figure 11

The black curves show $E0,E1,E2$, and $E3$ strength distributions for ${}^{28}\mathrm{Si}$ [(a): $E0$, (b): $E1$, (c): $E2$, and (d): $E3$] obtained from analysis of ${}^6\mathrm{Li}$ inelastic scattering. The gray curves show those obtained with $\alpha$ inelastic scattering [16]. Error bars represent the uncertainty due to the fitting of the angular distributions and different choices of the continuum.

Figure 12

$E0$ strength distribution obtained from analysis of ${}^6\mathrm{Li}$ scattering compared to that obtained from analysis of $\alpha$ scattering (gray curve) without continuum subtraction [19].

Figure 13

$E1$ strength distribution obtained from analysis of ${}^6\mathrm{Li}$ scattering compared to that obtained from analysis of $\alpha$ scattering (gray curve) without continuum subtraction [19].

Figure 14

$E2$ strength distribution obtained from analysis of ${}^6\mathrm{Li}$ scattering compared to that obtained from analysis of $\alpha$ scattering (gray curve) without continuum subtraction [19].

Figure 15

The black curves show multipole EWSR strength distributions for ${}^{24}\mathrm{Mg}$ [(a): $E0$, (b): $E1$, (c): $E2$, and (d): $E3$] obtained from analysis of ${}^6\mathrm{Li}$ inelastic scattering. The gray curves show $E0,E1,E2$, and $E3$ strength distributions [13] obtained with $\alpha$ inelastic scattering. Error bars represent the uncertainty due to the fitting of the angular distributions and different choices of the continuum.

Figure 16

The black curves show multipole EWSR strength distributions for ${}^{24}\mathrm{Mg}$ [(a): $E0$, (b): $E1$, (c): $E2$, and (d): $E3$] obtained from analysis of ${}^6\mathrm{Li}$ inelastic scattering. The gray curves show those obtained with new analysis of $\alpha$ inelastic scattering [60]. Error bars represent the uncertainty due to the fitting of the angular distributions and different choices of the continuum.

Figure 17

$E0$ strength distribution obtained for ${}^{24}\mathrm{Mg}$ (black line) in this work compared to that obtained from previous 156 MeV ${}^6\mathrm{Li}$ scattering [17] multiplied by 0.5 (gray line). See the text for discussion of the 0.5 factor. The percentages shown in the figure represent the total EWSR strength found.

Figure 18

The excitation energy spectra obtained in ${}^6\mathrm{Li}$ scattering (black curve) at ${\theta }_{\mathrm{c}.\mathrm{m}.}={1.3}^{°}$ and in $\alpha$ scattering (gray curve) at ${\theta }_{\mathrm{c}.\mathrm{m}.}={1.2}^{°}$.

Figure 19

$E0$–$E2$ strength distributions [(a): $E0$, (b): $E1$, and (c): $E2$] of ${}^{28}\mathrm{Si}$ calculated by Péru et al. [61] with QRPA $+$ HBF theory (shown as straight gray discrete lines), compared to that obtained in this work (black line) and in $\alpha$ scattering (light gray lines). The gray smooth curves represent the convolutions of calculated discrete spectra with 2 MeV width Lorentzian distributions.

Figure 20

$E0$–$E2$ strength distributions of ${}^{24}\mathrm{Mg}$ [(a): $E0$, (b): $E1$, and (c): $E2$] calculated by Péru et al. [61] with QRPA $+$ HBF theory (shown as straight discrete gray line), compared to those obtained in this work (black line) and in $\alpha$ scattering (light gray line). The smooth gray curves represent the convolutions of calculated discrete spectra with 2 MeV width Lorentzian distributions.