Isoscalar $E0-E3$ strength in ${}^{116}\mathrm{Sn}$, ${}^{144}\mathrm{Sm}$, ${}^{154}\mathrm{Sm}$, and ${}^{208}\mathrm{Pb}$

The giant resonance region from $10\text{MeV}<E_x<55\text{MeV}$ in ${}^{116}\mathrm{Sn}$, ${}^{144}\mathrm{Sm}$, ${}^{154}\mathrm{Sm}$, and ${}^{208}\mathrm{Pb}$ has been studied with inelastic scattering of $240\text{MeV}$ $\alpha$ particles at small angles including $0°$. Essentially all of the expected isoscalar $E0$, $E1$, $E2$, and $E3$ strength was identified in these nuclei.

Figure 1

Inelastic $\alpha$ spectra obtained at two angles for ${}^{208}\mathrm{Pb}$. The thick gray lines show the continuum chosen for the analysis. The dashed line below $22\text{MeV}$ represents a contaminant present at some angles in the spectra taken with the spectrometer at $0°$. This was subtracted before the multipole analysis was done.

Figure 2

Inelastic $\alpha$ spectra obtained for ${}^{144}\mathrm{Sm}$ and ${}^{154}\mathrm{Sm}$. The thick gray lines show the continuum chosen for the analysis. The dashed line below $10\text{MeV}$ represents a contaminant peak present at some angles in the spectra taken with the spectrometer at $0°$. This was subtracted before the multipole analysis was done.

Figure 3

Inelastic $\alpha$ spectra obtained at several angles for ${}^{116}\mathrm{Sn}$. The thick gray lines show the continuum chosen for the analysis. Thin black lines in three of the spectra indicate the extent of variation of the continuum as discussed in the text. The dashed line below $10\text{MeV}$ in the $1.1°$ spectrum represents a contaminant peak present at some angles in the spectra taken with the spectrometer at $0°$. This was subtracted before the multipole analysis was done.

Figure 4

The angular distributions of the ${}^{116}\mathrm{Sn}$ cross sections for a $800\text{keV}$ wide bin centered at the excitation energy indicated on the figure for inelastic $\alpha$ scattering for three excitation ranges of the GR peak and the continuum. The lines through the data points indicate the multipole fits. Contributions of each multipole are shown. Where errors are not shown, they are smaller than the data points.

Figure 5

The angular distributions of the ${}^{208}\mathrm{Pb}$ cross sections for a $640\text{keV}$ wide bin centered at the excitation energy indicated on the figure for inelastic $\alpha$ scattering for three excitation ranges of the GR peak and the continuum. The lines through the data points indicate the multipole fits. Contributions of each multipole are shown with the same line types as in Fig. 4. Where errors are not shown, they are smaller than the data points.

Figure 6

Strength distributions obtained from the peak analysis for ${}^{116}\mathrm{Sn}$ and ${}^{208}\mathrm{Pb}$ are shown by the histograms. Error bars represent the uncertainty due to the fitting of the angular distributions and different choices of the continuum as described in the text. The lines on the $E1$ distribution represent Gaussians calculated with the parameters in Table .

Figure 7

Strength distributions obtained from the peak analysis for ${}^{144}\mathrm{Sm}$ and ${}^{154}\mathrm{Sm}$ are shown by the histograms. Error bars represent the uncertainty due to the fitting of the angular distributions and different choices of the continuum as described in the text. The lines on the $E1$ distribution for ${}^{144}\mathrm{Sm}$ represent Gaussians calculated with the parameters in Table .

Figure 8

Strength distributions obtained from analysis of the continuum for ${}^{116}\mathrm{Sn}$ are shown by the histograms.

Figure 9

Inelastic $\alpha$ spectra for ${}^{116}\mathrm{Sn}$ obtained at ${\theta }_{\mathrm{c}\text{.m}\mathrm{.}}\sim 5.7°$ in two runs at different spectrometer angles.

Figure 10

$E0$ strength distributions obtained in this work are shown as black histograms and compared to those from Ref. 11, shown in gray.

Figure 11

$E1$ strength distributions obtained in this work are shown as black histograms and compared to those from Ref. 13, shown in gray. The vertical scales of the $E1$ distributions from Ref. 13 have been divided by three as discussed in the text.

Figure 12

The $E1$ strength distributions obtained (shown by the histograms) for ${}^{116}\mathrm{Sn}$, ${}^{144}\mathrm{Sm}$, and ${}^{208}\mathrm{Pb}$ are compared to calculations by Colo et al. [29] shown by the thick gray lines and by Vretenar, Wandelt, and Ring [30] shown by the thick black line.

Figure 13

The $E0$ strength distribution obtained for ${}^{154}\mathrm{Sm}$ is shown by the histograms in the top two panels. In the top panel, a calculation using the parameters of Abgrall et al. [40] is shown by the dashed line and one using the parameters of Nishizaki and Ando [41] is shown by the gray line. A two Gaussian fit to the $E0$ distribution with the parameters in Table is shown in the middle panel. The $E2$ strength distribution obtained for ${}^{154}\mathrm{Sm}$ is shown by the histogram in the bottom panel and a calculation using the parameters of Nishizaki and Ando [41] is shown by the gray line.

Figure 14

The $E1$ ($E3$) strength distribution obtained for ${}^{154}\mathrm{Sm}$ is shown by the histogram in the top (bottom) panel. Calculations using the parameters of Nishizaki and Ando [41] are shown by the gray lines. The dashed line is the shifted ${}^{144}\mathrm{Sm}$ distribution for the lower component of the ISGDR as described in the text. The gray line for the $E1$ distribution includes the contribution illustrated by the dashed line.