Isoscalar giant resonance strengths in ${}^{32}$S and possible excitation of superdeformed and ${}^{28}$Si $+$ $\alpha$ cluster bandheads

Isoscalar giant resonances and low spin states in ${}^{32}$S have been measured with inelastic $\alpha$ scattering at extremely forward angles including zero degrees at $E$${}_{\alpha }=386$ MeV. By applying multipole decomposition analysis, various excited states are classified according to their spins and parities (J${}^{\pi }$), and are discussed in relation to the superdeformed and ${}^{28}$Si $+$ $\alpha$ cluster bands.

Figure 1

Excitation energy spectra for ${}^{32}$S($\alpha$,${\alpha }^{\prime }$) at averaged laboratory angles of ${\theta }_{\mathrm{lab}}=0.7^{\circ }$ and ${\theta }_{\mathrm{lab}}=4.7^{\circ }$. The black line shows the energy spectrum obtained from the low-excitation measurement. The red (gray) line shows that obtained from the high-excitation measurement.

Figure 2

(a) Angular distribution of the ratio of the differential cross sections for elastic scattering to Rutherford scattering for 386 MeV $\alpha$ particles from ${}^{32}$S. (b) Angular distribution of differential cross sections for the 2.23 MeV 2${}^{+}$ state. In both cases, the solid lines show the results of the DWBA calculations using the single-folding model (see text).

Figure 3

Distributions with 1-MeV bins for the $E$0, $E$1, $E$2, and $E$3 strengths are presented in panels (a), (b), (c), and (d), respectively. The lines are given as guides for the eye.

Figure 4

Typical angular distributions of inelastic $\alpha$ scattering. The line through the data shows the sum of various multipole components obtained by the MDA. Each multipole contribution is represented by a line and the transferred angular momentum $L$ is indicated. The blue (light gray) line shows the contribution of the IVGDR estimated from the $\gamma$ absorption cross section (see text).

Figure 5

Strength distributions with a 200-keV bin for the $E0,E1,E2,E3$, and $E$4 transitions in the region from 6 to 15 MeV are presented in panels (a), (b), (c), (d), and (e), respectively. The red (gray) lines show the excitation energy spectra for the ${}^{32}$S($\alpha$,${\alpha }^{\prime }$) reaction at (a) ${\theta }_{\mathrm{lab}}=0.7^{\circ }$, (b) 2.0${}^{\circ }$, (c) 3.4${}^{\circ }$, (d) 4.8${}^{\circ }$, and (e) 5.6${}^{\circ }$, respectively, scaled to fit in the figures. Some differences of peak positions between the excitation energy spectrum at ${\theta }_{\mathrm{lab}}=0.7^{\circ }$ and the $E$0 strength distribution arise from primarily an artifact of histogramming. The differences, if any, are within the uncertainty of 0.05 MeV in peak positions.

Figure 6

Excitation energies are plotted vs $J(J+1)$ for the states obtained in this experiment. The open and closed circles show the positive-parity states. The open squares show the negative-parity states. Candidates for the SD band are plotted filled circles. The lines are displayed to guide the eye. The rotational constants $k$ corresponding to the solid, dashed, and dotted lines are 83, 234, and 125 keV, respectively.