Systematics of the bimodal isoscalar giant dipole resonance

The systematic behavior of the isoscalar giant dipole resonance (ISGDR) in ${}^{90}\mathrm{Zr}$, ${}^{116}\mathrm{Sn}$, ${}^{144}\mathrm{Sm}$, and ${}^{208}\mathrm{Pb}$ is studied with inelastic $\alpha$ scattering at $E_{\alpha }=386\mathrm{MeV}$. Multipole-decomposition analysis is applied to extract the excitation strengths of giant resonances from the $(\alpha ,{\alpha }^{\prime })$ differential cross sections at ${\theta }_{\mathrm{lab}}=0.64°–13.5°$. The bimodal structure of the ISGDR is discussed and compared with recent theoretical results from $\text{Hartree}\text{‐}\text{Fock}+\text{random}\text{‐}\text{phase}\text{‐}\text{approximation}$ calculations.

Figure 1

Excitation energy spectra for ${}^{90}\mathrm{Zr}$, ${}^{116}\mathrm{Sn}$, ${}^{144}\mathrm{Sm}$, and ${}^{208}\mathrm{Pb}$ at $\theta =0.64°$. The arrows indicate the locations of the HE ISGDR. Note that the ${}^{144}\mathrm{Sm}(\alpha ,{\alpha }^{\prime })$ spectrum from our previous work [21] is also included.

Figure 2

Angular distributions of selected $1\mathrm{MeV}$ bins for the ${}^{116}\mathrm{Sn}(\alpha ,{\alpha }^{\prime })$ reaction at $386\mathrm{MeV}$. (a) Results for $E_x=15.5\mathrm{MeV}$, where the ISGMR is dominant. (b) Results for $E_x=25.5\mathrm{MeV}$, where the ISGDR is expected to be enhanced. The solid circles are the experimental data. The lines show contributions from $L=0$ (thin solid line), $L=1$ (thick solid line), $L=2$ (dotted line), $L=3$ (dashed line), and other higher components including IVGDR (dot-dashed line).

Figure 3

Experimentally obtained strength distributions of the ISGMR and the ISGDR in ${}^{90}\mathrm{Zr}$, ${}^{116}\mathrm{Sn}$, and ${}^{208}\mathrm{Pb}$. The error bars are determined by changing the $E1$ strength within ${\chi }^{\text{total}}⩽{\chi }_{\min }^{\text{total}}+1$ in the MDA. In the case of the ISGMR, the results of fitting with a Breit-Wigner function are indicated. In the ISGDR’s case, the results of fitting with two Breit-Wigner functions for the region of $E_x>10\mathrm{MeV}$, and a Gaussian function for the peak at $E_x<10\mathrm{MeV}$ are included.

Figure 4

Systematics of (a) the ISGDR peak energy and (b) the $E1$ EWSR fraction as a function of mass number. The solid squares, open circles, open triangles and stars are the results from the present work, from Clark et al. [8], current results from Youngblood et al. [33], and the theoretical calculation by Colò et al. [11], respectively. The error bars quoted for the EWSR fractions are only statistical. The systematic errors for the HE component of the ISGDR are estimated to be large due to the $L=1$ contributions from the continuum, especially at high excitation energies $(28<E_x<32\mathrm{MeV})$, which might result from processes unaccounted for in our analysis (for example, quasifree scattering and second-order effects). A $133A^{-1∕3}$ curve, adjusted to pass through the ${}^{144}\mathrm{Sm}$ and ${}^{208}\mathrm{Pb}$ data points, is shown to guide the eye.