New Method for Precise Determination of the Isovector Giant Quadrupole Resonances in Nuclei

The intense, nearly monoenergetic, 100% polarized $\overrightarrow{\gamma }$-ray beams available at the $\mathrm{HI}\overrightarrow{\gamma }\mathrm{S}$ facility, along with the realization that the $E1\mathrm{\text{−}}E2$ interference term that appears in the Compton scattering polarization observable has opposite signs in the forward and backward angles, make it possible to obtain an order-of-magnitude improvement in the determination of the parameters of the isovector giant quadrupole resonance (IVGQR). Accurate IVGQR parameters will lead to a more detailed knowledge of the symmetry energy in the nuclear equation of state which is important for understanding nuclear matter under extreme conditions such as those present in neutron stars. Our new method is demonstrated for the case of ${}^{209}\mathrm{Bi}$.

Figure 1

NaI(Tl) detector spectra after the applied timing cut at a beam energy of 15.1 MeV. The dashed (red) curves are the simulated detector response functions. The forward-angle spectrum requires an exponential background represented by the dotted (blue) curve to be added to the detector response function, resulting in the solid (green) curve for the total spectrum.

Figure 2

Shown are the polarization ratios and their associated statistical uncertainties obtained in the current experiment. The solid curves were obtained using Eq. (1) and a three-parameter fit to the energy, width, and strength of the IVGQR. The dotted curves are the “No-$E2$” results from Eq. (1) including a correction factor for detector misalignment.

Figure 3

The IVGQR parameters and their uncertainties as reported in Pitthan et al. [22] are shown as the open (blue) circles here as a function of $A$, along with the present results for ${}^{209}\mathrm{Bi}$, shown as solid (black) triangles. For visual clarity, the present ${}^{209}\mathrm{Bi}$ results have been shifted by 10 mass numbers. Statistical only as well as statistical plus systematic errors are shown for the present results (see text).