Probing isospin mixing with the giant dipole resonance in the ${}^{60}\mathrm{Zn}$ compound nucleus

An experimental study of the isospin mixing in the mass region $A=60$ was made by measuring the $\gamma$ decay from the giant dipole resonance in the compound nuclei ${}^{60}\mathrm{Zn}$ and ${}^{62}\mathrm{Zn}$. These compound nuclei were populated at two different excitation energies, $E^{*}=47$ MeV and $E^{*}=58$ MeV using the fusion evaporation reactions ${}^{32}\mathrm{S}+{}^{28}\mathrm{Si}$ at the bombarding energy of 86 and 110 MeV and ${}^{32}\mathrm{S}+{}^{30}\mathrm{Si}$ at 75 and 98 MeV. In the experiment, performed at the Laboratori Nazionali di Legnaro of the Istituto Nazionale di Fisica Nucleare (INFN), the $\gamma$ rays were measured with the GALILEO detection system in which large-volume ${\mathrm{LaBr}}_3$(Ce) detectors were added to the HPGe detectors. The Coulomb spreading width was obtained from the comparison of the two reactions and then the isospin mixing parameter at zero temperature and the isospin-symmetry-breaking correction for beta decay were deduced. The present results were compared with data of the same type in other mass regions and with data from mass and beta-decay measurements and with theory. The present data allow us to deduce for the first time a consistent picture for mass dependence of isospin mixing and for the corresponding correction for the beta decay, supporting a reliable extension to the very interesting region of ${}^{100}\mathrm{Sn}$.

Figure 1

(a) Experimental spectra for ${}^{62}\mathrm{Zn}$ at $T=2$ MeV (blue points) and $T=2.4$ MeV (red points) and the best-fitting statistical model calculations corresponding to the minimum of the FOM for the variation of energy and width of the GDR ($E_{GDR}, {\mathrm{\Gamma }}_{GDR}$). The occurrences distribution for which the FOM is minimized is displayed in the inset for the ${}^{62}\mathrm{Zn}$ nucleus at $T=2$ MeV. (b) Experimental spectra for ${}^{60}\mathrm{Zn}$ at $T=2$ MeV (blue points) and $T=2.4$ MeV (red points) and statistical model calculations corresponding to the values of the Coulomb spreading width obtained by fitting the ratio spectra of Fig. 2.

Figure 2

The experimental and calculated ratio spectra ${}^{60}\mathrm{Zn}/{}^{62}\mathrm{Zn}$ are shown in panels (a) and (b) for $T=2$ and 2.4 MeV, respectively. The curves (shown with different colors as indicated in the legend) are statistical model calculations corresponding to different values of the Coulomb spreading width, namely ${\mathrm{\Gamma }}^{\downarrow }=0$, 5 keV for $T=2$ MeV; 0 and 7 keV for $T=2.4$ MeV; and 10, 15, 50 keV for both temperatures. In the insets are displayed the occurrence distributions for which ${\chi }^2$ is minimized.

Figure 3

The Coulomb spreading width obtained in the present work shown together with the values for other mass regions deduced from GDR $\gamma$-decay measurements in compound-nucleus reactions [13, 14, 15]. The colored bars indicate the spread of values reported in literature and obtained with other methods.

Figure 4

Data and predictions for the isospin-mixing coefficient ${\alpha }_{>}^2$ at $T=0$. The violet and red stars, from GDR $\gamma$ decay, are for ${}^{60}\mathrm{Zn}$ (this work) and ${}^{80}\mathrm{Zr}$ [15], respectively. The green square shows the value for ${}^{64}\mathrm{Ge}$ from Ref. [27] deduced from a low-lying $E1$ transition. The curves are calculations from Ref. [4]. The dash-point (dash) line, indicated as Theory 1 (Theory 2), corresponds to calculations obtained after (before) performing a rediagonalization on the isospin basis. The inset displays the isospin-mixing correction ${\delta }_{\text{C}}$, related to ${\alpha }_{>}^2$, which is employed to extract the $ft$ values from $\beta$ decay. Black circles, from Ref. [2], were deduced from $\beta$ decay, the blue triangle was obtained from the mass measurement [28], the red star is from Ref. [15], while the violet star is from the present work. The black line in the inset is extracted, through Eq. (3), from the predictions of ${\alpha }_{>}^2$ ($T=0$) of Ref. [4], here denoted “Theory 1.”