Direct study of the $\alpha$-nucleus optical potential at astrophysical energies using the ${}^{64}\mathrm{Zn}(p,\alpha ){}^{61}\mathrm{Cu}$ reaction

In the model calculations of heavy element nucleosynthesis processes the nuclear reaction rates are taken from statistical model calculations which utilize various nuclear input parameters. It is found that in the case of reactions involving $\alpha$ particles the calculations bear a high uncertainty owing to the largely unknown low-energy $\alpha$-nucleus optical potential. Experiments are typically restricted to higher energies and therefore no direct astrophysical consequences can be drawn. In the present work a ($p,\alpha$) reaction is used for the first time to study the $\alpha$-nucleus optical potential. The measured ${}^{64}\mathrm{Zn}(p,\alpha ){}^{61}\mathrm{Cu}$ cross section is uniquely sensitive to the $\alpha$-nucleus potential and the measurement covers the whole astrophysically relevant energy range. By the comparison to model calculations, direct evidence is provided for the incorrectness of global optical potentials used in astrophysical models.

Figure 1

Sensitivity of the calculated ${}^{64}\mathrm{Zn}(p,\alpha ){}^{61}\mathrm{Cu}$ cross section to the variation of the various partial widths. The shaded area shows the astrophysically relevant energy window for the inverse ${}^{61}\mathrm{Cu}$ + $\alpha$ system. See text for details.

Figure 2

Activation $\gamma$ spectra measured on a ${}^{64}\mathrm{Zn}$ target irradiated with a proton beam of 7 MeV. The upper panel (a) shows the first part of the counting where the spectrum is dominated by the decay of the short-lived ${}^{64}\mathrm{Zn}(p,\gamma ){}^{65}\mathrm{Ga}$ reaction product, while the lower panel (b) shows a spectrum with the decay lines of the longer-lived ${}^{64}\mathrm{Zn}(p,\alpha ){}^{61}\mathrm{Cu}$ reaction product (see the indicated waiting and counting times, $t{}_{\mathrm{w}}$ and $t{}_{\mathrm{c}}$, respectively). The peaks of the $\gamma$ transitions used for the analysis are marked.

Figure 3

Experimental $S$ factor of the ${}^{64}\mathrm{Zn}(p,\alpha ){}^{61}\mathrm{Cu}$ (upper panel) and ${}^{64}\mathrm{Zn}(p,\gamma ){}^{65}\mathrm{Ga}$ (lower panel) reactions and the predictions of statistical model calculations using the standard settings of the codes and a modified $\alpha$-nucleus optical potential and $\gamma$-ray strength function, respectively. The Gamow window for the inverse ${}^{61}\mathrm{Cu}$ + $\alpha$ system is shown again as a shaded area.