$\alpha$ scattering and $\alpha$-induced reaction cross sections of ${}^{64}\mathrm{Zn}$ at low energies

Background: $\alpha$-nucleus potentials play an essential role for the calculation of $\alpha$-induced reaction cross sections at low energies in the statistical model. Uncertainties of these calculations are related to ambiguities in the adjustment of the potential parameters to experimental elastic scattering angular distributions and to the energy dependence of the effective $\alpha$-nucleus potentials.

Purpose: The present work studies the total reaction cross section ${\sigma }_{\mathrm{reac}}$ of $\alpha$-induced reactions at low energies which can be determined from the elastic scattering angular distribution or from the sum over the cross sections of all open nonelastic channels.

Method: Elastic and inelastic ${}^{64}\mathrm{Zn}(\alpha ,\alpha ){}^{64}\mathrm{Zn}$ angular distributions were measured at two energies around the Coulomb barrier, at 12.1 and 16.1 MeV. Reaction cross sections of the $(\alpha ,\gamma ), (\alpha ,n)$, and $(\alpha ,p)$ reactions were measured at the same energies using the activation technique. The contributions of missing nonelastic channels were estimated from statistical model calculations.

Results: The total reaction cross sections from elastic scattering and from the sum of the cross sections over all open nonelastic channels agree well within the uncertainties. This finding confirms the consistency of the experimental data. At the higher energy of 16.1 MeV, the predicted significant contribution of compound-inelastic scattering to the total reaction cross section is confirmed experimentally. As a by-product it is found that most recent global $\alpha$-nucleus potentials are able to describe the reaction cross sections for ${}^{64}\mathrm{Zn}$ around the Coulomb barrier.

Conclusions: Total reaction cross sections of $\alpha$-induced reactions can be well determined from elastic scattering angular distributions. The present study proves experimentally that the total cross section from elastic scattering is identical to the sum of nonelastic reaction cross sections. Thus, the statistical model can reliably be used to distribute the total reaction cross section among the different open channels.

Figure 1

Two typical scattering spectra measured at 16.12 MeV $\alpha$ energy at forward (${35}^{\circ }$, upper panel) and backward (${165}^{\circ }$, lower panel) angles. The origin of the most prominent peaks are indicated.

Figure 2

Elastic ${}^{64}\mathrm{Zn}$($\alpha ,\alpha$)${}^{64}\mathrm{Zn}$ scattering cross section at energies from 12 to 50 MeV. The new data at 12.1 and 16.1 MeV are shown in red and labeled in bold. The other experimental data are taken from Di Pietro et al. [42] (13.6 MeV), Robinson and Edwards [43] (15.0, 17.9, and 19.0 MeV), Fulmer et al. [44] (21.3 MeV), England et al. [45] and Ballester et al. [46] (25 MeV), Baktybaev et al. [47] (29, 38, and 50.5 MeV), Alpert et al. [49] (31 MeV), McDaniels et al. [50] (41 MeV), and Pirart et al. [52] (48 MeV).

Figure 3

(a) Elastic ${}^{64}\mathrm{Zn}$($\alpha ,\alpha$)${}^{64}\mathrm{Zn}$ scattering cross section at $E=12.1$ MeV, compared to a phase shift analysis (PSF; solid black line) and to OM fits using a real folding and an imaginary surface Woods-Saxon potential. The fits use the full data set (green dotted line) and restricted data sets with $\vartheta \lesssim {155}^{\circ }$ (red dashed line), $\vartheta \lesssim {135}^{\circ }$ (blue long-dashed line), and $\vartheta \lesssim {115}^{\circ }$ (orange dash-dotted line). (b) OM fits normalized to the PSF, and (c) OM fits using volume Wood-Saxon potentials, again normalized to the PSF. For further discussion see text.

Figure 4

Same as Fig. 3, but for the angular distribution at $E=16.1$ MeV.

Figure 5

Phase shifts ${\delta }_L$, reflection coefficients ${\eta }_L$, and contribution ${\sigma }_L$ of the $L\mathrm{th}$ partial wave to ${\sigma }_{\mathrm{reac}}$ in Eq. (5) at $E_{\mathrm{lab}}=12.05$ MeV for the OMP fits using a folding potential in the real part and a surface WS potential in the imaginary part (from bottom to top). For further discussion see text.

Figure 6

Same as Fig. 5, but for the OMP fits with a volume WS potential in the real and imaginary part of the nuclear potential. For further discussion see text.

Figure 7

Same as Fig. 5, but at $E_{\mathrm{lab}}=16.12$ MeV. For further discussion see text.

Figure 8

Same as Fig. 7, but for the OMP fits with a volume WS potential in the real and imaginary parts of the nuclear potential. For further discussion see text.

Figure 9

Reduced reaction cross sections ${\sigma }_{\mathrm{red}}$ versus reduced energy $E_{\mathrm{red}}$ for various targets in a broad energy range. Except for ${}^{64}\mathrm{Zn}$, the data are taken from [9, 21, 41, 63].

Figure 10

Inelastic ${}^{64}\mathrm{Zn}$($\alpha ,{\alpha }^{\prime }$)${}^{64}\mathrm{Zn}$ scattering cross sections at the energy 12.1 MeV: (a) the elastic angular distribution (normalized to Rutherford) and (b) the inelastic angular distributions for the first $2^{+}$ state (blue), the sum of $0^{+}$ and $2_2^{+}$ (red), and the $4^{+}$ state (green). In addition, for the best-fit calculation (solid lines) a decomposition into the $0^{+}$ (orange) and $2_2^{+}$ states (magenta) is shown. For explanation of the various calculations, see text.

Figure 11

Inelastic ${}^{64}\mathrm{Zn}$($\alpha ,{\alpha }^{\prime }$)${}^{64}\mathrm{Zn}$ scattering cross section at the energy 16.1 MeV. For explanations, see Fig. 10.

Figure 12

Cross sections of the ${}^{64}\mathrm{Zn}$($\alpha ,\gamma$)${}^{68}\mathrm{Ge}, {}^{64}\mathrm{Zn}$($\alpha ,n$)${}^{67}\mathrm{Ge}$, and ${}^{64}\mathrm{Zn}$($\alpha ,p$)${}^{67}\mathrm{Ga}$ reactions. The experimental data are taken from our previous work [37] except the new results at the highest energy $E_{\alpha }=16.1$. The calculations are based on different global $\alpha$-nucleus optical potentials [9, 11, 29, 31, 75]. For better readability, two versions of [31] have been omitted. The differences between the predictions from various $\alpha$-nucleus potentials are relatively small. talys default parameters have been used in general except for the $\gamma$-ray strength function; the default $\gamma$-ray strength underestimates the ($\alpha ,\gamma$) cross section (thin red long-dashed line). For further discussion see text.