Systematic study of $(\alpha ,\gamma )$ reactions for stable nickel isotopes

A systematic measurement of the $(\alpha ,\gamma )$ reaction for all the stable nickel isotopes has been performed using the $\gamma$-summing technique. For two of the isotopes, ${}^{60}\mathrm{Ni}$ and ${}^{61}\mathrm{Ni}$, the $\alpha$-capture cross sections have been experimentally measured for the first time. For ${}^{58,62,64}\mathrm{Ni}$, the current measurement is in excellent agreement with earlier results found in the literature, and additionally extends the energy range of the measured cross sections up to 8.7 MeV. The data provided a tool for testing the cross section predictions of Hauser-Feshbach calculations. The experimental results were compared to the cross sections calculated with the talys 1.6 code and commonly used databases non-smoker and bruslib. For each of the investigated isotopes a combination of input parameter for talys was identified that best reproduces the experimental data, and recommended reaction rate has been calculated. Additionally, a set of inputs for Hauser-Feshbach calculations was given that, simultaneously for all the isotopes under consideration, reproduces the experimental data within the experimental uncertainties.

Figure 1

Sample histograms of the sum peaks obtained for 7 MeV $\alpha$ beam for each of the targets. The shift of the position of the peaks due to differences in the reaction $Q$ value is clearly visible. For each sum-peak the fitted combination of peak and background is shown (red) and the background under the sum peak is denoted in green. For the ${}^{61}\mathrm{Ni}$ target additional structure resulting from the neutron from the $(\alpha ,n)$ channel is also present.

Figure 2

${}^{58}\mathrm{Ni}(\alpha ,\gamma ){}^{62}\mathrm{Zn}$ cross sections obtained in this work (solid circles) and data found in the literature [23] (open symbols). The talys 1.6 calculation for the model parameter combination which gives the minimum ${\chi }^2$ for the ${}^{58}\mathrm{Ni}(\alpha ,\gamma ){}^{62}\mathrm{Zn}$ data set, 2-4-4, is shown as a solid line. The broken lines correspond to the model parameter combinations which resulted in a minimum ${\chi }^2$ for other analyzed targets and the long-dashed line is the 2-4-3 model that gives the best description to all the targets simultaneously (see Sec. 3 for detailed explanation). The double-dotted and dot-dashed lines show the cross sections from the non-smoker and bruslib databases, respectively.

Figure 3

Same as Fig. 2, but for ${}^{60}\mathrm{Ni}(\alpha ,\gamma ){}^{64}\mathrm{Zn}$. The solid line corresponds to the model parameters set 5-1-2.

Figure 4

Same as Fig. 2, but for ${}^{61}\mathrm{Ni}(\alpha ,\gamma ){}^{65}\mathrm{Zn}$. The solid line corresponds to the model parameters set 5-3-4.

Figure 5

Same as Fig. 2, but for ${}^{62}\mathrm{Ni}(\alpha ,\gamma ){}^{66}\mathrm{Zn}$. The solid line corresponds to the model parameters set 5-1-2. The open symbols correspond to the data from [22, 24].

Figure 6

Same as Fig. 2, but for ${}^{64}\mathrm{Ni}(\alpha ,\gamma ){}^{68}\mathrm{Zn}$. The solid line corresponds to the model parameters set 1-5-3. The open symbols denote data from [24].

Figure 7

Cumulative number of levels calculated for ${}^{62}\mathrm{Zn}$ for the six level density models in the talys 1.6 package. The black dotted line refers to the experimentally known levels in ${}^{62}\mathrm{Zn}$ [26]. At high energies, the experimental data no longer provide a true estimate of the level density. Numbers in brackets refer to the model number in talys 1.6.

Figure 8

$E1 \gamma$-strength functions for the five models in the talys 1.6 package, as well as the model used by the non-smoker code (DLO) [16, 17]. Numbers in brackets refer to the model number in talys 1.6.