Cross section of $\alpha$-induced reactions on ${}^{197}\mathrm{Au}$ at sub-Coulomb energies

Background: Statistical model calculations have to be used for the determination of reaction rates in large-scale reaction networks for heavy-element nucleosynthesis. A basic ingredient of such a calculation is the $\alpha$-nucleus optical model potential. Several different parameter sets are available in literature, but their predictions of $\alpha$-induced reaction rates vary widely, sometimes even exceeding one order of magnitude.

Purpose: This paper presents the result of $\alpha$-induced reaction cross-section measurements on gold which could be carried out very close to the astrophysically relevant energy region. The new experimental data are used to test statistical model predictions and to constrain the $\alpha$-nucleus optical model potential.

Method: For the measurements, the activation technique was used. The cross section of the ($\alpha ,n$) and ($\alpha ,2n$) reactions was determined from $\gamma$-ray counting, while that of the radiative capture was determined via x-ray counting.

Results: The cross section of the reactions was measured below $E_{\alpha }=20.0$ MeV. In the case of the ${}^{197}\mathrm{Au}(\alpha ,2n){}^{199}\mathrm{Tl}$ reaction down to 17.5 MeV with 0.5-MeV steps, reaching closer to the reaction threshold than ever before. The cross section of ${}^{197}\mathrm{Au}(\alpha ,n){}^{200}\mathrm{Tl}$ and ${}^{197}\mathrm{Au}(\alpha ,\gamma ){}^{201}\mathrm{Tl}$ was measured down to $E_{\alpha }=13.6$ and 14.0 MeV, respectively, with 0.5-MeV steps above the ($\alpha ,2n$) reaction threshold and with 1.0-MeV steps below that.

Conclusions: The new data set is in agreement with the available values from the literature, but is more precise and extends toward lower energies. Cross sections two orders of magnitude lower than those in previous experiments which used $\gamma$-ray counting only were successfully measured, thus providing experimental data at lower energies than ever before. The new precision dataset allows us to find the best-fit $\alpha$-nucleus optical model potential and to predict cross sections in the Gamow window with smaller uncertainties.

Figure 1

In left column are typical PIXE spectra in the case of a self-supporting (top) and an evaporated (bottom) target. Middle top figure shows a proton-RBS spectrum of a self-supporting target, while bottom middle is an $\alpha$-RBS spectrum of an evaporated target. Right panel: $\alpha$-spectra of a triple-nuclide $\alpha$ source used for the target thickness measurement is presented, where the black and gray points are the measured energy spectra with and without the gold foil, respectively. The energy calibration fit is plotted with light blue, while the energy loss fit with dark blue lines (see text for details).

Figure 2

A typical beam current variation is shown by blue solid line. The time evolution of the effective fluence for the different isotopes are presented by black dashed, red dotted, and green dot-dashed lines for ${}^{199}\mathrm{Tl}, {}^{200}\mathrm{Tl}$, and ${}^{201}\mathrm{Tl}$, respectively.

Figure 3

The measured detector efficiency at 10 cm (black point) and the fit functions (blue and red curves). Vertical lines indicate the energy of the $\gamma$ rays and the X ray used for the analysis.

Figure 4

A 1-h-long spectrum taken 10 h after the 18.0-MeV irradiation. Insets (a)–(d) show the enlarged regions around the peaks used for the for ${}^{199}\mathrm{Tl}$ activity determination, while panels (e)–(h) show those for ${}^{200}\mathrm{Tl}$.

Figure 5

Relative activity as a function of time. The dots are the measured values for a given transition. Horizontal solid lines are the average values, while dotted lines indicate the uncertainty of the average (if it is smaller than the line width of the average, then the lines are not shown). The left and right panels are for the transitions of the ($\alpha ,2n$) and ($\alpha ,n$) reaction products, respectively.

Figure 6

The 101-h-long spectrum collected 150 h after the 17.5-MeV irradiation. The inset shows the $\gamma$ peak of ${}^{201}\mathrm{Tl}$.

Figure 7

The 11-h-long spectrum collected 453 h after the 17.5-MeV irradiation. The inset shows the x-ray peak of ${}^{201}\mathrm{Tl}$, together with the x-ray fluorescence peaks of gold. When comparing this spectrum to the one in Fig. 6, the higher sensitivity of the x-ray counting method is clearly seen.

Figure 8

Time evolution of the count rate in the x-ray peak (black dots). The upper panel shows the dual exponential fit after the 19.5-MeV irradiation. Gray, blue, and green solid lines represent the fitted ${}^{199}\mathrm{Tl}$ and ${}^{200}\mathrm{Tl}$ contribution and their sum, respectively. Lower panel shows a single exponential fit in the case of the 17.0-MeV measurement, where the blue line is the fitted exponential with the ${}^{200}\mathrm{Tl}$ half-life.

Figure 9

Upper panel shows the time evolution of the count rate in the x-ray peak (black dots) together with the calculated contribution from the ($\alpha ,n$) reaction channel (blue line with error bars) in the case of the last 150 hours of counting of the 17.5-MeV sample. The lower panel shows the relative activity from the x-ray measurement of ${}^{201}\mathrm{Tl}$. Red dots are the decay and counting corrected peak areas after subtraction. The subtraction was possible with reasonable accuracy only after 400 h.

Figure 10

${}^{197}\mathrm{Au}$($\alpha ,\alpha$)${}^{197}\mathrm{Au}$ elastic scattering at $E_{\alpha }=24.7$ MeV: a total reaction cross section ${\sigma }_{\mathrm{reac}}$ = $520\pm 20$ mb is derived from the angular distribution of Ref. [52].

Figure 11

Experimental cross sections compared to the best-fit statistical model calculation using the AVR A-OMP. Green downward-pointing triangle, blue upward-pointing triangles, black dots, and red squares stands for the total, ($\alpha ,2n$), ($\alpha ,n$), and ($\alpha ,\gamma$) cross sections, respectively. Full symbols are the present data, while open symbols are from Ref. [28] and the calculated total cross section are from Ref. [52]. Green full line is the SM predicted total cross sections, while blue dashed, black dotted, and red dot-dashed lines are the ($\alpha ,2n$), ($\alpha ,n$), and ($\alpha ,\gamma$) cross sections, respectively.