Experimental cross sections of ${}^{165}\mathrm{Ho}$$(\alpha ,n)$${}^{168}\mathrm{Tm}$ and ${}^{166}\mathrm{Er}$$(\alpha ,n)$${}^{169}\mathrm{Yb}$ for optical potential studies relevant for the astrophysical $\gamma$ process

Background: Optical potentials are crucial ingredients for the prediction of nuclear reaction rates needed in simulations of the astrophysical $\gamma$ process. Associated uncertainties are particularly large for reactions involving $\alpha$ particles. This includes $(\gamma ,\alpha )$ reactions which are of special importance in the $\gamma$ process.

Purpose: The measurement of $(\alpha ,n)$ reactions allows for an optimization of currently used $\alpha$-nucleus potentials. The reactions ${}^{165}\mathrm{Ho}$$(\alpha ,n)$ and ${}^{166}\mathrm{Er}$$(\alpha ,n)$ probe the optical model in a mass region where $\gamma$ process calculations exhibit an underproduction of $p$ nuclei which is not yet understood.

Method: To investigate the energy-dependent cross sections of the reactions ${}^{165}\mathrm{Ho}$$(\alpha ,n)$ and ${}^{166}\mathrm{Er}$$(\alpha ,n)$ close to the reaction threshold, self-supporting metallic foils were irradiated with $\alpha$ particles using the FN tandem Van de Graaff accelerator at the University of Notre Dame. The induced activity was determined afterwards by monitoring the specific $\beta$-decay channels.

Results: Hauser-Feshbach predictions with a widely used global $\alpha$ potential describe the data well at energies where the cross sections are almost exclusively sensitive to the $\alpha$ widths. Increasing discrepancies appear towards the reaction threshold at lower energy.

Conclusions: The tested global $\alpha$ potential is suitable at energies above 14 MeV, while a modification seems necessary close to the reaction threshold. Since the $\gamma$ and neutron widths show non-negligible impact on the predictions, complementary data are required to judge whether or not the discrepancies found can be solely assigned to the $\alpha$ width.

Figure 1

Sensitivities of the investigated laboratory cross sections to four different channel widths versus center-of-mass energy [21]. See text for details.

Figure 2

Sketches of the setups used during the campaign. Setup A (left side) was used in the first period, while the improved setup B was used during the two subsequent periods. Both setups feature a beam current measurement, a suppression voltage, and a Si detector. The vacuum lock integrated in setup B allows a rapid exchange of samples. Note that the setups are not drawn to scale.

Figure 3

Spectrum emitted by an erbium sample (black) after irradiation at $E_{\alpha }=13.5$ MeV compared to the corresponding background spectrum (gray). The x-ray $(*)$ and $\gamma$-ray $\left(▾\right)$ transitions of ${}^{169}\mathrm{Tm}$ used for cross section analysis are marked. In order to ensure comparability, both spectra are shown in counts per $0.166$ keV s. The sample spectrum was taken for 14 days while the background was measured for one month.

Figure 4

RBS spectrum of $\alpha$ particles scattered off an erbium sample. The plateau above 13 MeV corresponds to Rutherford scattering on erbium atoms. Its width is used to calculate the thickness of the sample. The small structure at the low-energy tail of the erbium plateau is caused by a low amount of heavy impurities in the sample and does not disturb the analysis. At lower energies the scattering off the surface layers consisting of oxygen and carbon can be observed.

Figure 5

Comparison of the different experimental data sets for the cross section of the ${}^{165}\mathrm{Ho}$$(\alpha ,n)$ reaction. Reasonable agreement can be observed in the overlapping region around 15 MeV.

Figure 6

Experimental cross sections of the reactions ${}^{166}\mathrm{Er}$$(\alpha ,n)$ (left side) and ${}^{165}\mathrm{Ho}$$(\alpha ,n)$ (right side) compared to predictions of the code smaragd using different input parameters. Upper panels: Different global $\alpha$-nucleus potentials; also shown are results obtained with talys (labels including asterisks). Middle panels: McF potential and scaled $\gamma$-transmission coefficients. Lower panels: Predictions based on modifications of the McF potential. See text for further discussion.