$\alpha$-induced reactions on ${}^{115}\mathrm{In}$: Cross section measurements and statistical model analysis

Background: $\alpha$-nucleus optical potentials are basic ingredients of statistical model calculations used in nucleosynthesis simulations. While the nucleon+nucleus optical potential is fairly well known, for the $\alpha$+nucleus optical potential several different parameter sets exist and large deviations, reaching sometimes even an order of magnitude, are found between the cross section predictions calculated using different parameter sets.

Purpose: A measurement of the radiative $\alpha$-capture and the $\alpha$-induced reaction cross sections on the nucleus ${}^{115}\mathrm{In}$ at low energies allows a stringent test of statistical model predictions. Since experimental data are scarce in this mass region, this measurement can be an important input to test the global applicability of $\alpha$+nucleus optical model potentials and further ingredients of the statistical model.

Methods: The reaction cross sections were measured by means of the activation method. The produced activities were determined by off-line detection of the $\gamma$ rays and characteristic x rays emitted during the electron capture decay of the produced Sb isotopes. The ${}^{115}\mathrm{In}(\alpha ,\gamma ){}^{119}\mathrm{Sb}$ and ${}^{115}\mathrm{In}(\alpha ,n){}^{118}\mathrm{Sb}^m$ reaction cross sections were measured between $E_{\mathrm{c}.\mathrm{m}.}=8.83$ and 15.58 MeV, and the ${}^{115}\mathrm{In}(\alpha ,n){}^{118}\mathrm{Sb}^g$ reaction was studied between $E_{\mathrm{c}.\mathrm{m}.}=11.10$ and 15.58 MeV. The theoretical analysis was performed within the statistical model.

Results: The simultaneous measurement of the ($\alpha ,\gamma$) and ($\alpha ,n$) cross sections allowed us to determine a best-fit combination of all parameters for the statistical model. The $\alpha$+nucleus optical potential is identified as the most important input for the statistical model. The best fit is obtained for the new Atomki-V1 potential, and good reproduction of the experimental data is also achieved for the first version of the Demetriou potentials and the simple McFadden-Satchler potential. The nucleon optical potential, the $\gamma$-ray strength function, and the level density parametrization are also constrained by the data although there is no unique best-fit combination.

Conclusions: The best-fit calculations allow us to extrapolate the low-energy ($\alpha ,\gamma$) cross section of ${}^{115}\mathrm{In}$ to the astrophysical Gamow window with reasonable uncertainties. However, still further improvements of the $\alpha$-nucleus potential are required for a global description of elastic ($\alpha ,\alpha$) scattering and $\alpha$-induced reactions in a wide range of masses and energies.

Figure 1

Measured RBS (a) and PIXE (b) spectra used to characterize the targets. Peaks used for the analysis are marked. Peaks belonging to impurities in the target and/or the backing are indicated too.

Figure 2

Off-line $\gamma$-ray spectrum measured using Det1 (a), taken after irradiating an In target with $E_{\alpha }=14.0$-MeV beam. The peaks used for the analysis are marked. The other peaks belong to the decay of ${}^{116}\mathrm{Sb}$ (1293.6 keV) and ${}^{118}\mathrm{Sb}^m$ (1050.7 keV) and to beam induced background—${}^{56}\mathrm{Co}$ (1238.3 keV), ${}^{60}\mathrm{Co}$ (1173.2 keV and 1332.5 keV). The dead time and relative intensity corrected peak areas (decay curves) of the transitions used to determine the ${}^{115}\mathrm{In}(\alpha ,n){}^{118}\mathrm{Sb}^g$ reaction cross section is shown, too (b). The 1229.3-keV $\gamma$ ray is emitted during the decay of both the produced ${}^{118}\mathrm{Sb}^g$ and ${}^{118}\mathrm{Sb}^m$ isotopes. Therefore, the yield of this transition was fitted as the sum of two exponential functions in order to disentangle the two reaction channels. For further details see text.

Figure 3

Off-line $\gamma$-ray spectra measured using the LEPS detector (a), taken after irradiating an In target with $E_{\alpha }=11.5$-MeV beam. The peaks used for the analysis are marked. The inset shows the spectrum taken 72 h after the end of the irradiation to highlight the transitions used to derive the $\alpha$-capture cross sections. The dead time and relative intensity corrected peak areas (decay curves) of the transitions used to determine the ${}^{115}\mathrm{In}(\alpha ,\gamma ){}^{119}\mathrm{Sb}$ and ${}^{115}\mathrm{In}(\alpha ,n){}^{118}\mathrm{Sb}^m$ reaction cross sections is shown, too (b). At the beginning of the counting the yield of the 23.9-keV transition was not sufficient for the analysis (due to the level of the background). For better visibility the yield of the 253.7-keV $\gamma$ line was scaled down by factor of 10 on the right side.

Figure 4

Experimental cross sections of the ${}^{115}\mathrm{In}(\alpha ,n){}^{118}\mathrm{Sb}^g$, ${}^{115}\mathrm{In}(\alpha ,n){}^{118}\mathrm{Sb}^m$, and ${}^{115}\mathrm{In}(\alpha ,\gamma ){}^{119}\mathrm{Sb}$ reactions compared to calculations using different combinations of input parameters of the statistical model. The curves—calculated using the talys code [33]—are labeled by the most important parameter which is the $\alpha$-nucleus OMP. For completeness the ($\alpha ,\gamma$) cross section predictions, calculated with the widely used non-smoker code [41] is plotted, too. For more details see text.

Figure 5

Rutherford normalized elastic scattering cross sections of the ${}^{115}\mathrm{In}(\alpha ,\alpha ){}^{115}\mathrm{In}$ reaction at $E_{\mathrm{Lab}}=16.15$ and 19.50 MeV vs the angle in center-of-mass frame. The lines correspond to the predictions calculated using the global optical potential parameter sets discussed in Sec. 3a.

Figure 6

Application of the best-fit parameters from ${}^{115}\mathrm{In}$ to the neighboring nucleus ${}^{113}\mathrm{In}$: The experimental data [40] are reasonably well reproduced without any further adjustment of parameters.

Figure 7

Sensitivity of the calculated cross sections to the chosen $\alpha$ OMP. All other ingredients were kept fixed at the best-fit results in Table 3: (a) ${}^{115}\mathrm{In}(\alpha ,n){}^{118}\mathrm{Sb}^g$, (b) ${}^{115}\mathrm{In}(\alpha ,n){}^{118}\mathrm{Sb}^m$, (c) ${}^{115}\mathrm{In}(\alpha ,\gamma ){}^{119}\mathrm{Sb}$. The numbers in the legend refer to the talys numbering of $\alpha$ OMPs. The full black line shows the best fit from Table 3.

Figure 8

Same as Fig. 7 for the sensitivity to the nucleon OMPs.

Figure 9

Same as Fig. 7 for the sensitivity to the $\gamma$-ray strength functions. For references to the parameters beyond Table 3, see the talys manual [33].

Figure 10

Same as Fig. 7 for the sensitivity to the level densities. For references to the parameters beyond Table 3, see the talys manual [33].