Experimental study of the astrophysical $\gamma$-process reaction ${}^{124}\mathrm{Xe}(\alpha ,\gamma ){}^{128}\mathrm{Ba}$

Background: The synthesis of heavy, proton rich isotopes in the astrophysical $\gamma$ process proceeds through photodisintegration reactions. For the improved understanding of the process, the rates of the involved nuclear reactions must be known. The reaction ${}^{128}\mathrm{Ba}(\gamma ,\alpha ){}^{124}\mathrm{Xe}$ was found to affect the abundance of the $p$ nucleus ${}^{124}\mathrm{Xe}$ in previous rate variation studies.

Purpose: Since the stellar rate for this reaction cannot be determined by a measurement directly, the aim of the present work was to measure the cross section of the inverse ${}^{124}\mathrm{Xe}(\alpha ,\gamma ){}^{128}\mathrm{Ba}$ reaction and to compare the results with statistical model predictions used in astrophysical networks. Modified nuclear input can then be used to provide an improved stellar reaction rate. Of great importance is the fact that data below the $(\alpha ,n)$ threshold was obtained. Studying simultaneously the ${}^{124}\mathrm{Xe}(\alpha ,n){}^{127}\mathrm{Ba}$ reaction channel at higher energy allowed to further identify the source of a discrepancy between data and prediction.

Method: The ${}^{124}\mathrm{Xe}(\alpha ,\gamma ){}^{128}\mathrm{Ba}$ and ${}^{124}\mathrm{Xe}(\alpha ,n){}^{127}\mathrm{Ba}$ cross sections were measured with the activation method using a thin window ${}^{124}\mathrm{Xe}$ gas cell and an $\alpha$ beam from a cyclotron accelerator. The studied energy range was between $E_{\alpha }=11$ and 15 MeV close above the astrophysically relevant energy range.

Results: The obtained cross sections are compared with Hauser-Feshbach statistical model calculations. The experimental cross sections are smaller than standard predictions previously used in astrophysical calculations. As a dominating source of the difference, the theoretical $\alpha$ width was identified. The experimental data suggest an $\alpha$ width lower by at least a factor of 0.125 in the astrophysically important energy range.

Conclusions: An upper limit for the ${}^{128}\mathrm{Ba}(\gamma ,\alpha ){}^{124}\mathrm{Xe}$ stellar rate was inferred from our measurement. The impact of this rate and lower rates was studied in two different models for core-collapse supernova explosions of 25 $M_{\odot }$ stars. A significant contribution to the ${}^{124}\mathrm{Xe}$ abundance via this reaction path would only be possible when the rate was increased above the previous standard value. Since the experimental data rule this out, they also demonstrate the closure of this production path.

Figure 1

Schematic view of the gas target system. In comparison to Fig. 1 of [42], a new vacuum-chamber section was introduced to avoid total beam-energy deposition in the gas target. (Not drawn to scale.)

Figure 2

Left: Deformation of the $6.6\mu \mathrm{m}$ Al foil measured off-site at 10 mbar pressure. Black dots show the measured positions. Negative values (colored with blue) mean increase of the target length. The positive values (colored with red) are consequences of a surface contamination producing reflection. Right: Average deformation of the foil as the function of the distance $R$ from the center of the foil.

Figure 3

Typical $\gamma$ spectrum measured with Det 1 on a catcher irradiated with an $\alpha$ beam of 14.0 MeV. The two $\gamma$ peaks used for the analysis are indicated. The other peaks can be identified as laboratory background or as the effect of the activated impurities in the catcher foil [47].

Figure 4

Reaction cross section of the ${}^{124}\mathrm{Xe}(\alpha ,\gamma ){}^{128}\mathrm{Ba}$ reaction.

Figure 5

Reaction cross section of the ${}^{124}\mathrm{Xe}(\alpha ,n){}^{127}\mathrm{Ba}$ reaction.

Figure 6

Sensitivity of the ${}^{124}\mathrm{Xe}(\alpha ,\gamma ){}^{128}\mathrm{Ba}$ cross section to variations of the neutron, $\alpha$, and $\gamma$ width as function of c.m. energy.

Figure 7

Sensitivity of the ${}^{124}\mathrm{Xe}(\alpha ,n){}^{127}\mathrm{Ba}$ cross section to variations of the neutron, $\alpha$, and $\gamma$ width as function of c.m. energy.

Figure 8

Ratio of the ${}^{128}\mathrm{Ba}(\gamma ,\alpha )$ rate to the largest competing rate, which is $(\gamma ,n)$ except for $(\gamma ,p)$ at the lowest temperature, as function of the stellar plasma temperature $T$. The temperature range affecting the Xe-Ba region is shown by the grey box.

Figure 9

Abundance $Y$ of ${}^{124}\mathrm{Xe}$ obtained with rates based on various $\alpha$ widths as function of $\alpha$ width variation factor. A similar dependence was obtained in two stellar models A and B (see text for details). The value inferred from the experimental data as an upper limit of the $\alpha$ width is marked by the box. Note that the ordinate is given on a logarithmic scale.