Cross-section measurement of the ${}^{130}\mathrm{Ba}(p,\gamma ){}^{131}\mathrm{La}$ reaction for $\gamma$-process nucleosynthesis

Background: Deviations between experimental data of charged-particle-induced reactions and calculations within the statistical model are frequently found. An extended data base is needed to address the uncertainties regarding the nuclear-physics input parameters in order to understand the nucleosynthesis of the neutron-deficient $p$ nuclei.

Purpose: A measurement of total cross-section values of the ${}^{130}\mathrm{Ba}(p,\gamma ){}^{131}\mathrm{La}$ reaction at low proton energies allows a stringent test of statistical model predictions with different proton+nucleus optical model potentials. Since no experimental data are available for proton-capture reactions in this mass region around $A \approx 130$, this measurement can be an important input to test the global applicability of proton+nucleus optical model potentials.

Method: The total reaction cross-section values were measured by means of the activation method. After the irradiation with protons, the reaction yield was determined by use of $\gamma$-ray spectroscopy using two clover-type high-purity germanium detectors. In total, cross-section values for eight different proton energies could be determined in the energy range between 3.6 MeV $\le E_p\le$ 5.0 MeV, thus, inside the astrophysically relevant energy region.

Results: The measured cross-section values were compared to Hauser-Feshbach calculations using the statistical model codes TALYS and SMARAGD with different proton+nucleus optical model potentials. With the semimicroscopic JLM proton+nucleus optical model potential used in the SMARAGD code, the absolute cross-section values are reproduced well, but the energy dependence is too steep at the lowest energies. The best description is given by a TALYS calculation using the semimicroscopic Bauge proton+nucleus optical model potential using a constant renormalization factor.

Conclusions: The statistical model calculation using the Bauge semimicroscopic proton+nucleus optical model potential deviates by a constant factor of 2.1 from the experimental data. Using this model, an experimentally supported stellar reaction rate for proton capture on the $p$ nucleus ${}^{130}\mathrm{Ba}$ was calculated. At astrophysical temperatures, an increase in the stellar reaction rate of 68% compared to rates obtained from the widely used NON-SMOKER code is found. This measurement extends the scarce experimental data base for charged-particle-induced reactions, which can be helpful to derive a more globally applicable proton+nucleus optical model potential.

Figure 1

Sensitivity s of the ${}^{130}\mathrm{Ba}(p,\gamma ){}^{131}\mathrm{La}$ reaction cross-sections, when the proton (p), neutron (n), $\alpha$, and $\gamma$ widths are varied by a factor of two, as a function of center-of-mass energies. The shaded area denotes the Gamow window for a temperature of 2.5 GK. Within the measured energy region the cross section is dominantly sensitive to the proton width.

Figure 2

X-ray spectrum obtained from a PIXE measurement for one of the Ba targets. One can clearly identify the characteristic Al ${\mathrm{K}}_{\alpha }$ transition stemming from the backing material as well as various x-ray transitions of Ba. Moreover, some lighter contaminants like Fe and Cu can be seen. The dashed line depicts the simulated continuous bremsstrahlung background.

Figure 3

Sketch of the target chamber used for nuclear astrophysics experiments. The suppression voltage of $U=-400$ V at the entrance is used to suppress secondary electrons in order to guarantee a reliable charge collection. The target itself is surrounded by a cooling trap at liquid nitrogen temperature to minimize residual gas deposits on the target. A silicon detector is also provided to measure the target thickness during the experiment by means of RBS.

Figure 4

Relevant part of a summed $\gamma$-ray spectrum measured with two HPGe clover detectors. This target was irradiated with 4.8 MeV protons. The dominant transitions used for data analysis are highlighted. Moreover, characteristic x-rays of Ba are clearly visible at the low-energy end of the spectrum. This spectrum was recorded for about 3.5 h. The remaining $\gamma$-ray transitions stem from naturally occurring background. The $\gamma$-ray transition with $E_{\gamma }=108.08$ keV was not used for data analysis, see text for details.

Figure 5

Summed experimental full-energy peak efficiencies of the two HPGe clover detectors for a target-to-detector distance of 1.3 cm, i.e., the used counting distance. To account for coincidence-summing effects, the efficiencies were measured at a distance of 10 cm where coincidence summing is negligible, and subsequently scaled to the counting distance of 1.3 cm using a ${}^{137}\mathrm{Cs}$ source. The experimental data are compared to a Geant4 simulation without summing effects and a very good agreement is found. See text for further details.

Figure 6

Experimental cross section of the ${}^{130}\mathrm{Ba}(p,\gamma ){}^{131}\mathrm{La}$ reaction as a function of center-of-mass energy. The total cross sections are compared to theoretical predictions obtained from the SMARAGD code [36], using the proton+nucleus OMP from Ref. [38] with low-energy modifications from Ref. [39]. A reasonable description of the experimental data is obtained $\left({\chi }_{\mathrm{red}}^2=4.38\right)$, but the energy dependence is too steep at the lowest energies. Furthermore, the experimental values are compared to calculations using the TALYS code [37], using the phenomenological proton+nucleus OMP from Ref. [46] (TALYS default), as well as the semi-microscopic OMP from Ref. [43] (TALYS Bauge). Scaling the “TALYS Bauge” cross-section values by a factor of 2.1 yields on average a better description of the energy dependence at low energies $\left({\chi }_{\mathrm{red}}^2=2.30\right)$. Details about the used proton+nucleus OMPs can be found in the text.