Proton capture cross section of ${}^{72}\mathrm{Ge}$ and astrophysical implications

This paper reports on the first cross section measurement of the ${}^{72}\mathrm{Ge}\left(p,\gamma \right){}^{73}\mathrm{As}$ reaction. The proton capture reaction on ${}^{72}\mathrm{Ge}$ is relevant to the astrophysical $p$-process and was identified in a sensitivity study as one of the important reactions required to estimate the abundances of the light $p$ nuclei. The $\gamma$-summing technique was employed using the summing NaI(Tl) detector (SuN) from the National Superconducting Cyclotron Laboratory. The experiment was performed at the University of Notre Dame using a 1.8–3.6 MeV proton beam. In order to test the predictive power of different theoretical calculations in the region, experimental values were compared to the results given by the nuclear reaction code talys1.6. The theoretical uncertainties in the cross section arising from different combinations of nuclear level densities, $\gamma$-ray strength functions, and optical model potentials were reduced to 10–18% by the experimental data. The recommended reaction rates from the standard astrophysical libraries, BRUSLIB and REACLIB, are found to be in good agreement with the experimental results.

Figure 1

$\gamma$ spectrum obtained for an incident beam energy of 3.6 MeV for a ${}^{\mathrm{nat}}\mathrm{Ge}$ target (blue solid line). In total, four sum peaks are observed. The peak marked as $n$-capture originates from the capture of free neutrons by the detector material, while ${}^{71}\mathrm{As},{}^{73}\mathrm{As}$, and ${}^{75}\mathrm{As}$ are from ${}^{70}\mathrm{Ge}\left(p,\gamma \right){}^{71}\mathrm{As},{}^{72}\mathrm{Ge}\left(p,\gamma \right){}^{73}\mathrm{As}$, and ${}^{74}\mathrm{Ge}\left(p,\gamma \right){}^{75}\mathrm{As}$ reactions, respectively. Due to low cross sections and isotopic abundances, neither ${}^{74}\mathrm{As}$ or ${}^{77}\mathrm{As}$ sum peaks are visible in the spectrum (see text). The inset shows the zoomed in region of the spectrum with the sum peak of ${}^{73}\mathrm{As}$ and the expected energy of $\gamma$ rays originating from the 428 keV isomeric state. For comparison, a $\gamma$ spectrum obtained with an enriched ${}^{74}\mathrm{Ge}$ target is shown as the red dashed line. The spectrum consists of a neutron capture peak and a sum peak for the production of ${}^{75}\mathrm{As}$ at an incident beam energy of 3.6 MeV. The experiment with enriched ${}^{74}\mathrm{Ge}$ target was performed using the same setup and experimental technique. A detailed description of that analysis and the results are given in Ref. [18].

Figure 2

Comparison of values obtained in the present work (solid squares) and in a previous experiment aimed at measuring the ${}^{74}\mathrm{Ge}{(p,\gamma )}^{75}\mathrm{As}$ cross sections. Reference data (solid circles) were taken from [18].

Figure 3

The experimentally measured cross section of the ${}^{72}\mathrm{Ge}\left(p,\gamma \right)$ reaction. (a) Solid line shows the total cross section calculated using talys 1.6 and dashed line represents the production of only the ground state excluding the isomeric state at 427.9 keV. Results of the calculations done with different combinations of nuclear level densities, $\gamma$-ray strength functions, and nuclear optical potentials lie within the grey shaded area. (b) Same as (a) with the recommended values for the reaction by BRUSLIB (solid line) and REACLIB (dashed line).