First cross-section measurements of the reactions ${}^{107,109}\mathbf{Ag}(p,\gamma ){}^{108,110}\mathbf{Cd}$ at energies relevant to the $p$ process

Background: One of the primary objectives of the field of Nuclear Astrophysics is the study of the elemental and isotopic abundances in the universe. Although significant progress has been made in understanding the mechanisms behind the production of a large number of nuclides in the isotopic chart, there are still many open questions regarding a number of neutron-deficient nuclei, the $p$ nuclei. To that end, experimentally deduced nuclear reaction cross sections can provide invaluable input to astrophysical models.

Purpose: The reactions ${}^{107,109}\mathrm{Ag}$($p,\gamma$)${}^{108,110}\mathrm{Cd}$ have been studied at energies inside the astrophysically relevant energy window in an attempt to provide experimental data required for the testing of reaction-rate predictions in terms of the statistical model of Hauser-Feshbach around the $p$ nucleus ${}^{108}\mathrm{Cd}$.

Methods: The experiments were performed with in-beam $\gamma$-ray spectroscopy with proton beams accelerated by the Tandem Van de Graaff Accelerator at NCSR “Demokritos” impinging a target of natural silver. A set of high-purity germanium detectors was employed to record the emitted radiation.

Results: A first set of total cross-section measurements in radiative proton-capture reactions involving ${}^{107,109}\mathrm{Ag}$, producing the $p$-nucleus ${}^{108}\mathrm{Cd}$, inside the astrophysically relevant energy window is reported. The experimental results are compared to theoretical calculations, using talys. An overall good agreement between the data and the theoretical calculations has been found.

Conclusions: The results reported in this work add new information to the relatively unexplored $p$ process. The present measurements can serve as a reference point in understanding the nuclear parameters in the related astrophysical environments and for future theoretical modeling and experimental works.

Figure 1

A schematic representation of the experimental apparatus with the HPGe detectors and the target chamber.

Figure 2

A partial level scheme showing the measured transitions feeding the ground state of the produced nucleus from the reaction ${}^{107}\mathrm{Ag}$($p,\gamma$)${}^{108}\mathrm{Cd}$ [48]. The broadening of the entry state due to energy loss of the beam inside the target can be found by transforming Eq. (2) in the center-of-mass frame and is represented with $\delta \epsilon$.

Figure 3

Consecutive parts of a typical high-gain spectrum of the studied reactions at a proton beam energy of 2.2 MeV and an angle of ${90}^{\circ }$. Photopeaks of interest resulting from the reaction ${}^{107}\mathrm{Ag}$($p,\gamma$)${}^{108}\mathrm{Cd}$ are marked with an asterisk ($*$), while those from the reaction ${}^{109}\mathrm{Ag}$($p,\gamma$)${}^{110}\mathrm{Cd}$ are marked with a hash (#). In inset (a) a more detailed view of the area of our interest is presented. The peak of ${}^{214}\mathrm{Bi}$ is from the natural background, while the ones from ${}^{137}\mathrm{Cs}$ and ${}^{60}\mathrm{Co}$ originate from calibration sources placed rather far from the apparatus and used to check on gain shifts during the runs. In inset (b), the part of the respective low-gain spectrum with the ${}^{108}\mathrm{Cd}{\gamma }_0$ and its respective escape peak is shown. The primary transition for ${}^{110}\mathrm{Cd}$ was not observed.

Figure 4

Comparison between theoretical calculations with talys and experimentally deduced cross sections (in $\mu \mathrm{b}$) for the reaction ${}^{107}\mathrm{Ag}$($p,\gamma$)${}^{108}\mathrm{Cd}$ (left panel) and the reaction ${}^{109}\mathrm{Ag}$($p,\gamma$)${}^{110}\mathrm{Cd}$ (right panel). Incident energy is expressed in the laboratory frame. See Table 3 for an explanation of the legend entries. Please note that $y$-axis scales are different in the plots. The shaded area is bounded by the maximum and minimum values found for each energy step during calculations.

Figure 5

The solid squares correspond to experimental cross sections (in mb) for the reaction ${}^{107}\mathrm{Ag}(p,n){}^{107}\mathrm{Cd}$ from Ref. [19]. The curves are talys1–talys8 output data produced simultaneously with the ones shown in the left-hand panel of Fig. 4 for the competing ($p,\gamma$) channel. The shaded area is as in Fig. 4.