Cross-section measurements of radiative proton-capture reactions in ${}^{112}\mathrm{Cd}$ at energies of astrophysical interest

Reactions involving the group of nuclei commonly known as $p$ nuclei are part of the nucleosynthetic mechanisms at astrophysical sites. The ${}^{113}\mathrm{In}$ nucleus is such a case with several open questions regarding its origin at extreme stellar environments. In this paper, the experimental study of the cross sections of the radiative proton-capture reaction ${}^{112}\mathrm{Cd}(p,\gamma ){}^{113}\mathrm{In}$ is attempted for the first time at energies lying inside the Gamow window with an isotopically enriched ${}^{112}\mathrm{Cd}$ target. Two different techniques, the in-beam $\gamma$-ray spectroscopy and the activation method, have been applied. The latter method is required to account for the presence of a low-lying ${}^{113}\mathrm{In}$ isomer at 392 keV having a half-life of $\approx 100\min$. From the cross sections, the astrophysical $S$ factors and the isomeric ratios have been additionally deduced. The experimental results are compared to detailed Hauser-Feshbach theoretical calculations using talys and discussed in terms of their significance to the optical model potential involved.

Figure 1

A sketch of the reaction flows in the vicinity of ${}^{113}\mathrm{In}$ adapted from Ref. [38] taking into account Ref. [37]. Contributions from the corresponding $s,r$, and $p$ processes are shown. The present paper focuses on the proton-capture channel by ${}^{112}\mathrm{Cd}$, which is marked in the figure with the strong-line box. See the text for details.

Figure 2

The x-ray fluorescence spectrum of the target (tgt) after background removal (wobg) and photopeak deconvolution (deconv) as compared to a standard Cd sample (std).

Figure 3

A computer-aided design model of the experimental setup used in the present paper. The target chamber was surrounded by an array of four HPGe detectors placed on a turntable to measure $\gamma$ singles from eight different angles.

Figure 4

A typical absolute efficiency curve for the detectors employed in the measurement. The particular one corresponds to the detector placed at ${55}^{\circ }$. Errors are smaller than the symbol size.

Figure 5

A partial level scheme of the low-lying energy levels of ${}^{113}\mathrm{In}$. The solid arrows represent decays feeding the ground state of ${}^{113}\mathrm{In}$ and were observed during our measurements. See the transitions marked with asterisks in Fig. 6.

Figure 6

A horizontal split view (300–2000 keV) of a typical spectrum recorded in singles in the detector placed at ${55}^{\circ }$ and at a beam energy of 3.4 MeV. Photopeaks feeding the ground state of ${}^{113}\mathrm{In}$ are marked with $*$'s, whereas transitions feeding the isomeric $1/2^{-}$ state are marked with #'s. Other deexcitations of ${}^{113}\mathrm{In}$ are marked with circles. Major background lines which are usually observed in the present setup, coming from natural radioactivity (e.g., ${}^{40}\mathrm{K},{}^{214}\mathrm{Bi}$) or elements present in the beamline components (e.g., ${}^{27}\mathrm{Al},{}^{28}\mathrm{Si}$) are also labeled. Please note that subfigure $y$ axes are not in scale.

Figure 7

Typical examples of angular distributions of the measured absolute yield for the transitions $5/2_1^{+}\to 9/2_{\mathrm{gs}}^{+}$ (top left), $7/2_1^{+}\to 9/2_{\mathrm{gs}}^{+}$ (top right), $5/2_2^{+}\to 9/2_{\mathrm{gs}}^{+}$ (bottom left), and ${(7/2,9/2)}^{+}\to 9/2_{\mathrm{gs}}^{+}$ (bottom left) at beam energy $E=3400\mathrm{keV}$.

Figure 8

Ground-state cross sections for the $(p,\gamma )$ channel deduced by the in-beam method. Energies are shown in the laboratory system. The shaded area corresponds to the full range of calculated values with every combination of models employed. The lines correspond to the best data-matching calculations, see the text for details.

Figure 9

Measured isomeric cross sections with both the activation (solid diamonds) and the in-beam (open circles) methods. The lines and shaded area are as in Fig. 8.

Figure 10

As in Fig. 8 but for the total reaction cross sections of the $(p,\gamma )$ channel deduced from the in-beam and activation methods.

Figure 11

As in Fig. 10 but for astrophysical $S$ factors. The only difference is that energies are shown in the center-of-mass system.

Figure 12

Isomeric ratios of the isomeric cross section to the ground-state cross section (left) and of the isomeric cross section to the total cross section (right) of the reaction ${}^{112}\mathrm{Cd}(p,\gamma ){}^{113}\mathrm{In}$. Please note the different scales of the $y$ axes.

Figure 13

Experimental data are compared to talys calculations for the total cross sections of the $(p,n)$ channel. The data have been retrieved from literature (Blaser et al. [33], Abramovich et al. [34], and Skakun et al. [35]). See also Fig. 8 for details regarding the shaded area and the line curves.