Total and partial cross sections of the ${}^{112}\mathrm{Sn}(\alpha ,\gamma ){}^{116}\mathrm{Te}$ reaction measured via in-beam $\gamma$-ray spectroscopy

Background: The nucleosynthesis of the neutron-deficient $p$ nuclei remains an open question in nuclear astrophysics. Beside uncertainties on the astrophysical side, the nuclear-physics input parameters entering Hauser-Feshbach calculations for the nucleosynthesis of the $p$ nuclei must be put on a firm basis.

Purpose: An extended database of experimental data is needed to address uncertainties of the nuclear-physics input parameters for Hauser-Feshbach calculations. Especially $\alpha$ + nucleus optical model potentials at low energies are not well known. The in-beam technique with an array of high-purity germanium (HPGe) detectors was successfully applied to the measurement of absolute cross sections of an $(\alpha ,\gamma )$ reaction on a heavy nucleus at sub-Coulomb energies.

Method: The total and partial cross-section values were measured by means of in-beam $\gamma$-ray spectroscopy. For this purpose, the absolute reaction yield was measured using the HPGe detector array HORUS at the FN tandem accelerator at the University of Cologne. Total and partial cross sections were measured at four different $\alpha$-particle energies from $E_{\alpha }=10.5\mathrm{MeV}$ to $E_{\alpha }=12\mathrm{MeV}$.

Results: The measured total cross-section values are in excellent agreement with previous results obtained with the activation technique, which proves the validity of the applied method. With the present measurement, the discrepancy between two older data sets is removed. The experimental data was compared to Hauser-Feshbach calculations using the nuclear reaction code talys. With a modification of the semi-microscopic $\alpha$ + nucleus optical model potential OMP 3, the measured cross-section values are reproduced well. Moreover, partial cross sections could be measured for the first time for an $(\alpha ,\gamma )$ reaction.

Conclusions: A modified version of the semimicroscopic $\alpha$ + nucleus optical model potential OMP3, as well as modified proton and $\gamma$ widths, are needed in order to obtain a good agreement between experimental data and theory. It is found that a model using a local modification of the nuclear-physics input parameters simultaneously reproduces total cross sections of the ${}^{112}\mathrm{Sn}(\alpha ,\gamma )$ and ${}^{112}\mathrm{Sn}(\alpha ,p)$ reactions. The measurement of partial cross sections turns out to be very important in this case in order to apply the correct $\gamma$-ray strength function in the Hauser-Feshbach calculations. The model also reproduces cross-section values of $\alpha$-induced reactions on ${}^{106}\mathrm{Cd}$, as well as of $(\alpha ,n)$ reactions on ${}^{115,116}\text{Sn}$, hinting at a more global character of the obtained nuclear-physics input.

Figure 1

Typical $\gamma$-ray spectrum taken during the bombardment of ${}^{112}\mathrm{Sn}$ with 12 MeV $\alpha$ particles. This spectrum was obtained by summing over all HPGe detectors at an angle of ${90}^{\circ }$ relative to the beam axis. Ground-state transitions in ${}^{116}\mathrm{Te}$ are marked with an asterisk. The spectrum is dominated by beam-induced background, mainly stemming from reactions occurring on ${}^{56}\mathrm{Fe}$ as a target impurity. The high-energy part (b) shows the deexcitations from the compound state to the ground state (${\gamma }_0$) as well as to the first (${\gamma }_1$) and third (${\gamma }_3$) excited states. The respective single-escape (SE) and double-escape (DE) peaks are marked as well, if visible.

Figure 2

Excerpt from a $\gamma \gamma$-coincidence spectrum of the ${}^{112}\mathrm{Sn}(\alpha ,\gamma )$ reaction with 12 MeV $\alpha$ particles. Panel (a) shows a summed singles spectrum of the detectors positioned at ${90}^{\circ }$, where no gate was applied. (b) A gate is set on the $\gamma$-ray transition from the first $J^{\pi }=2_1^{+}$ state to the ground state with an energy of $E_{\gamma }=678.9$ keV. The feeding transitions from higher-lying states in ${}^{116}\mathrm{Te}$ become clearly visible. Information about excitation energies, spins, and parities are adopted from Ref. [31]

Figure 3

Illustration of the excitation and decay of the compound nucleus, which is produced by bombarding ${}^{112}\mathrm{Sn}$ with $\alpha$ particles. The compound nucleus ${}^{116}\mathrm{Te}$ is formed in an excited state with energy $E_X\pm \frac{\delta E}{2}$. The entry state de-excites via $\gamma$ rays to the ground- or excited states (${\gamma }_i$, depicted by dashed arrows), or by cascading $\gamma$-ray transitions to the ground state (depicted by solid arrows). The excitation energies were adopted from Ref. [31].

Figure 4

Angular distribution for the $E_{\gamma }=678.9$ keV ground-state transition in ${}^{116}\mathrm{Te}$. The incident $\alpha$-particle energy was 11 MeV. The dashed line corresponds to the fit of Legendre polynomials to the experimental $W\left(\theta \right)$ values, which are calculated by normalizing the measured reaction yield to the number of incoming projectiles.

Figure 5

Experimental total cross section of the ${}^{112}\mathrm{Sn}(\alpha ,\gamma ){}^{116}\mathrm{Te}$ reaction as a function of center-of-mass energy. Results were obtained from this work as well as from activation measurements of Ref. [32] (Özkan et al., triangles) and Ref. [33] (Rapp et al., circles). The total cross-section values are compared to statistical model calculations using the talys code. Using the default settings (“TALYS default”), neither the energy dependence nor the absolute values are predicted well. Using the semimicroscopic OMP 3 of Ref. [37], the agreement is significantly improved (“TALYS OMP 3”). An adjustment of the $\alpha$-OMP as well as the proton- and $\gamma$ widths leads to an excellent accordance (“TALYS Fit”). Details about the input parameters can be found in the text.

Figure 6

Experimental total cross section of the ${}^{112}\mathrm{Sn}{(\alpha ,p)}^{115}\text{Sb}$ reaction. The experimental data were taken from Ref. [32]. Regarding the theoretical calculations, a pattern similar to the ${}^{112}\mathrm{Sn}(\alpha ,\gamma )$ case arises; see text for details.

Figure 7

Experimental partial cross sections $\sigma \left({\gamma }_i\right)$ for the ${}^{112}\mathrm{Sn}(\alpha ,\gamma )$ reaction as a function of center-of-mass energies. Cross-section values for the deexcitation of the entry state to the ground state, as well as first and third excited states, were extracted. The experimental values are compared to talys predictions. Four $\gamma$-ray strength functions were used: generalized Lorentzian [40], microscopic Hartree-Fock BCS [41], microscopic HFB + QRPA [39], and a microscopic hybrid model [42]. Very good agreement is found using the microscopic HFB + QRPA $\gamma$-ray strength function.

Figure 8

Total cross sections of $\alpha$-induced reactions on ${}^{106}\mathrm{Cd}$. The experimental data is taken from Ref. [43]. The models for the talys calculations are discussed in Sec. 4a. The model fitted to the $\alpha$-induced reactions on ${}^{112}\mathrm{Sn}$ (“TALYS Fit”) yield a reasonable agreement of the ${}^{106}\mathrm{Cd}(\alpha ,\gamma )$ and ${}^{106}\mathrm{Cd}(\alpha ,n)$ cross sections, whereas the ${}^{106}\mathrm{Cd}(\alpha ,p)$ cross-section values are significantly underestimated.

Figure 9

Cross sections of $(\alpha ,n)$ reactions on the isotopes ${}^{115,116}\text{Sn}$. Experimental data is taken from Ref. [44]. The model (“TALYS Fit”), see Sec. 4a, is able to correctly reproduce the total cross-section values of the ${}^{115}\mathrm{Sn}{(\alpha ,n)}^{118}\text{Te}$ reaction. For the ${}^{116}\mathrm{Sn}{(\alpha ,n)}^{119}\text{Te}$ case, minor differences arise at higher energies in describing the population of the ground state and isomeric state. However, the total cross-section values are in excellent agreement with the experimental data.