Elastic α scattering on ${}^{112}\mathrm{Sn}$ and ${}^{124}\mathrm{Sn}$ at astrophysically relevant energies

The cross sections for the elastic scattering reactions ${}^{112,124}\mathrm{Sn}(\alpha ,\alpha ){}^{112,124}\mathrm{Sn}$ at energies above and below the Coulomb barrier are presented and compared to predictions for global α-nucleus potentials. The high precision of the new data allows a study of the global α-nucleus potentials at both the proton- and neutron-rich sides of an isotopic chain. In addition, local α-nucleus potentials have been extracted for both nuclei and used to reproduce elastic scattering data at higher energies. Predictions from the capture cross section of the reaction ${}^{112}\mathrm{Sn}$($\alpha ,\gamma$)${}^{116}\mathrm{Te}$ at astrophysically relevant energies are presented and compared to experimental data.

Figure 1

(Color online) Spectra of the ${}^{112}\mathrm{Sn}$($\alpha ,\alpha$)${}^{112}\mathrm{Sn}$ and ${}^{124}\mathrm{Sn}$($\alpha ,\alpha$)${}^{124}\mathrm{Sn}$ reactions at $E_{\alpha }=$ 19.5 MeV at forward (${\vartheta }_{\mathrm{lab}}={40}^{°}$) and backward (${\vartheta }_{\mathrm{lab}}={125}^{°}$) angles, respectively. Elastic scattering on target contaminations (mainly ${}^{12}\mathrm{C}$ from the carbon backing) and inelastically scattered events are clearly separated from the elastic peak. A small target contamination with $A\approx 200$ that is visible only in the spectra at backward angles remains below 1% contribution to the elastic peaks. The pulser signals used for dead time correction are not seen in the spectra, as they lay above the shown energy region.

Figure 2

Relative yield of ${}^{12}\mathrm{C}$ recoil nuclei in coincidence with (a) elastically and (b) inelastically scattered α particles. A Gaussian fit to the experimental data (solid line) is shown to guide the eye. The shaded area presents the angle and the uncertainty expected from the measured reaction kinematics.

Figure 3

(Color online) Ratio of the measured scattering cross sections of ${}^{112}\mathrm{Sn}$($\alpha ,\alpha$)${}^{112}\mathrm{Sn}$ at 14.4 MeV (lower diagram) and 19.5 MeV (middle) and ${}^{124}\mathrm{Sn}$($\alpha ,\alpha$)${}^{124}\mathrm{Sn}$ at 19.5 MeV (upper) to the Rutherford cross section. The predictions from the global α-nucleus potentials from [22] (short dashed line), potential I from [23] (short dash-dotted line), [24] (long dashed line), and [25] (long dash-dotted line) are also shown. The overlap of the lines, mainly at forward angles, complicates their distinction. Note the logarithmic scale for the upper and middle diagrams ($E_{\alpha }=$ 19.5 MeV) and the linear scale for the lower diagram ($E_{\alpha }=$ 14.4 MeV).

Figure 4

(Color online) Ratio of the scattering cross sections $(\sigma /{\sigma }_{\mathrm{Ruth}}){}_{{}^{112}\mathrm{Sn}}/(\sigma /{\sigma }_{\mathrm{Ruth}}){}_{{}^{124}\mathrm{Sn}}$ at $E_{\alpha }=$ 19.5 MeV versus the angle in the center-of-mass (c.m.) frame. The predictions of the considered global α-nucleus potentials are also shown. Minor differences for the c.m. angle (below 0.2${}^{°}$) in the transformation to c.m. angles because of the different masses of ${}^{112}\mathrm{Sn}$ and ${}^{124}\mathrm{Sn}$ are neglected.

Figure 5

Volume integral values $J_R$ from the analysis of the measured data, together with values obtained in the study of elastic scattering data on doubly magic and semimagic nuclei [18, 20, 29]. The solid line shows a linear parametrization of $J_R$ extracted from the data. The Gauss parametrization proposed by Ref. 23 for the description of low energy data (dotted line) is also shown below 50 MeV. The astrophysically relevant energy region for p process nucleosynthesis is shown by the gray area.

Figure 6

(Color online) Ratio of the measured scattering cross sections to the Rutherford cross section (same as in Fig. 3), including the results of the OM analysis performed for both tin nuclei (solid line).

Figure 7

(Color online) Ratio of the scattering cross sections $(\sigma /{\sigma }_{\mathrm{Ruth}}){}_{{}^{112}\mathrm{Sn}}/(\sigma /{\sigma }_{\mathrm{Ruth}}){}_{{}^{124}\mathrm{Sn}}$ at $E_{\alpha }=$ 19.5 MeV versus the angle in the center-of-mass frame, including the results of the OM analysis performed in both tin nuclei (solid line). A significant improvement of the description of the experimental data is achieved.

Figure 8

(Color online) Elastic scattering data from the reactions ${}^{112}\mathrm{Sn}$($\alpha ,\alpha$)${}^{112}\mathrm{Sn}$ at $E_{\alpha }\approx$ 50 MeV [34] (left part of the figure) and ${}^{124}\mathrm{Sn}$($\alpha ,\alpha$)${}^{124}\mathrm{Sn}$ at $E_{\alpha }\approx$ 25 MeV [35] (right part of the Figure). The predictions from the derived potentials from the elastic scattering data presented in this work are also shown (dashed line). Results from a readjustment of the potential parameters (left) and a normalization of the cross section (right) are shown as a solid line. For details see text.

Figure 9

(Color online) Excitation function of the nucleus ${}^{112}\mathrm{Sn}$ at ${\vartheta }_{c.m.}=$ 178${}^{°}$ [36]. The results from the derived α-nucleus potential are also shown (solid line). The nice reproduction of the experimental data confirms the good knowledge of the α-nucleus potential in this energy region.

Figure 10

(Color online) Astrophysical S factor of the ${}^{112}\mathrm{Sn}$($\alpha ,\gamma$)${}^{116}\mathrm{Te}$ capture reaction. The experimental data from Ref. 16 are compared to the predictions from the global α-nucleus potentials and the optical potential obtained from the analysis of the elastic scattering data. The potential from Ref. 25 presents the best reproduction of the experimental data. The prediction from the optical potential derived in this work presents a satisfactory description of the measured cross sections, similar to the potential from Ref. 22.