Probing astrophysically important states in theMg26nucleus to study neutron sources for thesprocess

Background: The $^{22}\mathrm{Ne}(\ensuremath{\alpha},n)^{25}\mathrm{Mg}$ reaction is the dominant neutron source for the slow neutron capture process ($s$ process) in massive stars, and contributes, together with $^{13}\mathrm{C}(\ensuremath{\alpha},n)^{16}\mathrm{O}$, to the production of neutrons for the $s$ process in asymptotic giant branch (AGB) stars. However, the reaction is endothermic and competes directly with $^{22}\mathrm{Ne}(\ensuremath{\alpha},\ensuremath{\gamma})^{26}\mathrm{Mg}$ radiative capture. The uncertainties for both reactions are large owing to the uncertainty in the level structure of $^{26}\mathrm{Mg}$ near the $\ensuremath{\alpha}$ and neutron separation energies. These uncertainties affect the $s$-process nucleosynthesis calculations in theoretical stellar models.Purpose: Indirect studies in the past have been successful in determining the energies and the $\ensuremath{\gamma}$-ray and neutron widths of the $^{26}\mathrm{Mg}$ states in the energy region of interest. But, the high Coulomb barrier hinders a direct measurement of the resonance strengths, which are determined by the $\ensuremath{\alpha}$ widths for these states. The goal of the present experiments is to identify the critical resonance states and to precisely measure the $\ensuremath{\alpha}$ widths by $\ensuremath{\alpha}$-transfer techniques.Methods: The $\ensuremath{\alpha}$-inelastic scattering and $\ensuremath{\alpha}$-transfer measurements were performed on a solid $^{26}\mathrm{Mg}$ target and a $^{22}\mathrm{Ne}$ gas target, respectively, using the Grand Raiden Spectrometer at the Research Center for Nuclear Physics in Osaka, Japan. The $(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$ measurements were performed at $0.{45}^{\ensuremath{\circ}}, 4.{1}^{\ensuremath{\circ}}, 8.{6}^{\ensuremath{\circ}}$, and $11.{1}^{\ensuremath{\circ}}$ and the $(^{6}\mathrm{Li},d)$ measurements at ${0}^{\ensuremath{\circ}}$ and ${10}^{\ensuremath{\circ}}$. The scattered $\ensuremath{\alpha}$ particles and deuterons were detected by the focal plane detection system consisting of multiwire drift chambers and plastic scintillators. The focal plane energy calibration allowed the study of $^{26}\mathrm{Mg}$ levels from ${E}_{x}$ = 7.69--12.06 MeV in the $(\ensuremath{\alpha},{\ensuremath{\alpha}}^{\ensuremath{'}})$ measurement and ${E}_{x}$ = 7.36--11.32 MeV in the $(^{6}\mathrm{Li},d)$ measurement.Results: Six levels (${E}_{x}$ = 10717, 10822, 10951, 11085, 11167, and 11317 keV) were observed above the $\ensuremath{\alpha}$ threshold in the region of interest (10.61--11.32 MeV). The $\ensuremath{\alpha}$ widths were calculated for these states from the experimental data. The results were used to determine the $\ensuremath{\alpha}$-capture induced reaction rates.Conclusion: The energy range above the $\ensuremath{\alpha}$ threshold in $^{26}\mathrm{Mg}$ was investigated using a high resolution spectrometer. A number of states were observed for the first time in $\ensuremath{\alpha}$-scattering and $\ensuremath{\alpha}$-transfer reactions. The excitation energies and spin-parities were determined. Good agreement is observed for previously known levels in $^{26}\mathrm{Mg}$. From the observed resonance levels the ${E}_{x}$ = 10717 keV state has a negligible contribution to the $\ensuremath{\alpha}$-induced reaction rates. The rates are dominated in both reaction channels by the resonance contributions of the states at ${E}_{x}$ = 10951, 11167, and 11317 keV. The ${E}_{x}$ = 11167 keV state has the most appreciable impact on the $(\ensuremath{\alpha},\ensuremath{\gamma})$ rate and therefore plays an important role in the prediction of the neutron production in $s$-process environments.